Reconciling large- and small-scale structure in Twin Higgs models

Journal of High Energy Physics, Sep 2017

We study possible extensions of the Twin Higgs model that solve the Hierarchy problem and simultaneously address problems of the large- and small-scale structures of the Universe. Besides naturally providing dark matter (DM) candidates as the lightest charged twin fermions, the twin sector contains a light photon and neutrinos, which can modify structure formation relative to the prediction from the ΛCDM paradigm. We focus on two viable scenarios. First, we study a Fraternal Twin Higgs model in which the spin-3/2 baryon \( \widehat{\varOmega}\sim \left(\widehat{b}\widehat{b}\widehat{b}\right) \) and the lepton twin tau \( \widehat{\tau} \) contribute to the dominant and subcomponent dark matter densities. A non-decoupled scattering between the twin tau and twin neutrino arising from a gauged twin lepton number symmetry provides a drag force that damps the density inhomogeneity of a dark matter subcomponent. Next, we consider the possibility of introducing a twin hydrogen atom Ĥ as the dominant DM component. After recombination, a small fraction of the twin protons and leptons remains ionized during structure formation, and their scattering to twin neutrinos through a gauged U(1) B−L force provides the mechanism that damps the density inhomogeneity. Both scenarios realize the Partially Acoustic dark matter (PAcDM) scenario and explain the σ 8 discrepancy between the CMB and weak lensing results. Moreover, the self-scattering neutrino behaves as a dark fluid that enhances the size of the Hubble rate H 0 to accommodate the local measurement result while satisfying the CMB constraint. For the small-scale structure, the scattering of \( \widehat{\varOmega} \)’s and Ĥ’s through the twin photon exchange generates a self-interacting dark matter (SIDM) model that solves the mass deficit problem from dwarf galaxy to galaxy cluster scales. Furthermore, when varying general choices of the twin photon coupling, bounds from the dwarf galaxy and the cluster merger observations can set an upper limit on the twin electric coupling.

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Reconciling large- and small-scale structure in Twin Higgs models

HJE Reconciling large- and small-scale structure in Twin Higgs models Valentina Prilepina 0 1 3 Yuhsin Tsai 0 1 2 0 Stadium Dr. , College Park, MD, 20742 U.S.A 1 One Shield Ave , Davis, CA, 95616 U.S.A 2 Maryland Center for Fundamental Physics, Department of Physics, University of Maryland , USA 3 Physics Department, University of California Davis , USA We study possible extensions of the Twin Higgs model that solve the Hierarchy problem and simultaneously address problems of the large- and small-scale structures of the Universe. Besides naturally providing dark matter (DM) candidates as the lightest charged twin fermions, the twin sector contains a light photon and neutrinos, which can modify structure formation relative to the prediction from the Cosmology of Theories beyond the SM; Beyond Standard Model CDM paradigm. We focus on two viable scenarios. First, we study a Fraternal Twin Higgs model in which the spin-3/2 baryon ^ (^b^b^b) and the lepton twin tau ^ contribute to the dominant and subcomponent dark matter densities. A non-decoupled scattering between the twin tau and twin neutrino arising from a gauged twin lepton number symmetry provides a drag force that damps the density inhomogeneity of a dark matter subcomponent. Next, we consider the possibility of introducing a twin hydrogen atom H^ as the dominant DM component. After recombination, a small fraction of the twin protons and leptons remains ionized during structure formation, and their scattering to twin neutrinos through a gauged U(1)B L force provides the mechanism that damps the density inhomogeneity. Both scenarios realize the Partially Acoustic dark matter (PAcDM) scenario and explain the 8 discrepancy between the CMB and weak lensing results. Moreover, the self-scattering neutrino behaves as a dark uid that enhances the size of the Hubble rate H0 to accommodate the local measurement result while satisfying the CMB constraint. For the small-scale structure, the scattering of ^ 's and H^ 's through the twin photon exchange generates a self-interacting dark matter (SIDM) model that solves the mass de cit problem from dwarf galaxy to galaxy cluster scales. Furthermore, when varying general choices of the twin photon coupling, bounds from the dwarf galaxy and the cluster merger observations can set an upper limit on the twin electric coupling. 1 Introduction 2 3 4 5 6 1 2.1 2.2 The extended fraternal Twin Higgs model Asymmetric dark matter and dark uid Dark matter self-interaction and dark matter-dark uid scattering Large-scale structure: Twin lepton with acoustic oscillations Small-scale structure: Twin baryon with a self-interaction Solutions from the Twin hydrogen DM Discussion and conclusions 1 4 Introduction We study a non-minimal dark sector motivated by both Naturalness and cosmology considerations and explore its potential. By doing so, we provide a solution to the little hierarchy problem and, simultaneously, to various cosmological structure anomalies suggested by the current data related to the large- and small-scale structure of the universe. The existence of these issues may have revealed an intriguing clue to the nature of dark matter. The Twin Higgs mechanism [1{3] provides a solution to the little hierarchy problem in a hidden naturalness manner. The solution evades strong constraints from the Large Hadron Collider (LHC) on top-partners that are charged under Standard Model (SM) color by furnishing a hidden SM-like sector, in which the SM-neutral twin top is involved in stabilizing the Higgs mass. There have been several studies on formulating an ultraviolet completion of the model [4{14] and on the collider phenomenology related to the twin particle spectrum [15{19]. The existence of the mirror sector also provides a non-minimal dark sector containing stable charged fermions and twin gauge bosons, which introduces various applications to cosmology. Previous works on twin cosmology mainly focused on the thermal history of the dark matter candidates [20{23] and signatures in the (in-)direct detection experiments [ 24, 25 ]. In this work, we explore the physics of structure formation in the context of the Twin Higgs model. A dark sector that contains a SM-like particle spectrum has the potential to extend the cold collisionless dark matter paradigm in a way that resolves important cosmological issues [26{28]. In the twin sector, the dark matter candidates are the lightest charged baryon and lepton, which scatter with each other via twin photon exchange during the halo formation. The twin sector also contains a light twin neutrino, whose existence a ects the expansion rate of the universe and hence shifts H0, the value of the Hubble expansion rate today. If the twin sector is extended to include an e cient scattering between the twin neutrino and charged fermions during the structure formation time, a dark acoustic { 1 { oscillation exists, which damps the dark matter power spectrum and alters the large-scale structure. Interestingly, these adjustments to the dark matter structure formation in fact furnish solutions to the existing inconsistencies between the CDM prediction and both the large and small-scale structure observations. For many years, the well-accepted CDM paradigm has provided an excellent t to cosmological data on large scales, although there had been several long-standing problems on small scales, including the core-vs-cusp [29, 30] and toobig-to-fail problems [31]. With the advent of higher-precision measurements on large scales, however, the large-scale results have entered into tension with CDM as well. In particular, there is a 3 discrepancy between the value of today's Hubble rate H0 obtained from a t to the CMB and baryon acoustic oscillation (BAO) data [32] and the higher results from local measurements [33{37]. Further, the inferred value of 8 (roughly speaking the amplitude of matter density uctuations at a scale of 8h 1 Mpc) is in 2{3 tension [38{41] with the lower values from direct measurements by the weak lensing survey [ 42 ]. Resolving these anomalies would require a paradigm that generically reduces the value of 8 and enhances H0 as compared to the CDM model in a consistent way. One attempt to raise H0 from the CDM prediction is to introduce additional dark radiation (DR) to increase the energy density. Once the stringent CMB constraints are taken into account, however, such a solution comes at the cost of increasing the matter power spectrum, which exacerbates the 8 problem.1 A plausible solution is to have the dark radiation, which enhances H0, also act to damp the dark matter power spectrum so that the size of 8 gets reduced to agree with the weak lensing result [43]. One can consider coupling all the dark matter particles to the dark radiation. For this scenario, the full DMDR system undergoes dark acoustic oscillations, and hence all dark matter components are subjected to the same damping. Such a proposal would require a well-chosen small DM-DR coupling, which results in a DM-DR scattering that is slightly ine cient when compared to the Hubble expansion. Consequently, a numerical study is necessary to obtain the correct 8 suppression [44{46]. It is because of this slightly ine cient scattering process that we refer to this setup as the Quasi-Acoustic Dark Matter (QuAcDM) scenario. In the Twin Higgs model, such a scenario can be realized by gauging the twin B L symmetry. Here the twin neutrino plays the role of the additional dark radiation, and its scattering to the dark matter (twin baryon and charged lepton) damps the dark matter power spectrum, solving the 8 problem. Alternatively, one can consider a scenario where only a subcomponent of the total dark matter couples to the dark radiation. In a well-motivated general mechanism that was recently introduced in [47], one can allow the DM-DR scattering to be highly e cient. The Partially Acoustic Dark Matter (PAcDM) is a robust framework that e ectively resolves both the 8 and H0 large-scale structure anomalies in a natural way. It assumes the presence of tightly coupled dark radiation and supposes that the dark matter mass density is composed of two components, a cold and collisionless dominant one ( 1) and a cold subdominant one ( 2) that is tightly coupled to the dark radiation. The success of this 1For example, see the 8 H0 contours in gure 33 of [32]. { 2 { HJEP09(217)3 framework hinges on the feature that both the self-interaction of the dark radiation and the DR- 2 interaction remain e cient throughout the radiation domination phase and for a signi cant portion of the structure formation era. For this reason, one can perform an analytical estimation of the 8 suppression in the tightly coupled limit, as we will discuss in section 3. In this framework, the Hubble parameter anomaly can be reconciled by suitably xing the amount of tightly coupled dark radiation. Further, for the 8 anomaly, if the relevant modes enter the horizon before matter-radiation equality, the interaction between the dark radiation and 2 restricts the growth of density perturbations, subsequently decreasing the growth of uctuations in the collisionless DM 1. This is the case for modes sensitive to the 8 measurement, and hence the discrepancy can be resolved by an appropriate choice of the amount of subdominant DM, reducing the 8 value to match the observed deviation. Furthermore, the reduced growth of the matter power spectrum in this scenario results in a minor correction to the gravity perturbation during the CMB time, yielding a smaller change of the CMB spectrum as compared to the QuAcDM case. Hence, future precision CMB studies may be able to distinguish these two classes of models. We focus on the PAcDM scenario here in the context of the Twin Higgs model. Our particular realization is obtained by gauging either the twin lepton number symmetry U(1)L or the twin U(1)B L. In the U(1)L case, the heavy twin lepton scatters with the twin neutrino and plays the role of 2, while the twin baryon behaves as cold collisionless dark matter 1 throughout structure formation ( gure 1). In the U(1)B L case, the twin hydrogen behaves as 1, while the ionized twin proton plays the role of 2. The scattering between light twin particles also renders the light degrees of freedom a tightly coupled uid, which gives an extra contribution to Ne , and suitably solves the H0 problem, while satisfying a weaker CMB constraint [48{50]. In addition to the large-scale structure anomalies, there are several long-standing puzzles on small scales related to the structure of dark matter halos that cannot be addressed by the collisionless dark matter models. In particular, direct observations of dwarf galaxies ( kpc size) and galaxy clusters ( Mpc size) indicate lower dark matter masses in the inner regions of these objects than those predicted by N-body simulations with noninteracting DM. Although this anomaly may potentially be explained by lack of baryon interaction in the simulations [51, 52], none of the proposed solutions so far are able to cover such a broad range of halo sizes simultaneously.2 One attractive solution to the mass de cit problem on all halo scales is to suppose that the dark matter is self-interacting through a light mediator. As we show in this work, the charged twin baryon provides a plausible realization of this self-interacting dark matter (SIDM) scenario [54, 55] through an O(10) MeV-scale twin photon. Alternatively, the dark matter self-interaction can be realized for a DM particle with an extended geometrical size for the scattering, e.g. for atomic DM. As we will show, the formation of twin hydrogen gives a natural realization of atomic DM [56{60] and provides solutions to the mass de cit problem from dwarf galaxy to galaxy cluster scales [61]. 2See [53] for a review of current status on the small scale structure problems. { 3 { HJEP09(217)3 consideration. The blue (gray)-colored particles correspond to the stable (unstable) members of the spectrum. The gray arrows indicate the decay products of the unstable particles. Further, the primed elds correspond to the set of speci c anomaly compensators used in this paper. Right: the set of dominant processes involved in the solution of the large- and small-scale structure anomalies. The rst Feynman diagram represents the dominant process relevant for the self-interacting dark matter scenario through the exchange of twin photons. The second diagram corresponds to the relevant scattering for the partially acoustic oscillation scenario, and the third one is the process that keeps the dark radiation a tightly coupled uid. The rest of this paper is organized as follows. In section 2, we describe the Twin Higgs model that contains the necessary ingredients to solve both the large- and smallscale structure puzzles at the same time. The model is based on the Fraternal Twin Higgs model [16] but has a gauged twin lepton number symmetry that generates the 8 damping. In section 3, we explain how this model serves as a realization of the PAcDM framework to resolve the (H0; 8) anomalies. We give an analytical description of the partially acoustic oscillation and calculate the required mass ratio between the stable twin baryon and lepton that solves these problems. In section 4 we discuss the solution from the Twin Higgs model to the mass de cit problem and calculate the mass of the twin photon necessary to resolve it. At the end, when we admit more general choices of the twin electric coupling, we demonstrate how the dwarf galaxy and cluster merger observations enable us to set an upper bound on this coupling. In section 5, we discuss the more attractive solution to the cosmological structure formation problems with the twin hydrogen playing the role of the dominant DM component. An eminent virtue of this model is that it requires neither the breaking of twin electromagnetism nor the presence of anomaly compensators, which su er from strong experimental constraints. Moreover, it successfully accommodates two generations of fermions and does not compel one to introduce additional mass scales, thus keeping the twin gauge bosons massless. We conclude in section 6. 2 2.1 The extended fraternal Twin Higgs model Asymmetric dark matter and dark uid We investigate a dark sector motivated by the Twin Higgs model, which contains a twin top Yukawa and mirror gauge symmetries SU(3)0c U(1)Y 0 with SM-like couplings. In this framework, the SM Higgs arises as a pseudo-goldstone boson from a global SU(4) symmetry breaking, which then enjoys protection from various radiative corrections due to the approximate Z2 symmetry. Since the Higgs mass receives subdominant corrections from the Yukawa interactions of light twin fermions, all Yukawa couplings except for the twin top coupling are mildly constrained by Naturalness. For this reason, one can simplify the twin fermion spectrum by including only the third-generation fermions. In this Fraternal Twin Higgs model [16], the approximately Z2-symmetric gauge and top Yukawa couplings can adequately stabilize the Higgs mass, while the smaller number of light fermions is able to more exibly satisfy the restrictive Ne bound from the CMB. Since we mainly focus on the thermal history of the twin sector below a temperature of O(10) GeV, the twin particles relevant for this discussion are the spin-3=2 twin baryon ^ = (^b^b^b), the twin tau ^, the twin neutrino ^ (with both chiralities), and the twin photon ^. Their mass spectrum is similar to the SM spectrum due to the approximate Z2 symmetry. If we take the ratio between the twin and SM electroweak symmetry breaking scales, f and v, to be f =v = 3, which corresponds to a minor 2(v=f )2 ' 20% tuning and satis es current constraints on the Higgs coupling [16], the twin top and twin gauge bosons feature masses larger than the SM values by a factor of three. The approximately Z2-symmetric Yukawa couplings of light twin fermions ^b and ^, which result in small corrections to the Higgs mass, can be modi ed from the SM values, leading to some arbitrariness in the determination of the twin particle masses. We will therefore set the masses according to the solutions of the large- and small-scale structure problems. The relevant parameters are the twin photon mass m^, the twin baryon mass m^ , and the ratio of the twin tau mass density to the total dark matter density. We write the latter two quantities as m^ ' 3m^b + 5 ^ ; r m^ m^ + m^ : (2.1) Here, the contribution from the SU(3)0c con nement scale ^ is due to an approximation that comes from the lattice result in ref. [62] for a spin-3=2 baryon in the single- avor case [22]. When solving the mass de cit problem through the ^ self-scattering, the discussion in section 4 will demand mass ranges 10 . m^ . 20 MeV and 10 . m^ . 40 GeV. On the other hand, for the discussion in section 3, the appropriate damping of the 8 result will call for a mass ratio of r ' 2:5% and the existence of relativistic twin neutrinos. To simplify the discussion of thermal history, we assume the twin neutrinos to be massless during structure formation and focus on the following mass parameters: m^ = 40 GeV; m^ = 10 MeV; r = 2:5%: (2.2) twin con nement scale of ^ These imply that m^ ' 1 GeV. The ^ mass further implies that m^b ' 5 GeV for the ' 5 GeV, which comes from the two-loop RG running of Z2-symmetric QCD couplings at the cuto scale that we assume to be 5 TeV [16]. The Z2-breaking Yukawa couplings of ^b and ^ yield a cuto ( )-dependent correction to the For = 5 TeV, we nd no signi cant tuning of the Higgs mass, m2h ' (0:27 mh)2. Higgs mass, m2h ' 4 22 ( yb2 + y2), where y 2 b 3(y^2 b yb2) and y 2 (y2^ y2) [16]. { 5 { Assuming an unbroken twin electric symmetry, the twin electrically charged ^ and ^ particles are stable and can serve as dark matter candidates in this setup. The relic abundance of ^ can be generated through a similar baryogenesis mechanism as in the SM sector. With a small di erence in either the CP violation or rst order phase transition, we can achieve a di erent baryon asymmetry Y B^ ' Y B=8 relative to the SM. This generates the observed dark matter density. If we suppose that the twin-sector remains charge neutral from the twin baryogenesis, then given the absence of other stable charged particles, we expect the number of ^ in the late-time Universe to coincide with the number of ^. Besides the dark matter particles, light hadrons like the 0++ glueball, of mass mG^0++ ' 6:9 ^ = 35 GeV, and the pseudo-scalar bottomonium, of mass mB^0 + ' 2(m^b + ^ ) = 20 GeV, decay quickly into the SM bb or twin photons when they become non-relativistic. Hence, we do not consider them in the discussion of structure formation. Let us now discuss some observational constraints relevant to the dark sector. We rst turn to the direct detection constraint on the dominant dark matter component ^ . This is determined by the spin-independent cross section of ^ p ! ^ p through the Higgs portal exchange, given by [20] h ' 1 3 y^bv 2 p2f 2 ghp mN4^ ; 2 h (2.3) where N ^ is the reduced mass of the ^ -nucleon system and ghp = 1:2 10 3 [20, 63] gives the e ective Higgs coupling to nucleons. Since the momentum transfer in the scattering is much smaller than the inverse of the ^ radius, we assume that the Higgs mediation is dominated by the coherent scattering to three ^b's in the bound state, which includes a factor of 32 in the cross section. Taking m^b = 5 GeV, this expression gives h ' 3:4 This value falls below the current bound ' 1:0 experiment [64] at 40 GeV dark matter mass, but the cross section lies within the sensitivity of the proposed LZ experiment [65]. As is discussed in [22], the ^ -Higgs coupling can also be generated from a scalar glueball exchange. The resulting cross section may be comparable to the Higgs mediation result, but a concrete result relies on a future lattice study. 10 46 cm2 (90% CL) from the LUX 2.2 Dark matter self-interaction and dark matter-dark uid scattering Let us next turn to the dark matter interactions relevant to the formation of large- and small-scale structure. For the small-scale structure case, the model in question assumes that the dark matter particles ( ^ ; ^) carry twin electric charges and are endowed with self-couplings; hence, they elastically self-scatter. Although this self-scattering does not a ect the linear evolution of large-scale structure [66], it can in uence the dark matter structure formation. As we show later, we choose the same value for the twin and SM ne structure constants, ^ = , and a twin photon mass m^ 10 MeV that softly breaks the Z2 symmetry. The photon mass enables us to generate the appropriate velocity-dependent cross section that explains small-scale structure anomalies from dwarf to galaxy cluster scales. If the U(1)Y^ -breaking spurion m^ carries a fractional charge, then ^ and ^ can be easily made to be long-lived when compared to the cosmological time scale. Since m^ is larger than the binding energy m^ ^2 ' 40 keV, the two particles do not form a bound { 6 { state through the ^ exchange. We also note that ^ can also self-scatter via the exchange of twin mesons. However, this corresponds to a mediation scale that is above a GeV, in which case the resulting self-interaction is too weak to explain the anomalies. Having a new mass scale m^ in the twin sector complicates the UV-completion of the model. Since the hyper charge U(1)Y gives a negligible contribution to Higgs tuning, if the goal of the model is to only solve one of the small-scale structure problems, one can solve the dwarf anomaly by a Z2-breaking coupling ^ potential of the twin sector in addressing the structure formation issues, we will still aim for a solution to the small-scale structure anomalies on all scales and focus on the massive does not require a massive ^. In this scenario, the twin hydrogen plays the role of the SIDM, and the additional velocity dependence in the scattering cross section in both the elastic and inelastic scattering processes resolves both the dwarf and cluster anomalies, once the hyper ne structure of the twin atoms is taken into account. Turning to the large-scale structure in the ^ {^ scenario, we nd that in order to address the 8 puzzle in the PAcDM framework, we introduce a non-decoupled interaction between the subdominant dark matter ^ and dark radiation ^ that acts to damp the matter density contrast. Any such interaction between ^ and ^ but not ^ and ^ can serve this purpose. To provide a speci c scenario, we implement this interaction by gauging the twin lepton There is then an e cient scattering ^^ ! ^^ through a massless Z^L mediator. number symmetry and assuming that U(1)L^ is preserved throughout structure formation. Gauging the U(1)L^ symmetry results in local gauge anomalies. We can keep the U(1)L^ symmetry anomaly-free during structure formation by introducing anomaly compensators. For example, one way to achieve this is to include twin leptons ^lR0T = (^0; ^0)R (1; 1; 1=2; 1) and ^0 L (1; 1; 1=2; 1) charged under the twin SU(3)0c (1; 2; 0; 1), 3 We assume that the tau compensator, ^0, obtains a Yukawa mass from the term y^^lR0H^ ^L0 that is slightly heavier than that of ^, so that ^0 decays quickly into ^^^0 when it becomes nonrelativistic. We also assume that the twin neutrino compensator ^0 remains massless just like ^. This particle provides an additional contribution to and consequently helps to explain a higher value of H0 from the local measurements. A potential cause for concern is the allowed decay of ^ into the neutral (^) and charged (^0) neutrinos, which comes from a dimension-10 operator (^lLH^ ^R)(^L0 ^R)(^L0 ^R). However, this concern is eliminated if the mediation scale is above a TeV. In our discussion of the acoustic oscillation, we take the size of the U(1)L^ coupling to be gL^ & 10 4 to ensure that the ^-neutrino scattering rate is always larger than the Hubble expansion rate. Further, it turns out that in order to evade the stringent bound from searches for a fth force in the SM sector (see [68] for a review of the constraints), we are led to 3Instead of having anomaly compensators simply as chirality- ipped twin fermions [67], here we assign di erent U(1)Y^ charges to the neutrino compensators, so that they do not introduce vectorized neutrino masses, and the twin photon can decay into ^0's before BBN. Having the twin photon decay into dark radiation can avoid the stringent direct detection constraints as compared to the decay into SM particles through a kinetic mixing. { 7 { retain the SM U(1)L as un-gauged, otherwise the same anomaly compensators in the SM su er from stringent collider constraints. Since the U(1)L^ interaction only a ects the twin Higgs mass at two-loop level, this minor Z2 breaking has a negligible e ect on the naturalness of the electroweak scale. In the discussion of twin hydrogen DM in section 5, the scattering between the ionized twin atom and ^ is given by a gauged U(1)B L symmetry. Since U(1)B L is anomaly-free, there is no need to introduce the unattractive anomaly compensators. Hence, it is easier to UV-complete the model by gauging U(1)B L in both sectors, and break the SM U(1)B L through the same Z2 breaking as in the Higgs potential. Another possible cause for concern is the Weibel plasma instability. Inside the halo, the twin tau in the dark uid behaves like a charged plasma, and there may be potential constraints on the U(1)L^ coupling from the plasma instability [69, 70]. However, since the twin tau density is only 2:5% of the overall dark matter density, we do not expect this bound to be strong. Incidentally, we should note that the precise bound has not yet been formulated and is currently still under construction. In our PAcDM scenario, the ^ ^ scattering is highly e cient, rendering the dark radiation (^; ^0; Z ^ ) a tightly coupled L contributes to the e ective number of neutrino species uid. Like free-streaming radiation, this dark uid e N scatt. However, being self interacting, the uid is subject to a weaker CMB constraint when compared to the free streaming case with space to accommodate To determine the e e N scatt e N scatt < 1:06 (2 ) [49, 50]. This feature has the e ect of freeing up N scatt in our model, we refer to the state of the Universe around the ' 0:4{1, which furnishes a solution to the H0 problem [35]. kinetic decoupling time between the SM and twin sectors. Kinetic equilibrium between the two sectors is maintained by the Higgs mediation, which decouples around the GeV scale. Immediately after the decoupling, the twin sector contains the relativistic particles (^; ZL^ ; ^; ^0). As soon as the temperature drops to T . 10 MeV, the twin photon ^ decays into ^0's, avoiding the stringent direct detection constraints it would su er if it were to instead decay into SM particles through a kinetic mixing before Big-bang Nucleosynthesis [71]. Now, after the twin photons decay, the twin sector is left with (^; ^0; ZL^ ), which contribute an overall enhance the Hubble rate, solving the H0 problem. An alternative solution to the (H0; 8) problems is to gauge the anomaly-free U(1)B L symmetry instead of gauging the twin lepton number. This is a realization of the QuAcDM framework. In contrast to the PAcDM for which only the subdominant dark matter component undergoes dark acoustic oscillations, here the acoustic oscillations are experienced by the full DM-DR system, namely by both ^ and ^ interacting with the dark radiation. These damp the power spectrum with a weak U(1)B L coupling. If we invoke the result in refs. [ 43, 44 ], we can reduce the size of 8 to the desired value by choosing ^B L for a 10 GeV-scale dark matter mass. 3 Large-scale structure: Twin lepton with acoustic oscillations The presence of a cold dark matter component ^ and a subcomponent dark matter ^ that couples to the self-scattering radiation (^; ^0; ZL^ ), modi es the values of (H0; 8) relative { 8 { ple), Partially Acoustic dark matter (PAcDM, blue), and Fully Acoustic dark matter (QuAcDM, orange) cases. In the QuAcDM scenario, which corresponds to the case when both ^ and ^ interact with the dark radiation, the oscillation delays the linear growth of the density contrast during the matter domination phase. This feature results in a suppression of the matter power spectrum. In the PAcDM scenario, which corresponds to the case when only ^ scatters with the dark radiation, the slower growth of the power spectrum allows a smaller deviation from the CDM case during the CMB time (a 10 3) and the same suppression of power spectrum today (a ' 1) as in the QuAcDM case. In order to illustrate the idea, we choose parameters that give a large 8 suppression. to the CDM model. The self-scattering radiation contributes an overall that serves to reconcile the values of H0 between the local and CMB measurements [ 33 ]. Moreover, during the matter-dominated era, the dark uid-^ scattering generates a dark acoustic oscillation that delays the structure formation of ^. As we show later, this not only reduces the ^ matter density contrast but also retards the growth of the ^ uctuations. The slower growth of the ^ structure results in a stronger suppression of the matter power spectrum at low redshift, as is shown in the blue curve of gure 2. Here we describe the way in which the acoustic oscillations experienced by the ^{DR system act to suppress 8 . A more detailed study is presented in ref. [47]. We employ the general formalism of Ma and Bertschinger [72] for scalar perturbations in the conformal Newtonian gauge. Working in momentum space, we express the coupled evolution equations in terms of the comoving wavenumber k and conformal time derivative _ = 1=d . Then the evolution of the over-density of ^ can be described by the linear equations _ ^ = _^ = a_ a ^ + k2 : (3.1) Here the over-density, s s= s, parametrizes the density perturbation relative to the average density of matter or radiation. Further, the parameter s = @j vsj is the divergence of a comoving 3-velocity, which modi es the density perturbation by having particles move out of the overdense region. In addition, and are the metric perturbations in the conformal Newtonian gauge ds2 = a( )2[ (1 + 2 )d 2 + (1 2 )dxidxj ]. Since the dark { 9 { radiation is tightly coupled, we take = in the equations and ignore the minor correction from SM neutrinos. We note that eq. (3.1) coincides with the corresponding evolution equation for the density perturbation of standard cold dark matter particles for a given metric perturbation , where evolves according to the Einstein equation k 2 with the largest s s contribution on the r.h.s. The evolution equations for the interacting dark matter component ^ are given by HJEP09(217)3 _^ = _^ = a_ a ^ + k2 + a ( DR ^); where hp^i dh p2^i=dt is the thermal averaged momentum transfer rate experienced by a ^ particle as it travels through the dark uid. Note that here t is the Minkowski time, since the rate is a microscopic quantity independent of the cosmological expansion. In the twin sector, this scattering rate is given by [43] to obtain (R^ 3 ^=4 DR) _DR = _DR = k 2 4 3 DR + 4 _; DR + 4 + 3 4 DR ^ a ( 2 DR); ^ + ^ R a_ a 1 + R^ _^ + k 2 3(1 + R^) ^ ' k2 : where T^ is the temperature of ^. In the tightly coupled limit, T^ equals the temperature of dark radiation. The tight-coupling approximation is valid as long as the interaction rate is comparable to or exceeds the Hubble rate during structure formation. We focus on the case for which is signi cantly larger than the Hubble expansion rate, which enables us to gain an analytical understanding of the oscillation physics. This is easily achieved provided that the U(1)L^ coupling satis es ^ L where T0 is the photon temperature today and T^ ' 0:4 T0. In this tightly coupled limit, we 1, which implies that the scattering term in eq. (3.3) dominates the ^ evolution. The consequence is that ^ = DR, which authorizes us to combine the evolution equations of the dark matter component ^ and the DR as follows: (3.2) (3.3) (3.4) (3.5) (3.6) (3.7) The resulting evolution equations indicate that in the tight-coupling limit, the ^{DR system behaves like a single coupled uid. Here we neglect terms containing higher-order conformal time derivatives of in order to focus on modes well within the horizon, for which k 1. We nd that the evolution of the over-density ^ is similar to that of the SM baryon. Let us now consider varying R^. In the regime R^ 1, the ^{DR uid is relativistic. In this limit, the rst two terms in eq. (3.7) generate an acoustic oscillation of ^ without building up the density perturbation. This has the e ect of delaying the growth of dark matter structure when the mode enters horizon, as is shown by the PAcDM (blue) and QuAcDM (orange) curves in gure 2. It is only when the dark radiation cools down and one enters the R^ 1 regime that the power spectrum begins to grow monotonically. This delay of the ^ structure formation results in ^ ^ upon entering the matter domination era. Inserting the density ratio r de ned in eq. (2.1), we can then express the total dark matter density perturbation as DM = [(1 DM r) ^ + r ^] ' (1 r) ^ : For modes well within the horizon, k 1, so that eq. (3.2) simpli es to k 2 ' 4 a2G DM (1 r) ^ = 6 where we have applied the Friedman equation and noted that the scale factor a is proportional to 2 during matter domination. Canceling the ^ in eq. (3.1) and inserting the above metric perturbation, we then have for the dominant dark matter component ( 1=d ) 0^0 + 2 0^ ' 6(1 r) 2 ^ / a aeq 1 0:6r+O(r2) ^ : : (3.8) (3.9) (3.10) (3.11) (3.12) Hence, the growth of the dark matter density perturbation obeys a reduced power law Further, since the power spectrum P of the dark matter density perturbation is proportional to the square of the over-density, D2M, we nd that the ratio of the power spectrum with and without the interacting component ^ is given by P (r) P (0) ' (1 r)2 2^ (r) 2^ (0) ' (1 2r) a amd 1:2r ; where amd ' 10 3 is the scale factor at which matter dominates the source term of the Einstein equation in eq. (3.2). In order to eliminate the 8 discrepancy through the reduction of the density perturbation by ' 10%, we need to suppress the matter power spectrum in eq. (3.12) by ' 20%. This requires r ' 2{3% and is the reason for the benchmark value in eq. (2.2). To obtain a more precise result, we determine the size of the over-density DM by numerically solving equations (3.1){(3.3) and (3.6), where we choose a U(1)L^ coupling that satis es eq. (3.5). We also incorporate the evolution equations for the SM photon and baryon by making the replacements DR! and ^ ! SM baryon (B), respectively. For the modes that enter the horizon during radiation (matter) domination, the initial conditions for solving the coupled system are given by r(;DmR) = 4 3 ^;^;B = 1 r(m) ; ^;^;DR;B; = 2 r(m)k2 ; (3.13) with the values 1r = . We make the following parameter choices when solving this coupled system of evolution equations: h = 0:68, h 2 = 2:47 has only a small e ect so that its precise value is not important for our purpose here. We choose N scatt = 0:46, assuming the presence of the e anomaly compensator ^0, and a slightly larger value of DMh 2 = 0:13 in order to keep the redshift at matter-radiation equality unchanged. This allows us to compare our matter power spectrum to that of a conventional single-component dark matter model without any dark radiation. We nd that the choice of r = 2:5% leads to an 8% suppression of the density perturbation around the scale k 0:2h Mpc 1 as compared to CDM, thereby solving the 8 problem. It should be noted that this corresponds to a ' 23% suppression when compared to the r = 0 case with the same amount of dark radiation, as displayed in the left panel of gure 3. In the same plot, we also show the ratio of the power spectrum, P (r)=P (0), during the CMB time with a 10 3 (dashed curve). Due to the redshift dependence in eq. (3.12), the suppression of the matter power spectrum is smaller at the earlier CMB time, and hence the correction to the metric perturbation is minor at this time. This feature allows the model to exibly accommodate bounds from the CMB temperature spectrum and CMB lensing, as is discussed in ref. [47]. If we consider an alternative scenario, in which both ^ and ^ scatter with the dark radiation through a gauged twin B L symmetry as a realization of the QuAcDM framework, we can obtain the same suppression by requiring B^ L^ 10 9:8. Distinct from the PAcDM setup, the QuAcDM scenario gives comparable suppressions to the matter density perturbation between today and the CMB time. As is shown in gure 2, the di erent corrections to the power spectrum provide a way to di erentiate between these dark sector scenarios through the CMB observation. 4 Small-scale structure: Twin baryon with a self-interaction In this section, we study the dark matter self-interaction through twin photon exchange ( gure 1) and make a connection to dark matter halo structures. Our twin sector contains the self-interacting dark matter particles ( ^ ; ^) and a dark uid scattering with ^, which gives rise to complicated dynamics for halo formation. A detailed N-body simulation of the halo structure is beyond the scope of this work. In the present analysis, we only focus on the dominant dark matter component ^ , which contains ' 98% of the dark matter density, and comment on the possible correction to the result from the presence of ^ and the dark uid. N scatt = 0:46. In the Twin Higgs setup discussed in this work, the dark matter ratio r is given e by r = m^=(m^ + m^). In the plot, the solid (dashed) curves are obtained by numerically solving the linear evolution equations described in section 3, all in the tight coupling limit and assuming no anisotropic stress. Results for di erent values of r are labelled in di erent colors, while earlier (a = 10 3) and late (a = 1) times are indicated by dotted and solid lines, respectively. Also see ref. [47] for more details. The halo structure formation depends on the average time scale of dark matter scattering hn v i 1, where n = c DM=mDM gives the number density, and the various relevant e ects are determined by the cross section mass ratio =mDM. In order to solve the mass de cit problem from dwarf galaxy to galaxy cluster scales, we require that =mDM be 1 cm2=g for dwarf galaxies and 0:1 cm2=g for galaxy clusters. One way to achieve this is to introduce a velocity-dependent dark matter self-scattering process with the mediator mass comparable to or lighter than the momentum exchange of the dark matter particles. Since the average collision velocity between dark matter particles in dwarf galaxies is about an order of magnitude smaller than the corresponding value for the galaxy clusters, the nonperturbative e ects in the scattering cross section, enhanced by a low dark matter velocity, can help to reconcile the required =mDM for di erent objects. In this work, we estimate the size of =mDM by applying standard partial wave methods discussed in ref. [73] to a range of twin photon masses and couplings. We focus on scattering outside of the Born regime, demanding that ^m^ =m^ & 1, so that the nonperturbative e ects of nonrelativistic scattering become important. Since the dark matter density contribution ^ arises from the twin baryon asymmetry, the dark matter particles are scattered by a repulsive potential V (r) = ^e m^r=r with ne structure constant ^ in the twin sector, and the transfer cross section of dark matter scattering can then be expressed as ( 2 ^m^=m^ v2) [73] ; (4.1) in the classical limit m^ v=m^ 1. For m^ v=m^ . 1, a good approximation is obtained by (4.2) (4.3) 0 i im^ v m^ 1 ) A ; Since the number density of the subcomponent dark matter ^ is comparable to that of the dominant dark matter ^ , the chance of having a ^ particle scatter with ^ is therefore comparable to the ^ self-scattering. However, given that m^ m^, the momentum transfer from the ^ {^ scattering is accordingly much smaller than that from the ^ selfscattering. It is then reasonable to consider only the ^ scattering to a good approximation. Our study focuses on dark matter halo structure anomalies in dwarf galaxies, low surface brightness galaxies (LSBs), and galaxy clusters. Instead of tting the result for each of these objects, we approximate the results for the ratio of the cross section to the dark matter mass in ref. [55] in terms of various ranges of this ratio. For dwarf galaxies, we take =mDM = 0:5{5 cm2=g and v = 60 km=s. Next, for LSB galaxies, we assume =mDM = 0:5{ 5 cm2=g and v = 100 km=s. Further, for galaxy clusters, we take =mDM = 0:05{0:5 cm2=g and v = 1200 km=s. When studying the cross section, we also consider bounds from the ensemble of merging clusters of =mDM < 0:47 cm2=g at 95% CL [74] at a collision velocity In the upper panel of gure 4, we show the allowed sizes of m^ and m^ required to solve the mass de cit problem in various galactic objects. The plot assumes Z2-symmetric electromagnetic couplings ^ = between the twin and SM sectors. It turns out that if we x the mass parameters to be in the range 10 . m^ . 40 GeV and 10 . m^ . 20 MeV, the self-interaction of the twin baryon can provide a plausible solution to the small-scale structure problem. In addition to explaining the anomaly, an analysis of the e ect of dark matter selfscattering on halo formation also sets a bound on the twin photon interaction. When we consider a twin sector that contains stable charged baryons carrying a SM-like baryon asymmetry, the self-coupling of the baryons is subject to an upper bound that ensures that the self-scattering does not violate the small-scale structure constraints. In the lower panel of gure 4, we investigate the upper bounds on the twin photon coupling by applying constraints from the merging cluster with =m^ < 0:47 cm2=g and the shape of dwarf halos with =m^ < 5 cm2=g. If we suppose that the twin baryon dominates the dark matter density, there then needs to be a breaking of the mirror symmetry either through a nonzero m^ or a smaller twin electric coupling. When we consider the e ect of the presence of ^ and the dark uid, then no matter whether ^ contributes to a core- or a cusp-like density pro le, the 2:5% dark matter density does not yield observable signatures in the current measurements of halo structure. One potential application of the ^-dark uid scattering is the following: if the dark uid is able ponent ^ and a Z2-symmetric twin photon coupling ^ = . See section 4 for the choice of cross section and velocity values. The dashed curve shows a lower bound on the dark matter mass from the cluster merger constraint. The overlap area (gray) among di erent allowed regions gives solutions to the mass de cit problem for the three types of galactic objects. Right: upper bounds on the twin electromagnetic coupling from the cluster merger and dwarf halo constraints. The kinks of the curves in both plots correspond to the transition points between di erent analytical approximation regimes in eq. (4.1) and (4.2) for the cross section calculation. For example, in the m^ = 10 GeV cluster merger curve, the rst kink from the left corresponds to ' 1, and the second kink corresponds to m^ v=m^ ' 1. to cool down the ^ particles enough such that the subcomponent dark matter falls into the galactic center, this mechanism would provide a possible explanation of the origin of supermassive blackholes [75]. When nonlinear halo formation sets in around a redshift of z = 10{20 [ 76 ], the dark uid is much colder than the virial temperature of ^, given by ' (m^=1 GeV) keV. So, if the uid is able to rapidly transport heat outside the halo, the dark matter ^ can accordingly undergo e cient cooling and collapse into a black hole. However, since the free streaming length of the dark uid is in fact very short, expected to be only 10 m for a twin coupling of size ^ T 10 4 eV, a dark uid particle makes a random walk across a distance 10 3 pc until L^ ' 10 2 and a uid temperature of about today [77], which is negligible relative to a 10 kpc-size halo. Hence, we conjecture that the dark uid does not dissipate heat e ciently through di usion and expect that a better cooling mechanism such as convection is required to form the black hole. 5 Solutions from the Twin hydrogen DM The extended Fraternal Twin Higgs model described above contains two questionable assumptions of the Z2 breaking. The rst one is that in order to accommodate the mass de cit problem, it is necessary to break the twin electromagnetism U(1)L at the MeV scale, thus introducing an additional scale which is not associated with any other mass scales in the model. The second assumption is that if we choose to gauge the U(1)L symmetry, we are compelled to include anomaly compensators in the SM. These su er from strong experimental constraints, and an additional Z2 breaking is required to lift the compensator mass. EWSB scales by p B L with B L & 10 4 [78]. Rather than adding extra layers of the model, here we present an alternative solution to the structure problems that does not require the twin U(1)EM breaking and the introduction of additional fermions in the TH model. We will see below that in this scenario, the required Z2 breaking will be a ' 60% deviation between the SM and twin electric couplings and that the solution will feature di erent Yukawa couplings of the light fermions. Let us rst describe the main idea of the model. When the temperature of the twin sector drops below the twin con nement scale, we assume that the twin sector contains the following spectrum: the twin proton p^+, twin lepton `^ , light twin neutrinos ^; N^ , as well as massless gauge bosons ^; ^B L. Instead of gauging the twin lepton number, here we gauge the twin U(1)B L that is anomaly-free assuming the presence of right-handed neutrinos. In this scenario, we can break the SM U(1)B L above the EW scale through the same Z2 breaking as in the Higgs potential. For example, upon getting a VEV, the Z2-odd scalar in the Z2-symmetric potential L can induce the breaking of SM U(1)B L through the B (jHAj 2 jHBj2) + 0 (j Aj 2 j Bj2) L charged scalar and split the h i in the two sectors. In order to achieve a successful PAcDM scenario, the U(1)B L coupling required to resolve the LSS problem can be as small as 10 8, and existing constraints from the Z0 search only cover the TeV scale B L Twin hydrogen H^ starts to form when the twin temperature drops below the binding energy between (p^+ `^ ). Following recombination, a small fraction of the twin particles remains ionized. Since H^ is neutral under both the U(1)EM and U(1)B L symmetries, it behaves as a cold DM particle during the structure formation. Meanwhile, the few ionized twin particles (p^+; `^ ) scatter with the twin neutrinos via the t-channel U(1)B L process. This process realizes the PAcDM framework in this scenario, furnishing the mechanism which suppresses 8 and enhances the Hubble value due to the presence of additional twin radiation. During the DM halo formation, the virial temperature of the dark plasma is lower than the binding energy. Hence, the twin hydrogen H^ remains stable and constitutes the dominant DM component inside halos. Characterized by an extended but nite size, the H^ atom furnishes a good SIDM candidate if its geometric size is around the barn scale. The reason stems from the property that the scattering between two H^ 's contains both elastic and inelastic processes. The elastic process comes from the collision between two atoms, which transfers energy from one atom to the other and acts to keep DM thermalized. Meanwhile, the inelastic process comes from the hyper ne splitting between `^ and p^. In the inelastic case, when `^ absorbs part of the collisional energy into the excited state, the subsequent decay into the ground state releases DM energy into soft ^. This cooling process is important when H^ carries a kinetic energy comparable to the hyper ne splitting, in which case the scattering process introduces an additional velocity dependence in the scattering cross section. A numerical study of the scattering cross section has been performed in [61]. From this, it emerges that the general trend is that the cross sections of dwarf halo particles with lower DM velocities tend to be larger than those of particles in cluster halos with higher velocities, which feature provides the correct behavior required to solve mass de cit problems in both cases. structure formation. can be approximated as [ 59 ] We rely on the results in refs. [ 59, 61 ] to determine reasonable parameters in the twin sector for our purposes. It turns out that in order to solve both the large- and small- scale structure problems simultaneously, we need the twin masses mp^ the twin electric coupling ^ 0:02, and the twin U(1)B L coupling ^B L & 10 9. The last bound is necessary to ensure that the t-channel p^ ^ ! p^ ^ scattering is e ective during 20 GeV, m^ ` 3 GeV, We next discuss some details of the parameters. First, the fraction of ionized atoms e 2 ' 0:5 is the ratio between the Twin and SM temperature today when the twin radiation contributes Ne ' 0:4 for solving the H0 problem. BH = 2 d H=2 is the binding energy of the dark hydrogen atom, and H is the reduced mass of the p^ `^ system. Upon choosing ^ = 0:02, mp^ = 20 GeV, and m`^ = 3 GeV, we nd that the resulting fraction is e ' 2:5%. As discussed in section 3, this value results in the appropriate amount of oscillating DM necessary to solve the 8 problem. For simplicity, we assume the U(1)B L coupling to be smaller than the electric coupling, ^B L < ^, so that the twin EM dominates the binding force. With the above choices, the binding energy is BH 400 keV, which signi cantly exceeds the virial temperature ' 2 keV of the twin atom during galaxy formation.4 Moreover, for the size of ^ we choose, the rate of collisional ionization between H^ atoms in cluster halos is always smaller than the cluster lifetime [61]. Hence, the twin atom remains in the ground state during halo formation. If we consider the case where the H^ atom is composed of a spin- 12 p^ and a spin- 12 `^, the hyper ne splitting for the chosen mass and coupling parameters is 100 eV. The value is above the `^ energy due to the virial velocity inside dwarf galaxies but below that inside galaxy clusters. Therefore, the hyper ne splitting plays a more important role in DM scattering inside galaxy clusters than dwarf galaxies. From the numerical study in [61], such an energy splitting generates di erent DM thermalization e ects at dwarf galaxies and galaxy clusters, which feature enables one to successfully solve the mass de cit problem in both systems. scale ^ Meanwhile, in the single-generation model, the lightest twin baryon (^b^b^b) is a spin- 32 particle, and a numerical study of the hyper ne splitting between a spin- 32 nucleus and a spin- 12 lepton in the H^ scattering is more involved and is beyond the scope of this work. In order to give a viable example of the model, we simply adapt the result in [61] by taking the nucleus to be a spin- 12 particle. We then assume two generations of twin fermions and take (^b; s^) to be the lightest twin quarks. In this case, (^b; s^) quarks remain stable and form protons, p^ = (^b^bs^) or (^bs^s^) , while the twin neutron is absent due to a fast c^ ! s^^^ decay. With two generations of quarks, RG running gives the twin con nement ' 270 MeV. Here we assume that m^b ' ms^. Although this choice introduces 4The virial temperature is given by Tvir 0:9 keV MMDgaMl 10 GeV Rvir 110 kpc , where M represents the mass of the virial cluster, MDgaMl = 1012M of a dark plasma particle (in our case this is = p^=np^ = 20 GeV) [79]. is the mass of DM in the Milky Way galaxy, and is the average mass additional Z2 breaking, it does not ruin Higgs tuning owing to the smallness of the Yukawa couplings for the ^b and s^ quarks and constitutes a better alternative to the introduction of anomaly compensators. Then, approximating the twin proton mass as mp^ ' 3(ms^ + ^ ), we nd that the lightest twin quarks feature a mass of 6:5 GeV. Twin muon carries a mass of 3 GeV and is combined with twin proton to form the twin hydrogen. In this case, the muons (with lifetime 10 6 sec) during the twin con nement. lightest twin hadron is the scalar glueball mG^0++ ' 2 GeV, which decays promptly into SM In this model, we nd that when the SM and twin sector decouple around the GeV scale, the light degrees of freedom from the dark radiation ^ ; ; N^ ; ; ^; ^B L contribute a Ne = 0:4, which is the required value for solving the Hubble problem. We thus see that this Twin Hydrogen scenario successfully resolves both the large- and small-scale structure problems without introducing additional mass scales or anomaly compensators. 6 Discussion and conclusions In this work, we take the viewpoint that the Hierarchy problem and the large- and smallscale structure anomalies are all indicative of the existence of a dark sector that extends beyond the CDM paradigm. We investigate potential solutions to these problems in the context of an extension of the Fraternal Twin Higgs model, which contains only the heavier-generation partners of SM fermions and a massless gauge boson that gives the DM and twin neutrino scattering. We rst discuss the ^ {^ scenario, which assumes a SM-like baryogenesis, the twin baryon ^ (^b^b^b) and the twin tau ^ become metastable dark matter particles due to twin baryon number and an approximate twin U(1)em symmetry. Through the exchange of a 10 MeV-scale twin photon, these dark matter particles have a selfinteraction cross section that successfully resolves the mass de cit problem on all scales, from the dwarf galaxies to the galaxy clusters. In the speci c implementation of the PAcDM framework that we consider, the gauged U(1)L^ force acts to suitably damp the dark matter power spectrum, supposing it remains e ective at the beginning of matter domination. In particular, if m^ ' 2:5% m^ , such a damping can indeed reduce the size of 8 by ' 8%, reconciling the 8 discrepancy. Moreover, the overall e N scatt, which receives contributions from the tightly coupled uid in the twin sector, including the massless neutrinos, U(1)L^ gauge boson, and its anomaly compensators, is able to exibly enhance the size of H0. Favored by a weaker CMB constraint on a tightly coupled uid, this model can e ciently reconcile the tension between the H0 results from the CMB and local measurements. We also discuss the scenario of the twin hydrogen DM. In this case, ' 2:5% twin protons remain ionized, and their scattering to twin neutrinos through a twin U(1)B L force damps the matter power spectrum realizing the PAcDM framework. The twin photon remains massless in this case, and the scattering between two twin hydrogens contains the required velocity dependence necessary to successfully resolve the mass de cit problem from dwarf galaxy to galaxy cluster scales. Our study is based on the Fraternal Twin Higgs model, which contains a smaller number of neutrinos than the full three-generation case and hence is able to more easily satisfy the Ne constraint. Alternatively, it may be possible to accommodate all three generations of fermions in the twin sector, provided that there is either a late-time reheating that preferentially goes into the SM sector [80{83] or a Z2 breaking of the Yukawa couplings [84]. In either of the cases, the stable charged twin fermions can still interact with each other through the twin photon exchange and a ect the halo formation. Further, if a component of the dark matter has acoustic oscillations, either through a twin baryon acoustic oscillation among the twin proton, twin electron, and twin photon, or through a twin lepton acoustic oscillation between the twin electron and twin neutrino through the anomaly-free gauge force U(1)L^i L^j , there are partially acoustic oscillations that can smoothly change the large-scale structure. We leave the study of this scenario to future work. Aside from explaining the possible anomalies, analysis of structure formation in the twin sector provides additional constraints on the Twin Higgs model. Given a sizable amount of stable charged twin particles, which can be found in a large chunk of parameter space, constraints from the dark matter self-interaction enable us to set an upper bound on the twin electric coupling ( gure 4). If the charged twin particles scatter with massless twin particles, studies of the CMB and the matter power spectrum also set upper bounds on such couplings. In the coming years, the experimental precision in the values of Ne and (H0; 8) is expected to improve signi cantly from both the CMB and weak lensing measurements [85]. Moreover, with the progress of the N-body simulation, we anticipate to better identify the signi cance of the mass de cit problem from baryonic grounds. No matter whether these puzzles of the large- and small-scale structure remain signi cant or disappear, the coming future results will more clearly reveal the details of the Twin Higgs model, opening the door to a stronger understanding of these issues and to novel connections between the dark sector and the Hierarchy problem. 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Valentina Prilepina, Yuhsin Tsai. Reconciling large- and small-scale structure in Twin Higgs models, Journal of High Energy Physics, 2017, 33, DOI: 10.1007/JHEP09(2017)033