Inflation and dark matter in the inert doublet model

Journal of High Energy Physics, Nov 2017

We discuss inflation and dark matter in the inert doublet model coupled non-minimally to gravity where the inert doublet is the inflaton and the neutral scalar part of the doublet is the dark matter candidate. We calculate the various inflationary parameters like n s , r and P s and then proceed to the reheating phase where the inflaton decays into the Higgs and other gauge bosons which are non-relativistic owing to high effective masses. These bosons further decay or annihilate to give relativistic fermions which are finally responsible for reheating the universe. At the end of the reheating phase, the inert doublet which was the inflaton enters into thermal equilibrium with the rest of the plasma and its neutral component later freezes out as cold dark matter with a mass of about 2 TeV.

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Inflation and dark matter in the inert doublet model

HJE In ation and dark matter in the inert doublet model Sandhya Choubey 0 1 2 3 4 5 Abhass Kumar 0 1 2 3 5 0 AlbaNova University Center , 106 91 Stockholm , Sweden 1 Anushaktinagar , Mumbai 2 Chhatnag Road, Jhunsi , Allahabad 211 019 , India 3 Homi Bhabha National Institute, Training School Complex 4 Department of Physics, School of Engineering Sciences, KTH Royal Institute of Technology 5 Harish-Chandra Research Institute 6 400094 , India We discuss in ation and dark matter in the inert doublet model coupled nonminimally to gravity where the inert doublet is the in aton and the neutral scalar part of the doublet is the dark matter candidate. We calculate the various in ationary parameters like ns, r and Ps and then proceed to the reheating phase where the in aton decays into the Higgs and other gauge bosons which are non-relativistic owing to high e ective masses. These bosons further decay or annihilate to give relativistic fermions which are Cosmology of Theories beyond the SM; Beyond Standard Model - nally responsible for reheating the universe. At the end of the reheating phase, the inert doublet which was the in aton enters into thermal equilibrium with the rest of the plasma and its neutral component later freezes out as cold dark matter with a mass of about 2 TeV. 1 Introduction 2 The standard model of particle physics has been very successful with highly accurate predictions. However, it still has no answer for various problems like dark matter and in ation. Both in ation and dark matter have been established very rmly through various observations particularly of the cosmic microwave background (CMB) radiation. In ation [1] has long been the most successful theory to answer cosmological problems like the horizon problem and homogeneity. The most popular in ationary models are those that have an extra scalar particle which acts as the in aton. Recent experiments like Planck [ 2 ] and WMAP7 [3] have placed bounds with high accuracy on in ationary parameters like the spectral index, the tensor to scalar ratio and the scalar power spectrum. There have been a variety of in ation models over the years. The Higgs in ation [4, 5] models are the most simple in the sense that they do not involve any extra eld and have just one more parameter through which the eld couples to gravity but they come with their share of problems. The quartic coupling of Higgs eld at high energy scales (& 1010 GeV) becomes negative. This can cause problems with the stablility of the vacuum [6]. Another problem comes in the form of non-unitarity. The scalar power spectrum bounds require 104 [7] which breaks unitarity at scales around mP l= 1013 GeV [8]. To avoid running into problems in a Higgs in ation model, often an extra scalar stabilizing eld is added and such scenarios are called s-in ation. These models have an extra gauge singlet scalar particle that acts as the in aton while the Higgs eld acts as a portal to the standard model to reheat the universe. There can be variations in this model and in [9] distinctions between the variations is studied. The in ationary potential is usually taken to be either a chaotic one or a Starobinsky one. Chaotic in ation [10] models include power law potentials like m2 2 + 4. These were the rst type of potentials used to study in ation. On the other { 1 { hand Starobinsky models have exponential potentials. We will discuss more about them later. A good review for in ationary cosmology in the light of data can be had in [11]. Dark matter has been studied extensively over the years. Thanks to the many experiments and observations, we now have a good estimate for dark matter distribution in and around our galaxy and in the universe at large. Planck results [12] together with other astronomical observations have put down the abundance of dark matter in the universe to dmh2 ' 0:12. The most commonly studied dark matter scenarios are the so called Weakly-Interacting Massive Particles (WIMP). In recent years however, as dark matter detection experiments have become better and colliders like LHC are probing higher energies, the absence of any new particle at the weak scale has put the WIMP scenario in a x and people have started looking at other options like axions, feebly interacting massive particles (FIMP) and strongly interacting massive particles (SIMP) [13{16] among others. One of the simplest models of dark matter | the scalar singlet dark matter model is still being sustained and there have been updates to it [17]; see also [18]. In more recent works, people have started to look for scenarios where both in ation and dark matter can be explained by the same eld. Gauge singlet scalar models in the s-in ation scenario is a case in point. In this paper, we have combined in ation and dark matter in the inert doublet model coupled non-minimally to gravity. Such a uni cation was rst shown to be possible in [19] in string theory landscape. In [20{22] a gauge singlet scalar is used as in ation and later after freeze out as the dark matter candidate. [23] has a situation similar to s-in ation where the in aton is very light and interacts very feebly to become FIMP dark matter later. In ation and dark matter in two Higgs doublet models was studied in [24]. A scalar WIMP dark matter candidate with non-minimal coupling to gravity acting as the in aton was studied in [25]. The motivation for using inert doublet model in our case is the fact that pure Higgs in ation is problematic and yet it is the only scalar eld present in the standard model. Another scalar doublet similar to Higgs doublet but stabilized by an extra Z2 symmetry such that it does not interact with leptons and quarks via Yukawa couplings can present a viable candidate for both in ation and dark matter. The components of the inert doublet can all act as in aton via a particular eld rede nition. At the same time, its neutral scalar component can later become the dark matter candidate. The inert doublet through its interactions with the vector gauge bosons and Higgs can also reheat the universe at the end of in ation to ensure that the universe gets populated by standard model particles. Another motivation for using this model is that it is similar to s-in ation models in that the potential turns out to be of the Starobinsky kind which gives some of the best t to in ationary parameters like the spectral index. We will also look at the reheating phase in some detail. In aton during reheating behaves as non-relativistic matter and decays via gauge and Higgs bosons to relativistic particles. We will look at the interactions happening during reheating and later when we discuss dark matter, we will point out the changes that take place in the interactions of the inert doublet compared to the reheating phase. The electroweak (EW) symmetry breaking will play a role in determining the type of interactions that the inert doublet undergoes. { 2 { This paper is organized in the following manner. We describe the model in the next section. In section 3, we study in ation and nd the value of the various in ationary parameters like the slow roll parameters, the spectral index and the tensor to scalar ratio. In section 4 we study reheating which progresses by the decay of the in aton into nonrelativistic vector and Higgs bosons which further annihilate into relativistic fermions. In this section, we calculate the energy density stored in the relativistic particles and nd some bounds on some model parameters. The inert doublet as a cold dark matter candidate is taken up in section 5 where we x some parameter values like the mass of dark matter through relic density calculations. We end in section 6 with conclusions. HJEP1(207)8 1 2 MP2 lR D 1D y 1 D 2D y 2 V ( 1; 2) 1 12R 2 22R ; 2 1. The extra doublet is inert in the sense that it does not have any Yukawa like couplings because of an inherent Z2 symmetry under which this doublet is odd ( 2 ! 2) while the Higgs and other standard model particles 1 ; , where stands for SM particles other than Higgs). The action (2.1) (2.2) (2.3) where D stands for the covariant derivative containing couplings with the gauge bosons. During in ation, there are no elds other than the in aton so that the covariant derivative will reduce to the normal derivative D The minus sign in the kinetic terms is in keeping with the metric convention of ( ; +; +; +). MP l is the reduced Planck mass, R is the Ricci scalar and 1 and 2 are dimensionless couplings of the doublets to gravity. The motivation behind these couplings is that quantum e ects invariably give rise to such couplings at Planck scales [26]. The potential is: V = m12j 1j2 + m22j 2j2 + 1(j 1j2)2 + 2(j 2j ) 2 2 + 3j 1j2j 2j2 + 4( y1 2)( y2 1) + 1 2 5[( y1 2)2 + c:c:]: The two doublets have the components: 1 = p 1 2 h ! and 2 = p 1 2 q x ei ! : 2 1 2 automatically satis es this condition 2 1 Note that there is no non-zero vacuum expectation value of the Higgs eld as the electroweak symmetry is intact at in ationary scales. We want the inert doublet to be the in aton. This is ensured if 22 21 . A choice where 1 and 1 are of the same order while { 3 { In ation The action in eq. (2.1) is written in the physical or the Jordan frame [27, 28] and has terms where the scalars 1;2 couple quadratically to gravity. This makes it di cult to derive meaningful results from the usual processes of quantum eld theory. We need to make some transformations where we can get rid of such coupled terms. This can be done by a conformal transformation to the so called Einstein frame. Einstein frame is useful as in this frame the action looks like a regular eld theory action with no explicit couplings to gravity. Results for physical observables remain the same independent of the frame chosen. After the end of in ation, the transformation parameter becomes almost 1, making the two HJEP1(207)8 frames equivalent. Following [28], we make the following conformal transformation on the metric and the elds to get the action in the Einstein frame: de ning = f ; h; q; x; g where: g~ = 2 g ; 2 = 1 + Gij = V~ = 1 V 4 : 2 ij + M1P2 l ( 2 + h2) + M2P2 l (q2 + x2); 2 (3.1) (3.2) (3.3) (3.4) (3.5) (3.6) The above G gives mixed kinetic terms. All these elds are always present in the lagrangian but during in ation, elds other than the inert doublet components give no contribution. 2 can also be simpli ed to exclude the MP l 1 ( 2 + h2) term. This allows us { 4 { Let us look at the kinetic terms. First, we expand the pre-factor G in a matrix form: G = 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 2 2+6 12 42=MP2 l 6 MP21l 2 h 2 2 66 6 MP21l 2 h 2+6 12h2=MP2 l 4 2 to simplify the matrix G as: 2 2+6 22q2=MP2 l 4 B = MP l q : MP l log x A further simpli cation to a completely diagonal kinetic form can be obtained by rearranging the elds as follows: Substituting this rede nition of elds into the kinetic part, we get a diagonal kinetic term which is: 1 + 1 2 + 1 12 2F (A) F (A) 2 2(1 + B2=MP2 l)2 (@ B)2 + F (A) B2 2 2(1 + B2=MP2 l) (3.10) where F (A) = 1 exp Eq. (3.10) is still apparently not canonical. However, at the scales relevant for in ation F (A) is of the order of 1 and the change in F (A) while A drops from values many times larger than MP l to MP l is very small. This can be seen in gure 1. With large 2 this which makes the kinetic term canonical. 12 and the other elds can have a constant rescaling All such terms from the Einstein frame potential in eq. (3.5) which are not quartic in q and x can be neglected owing to the largeness of these two elds. The only relevant term that remains is the quartic term 14 2 q2 + x2 2 which using the rede ned elds becomes: Ve 2MP4 l "1 exp potentials [29]; see also [30]. In gure 2 we show the in ationary potential vs. the eld 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 F(A) HJEP1(207)8 0 1 4 5 2 3 A/MPl where it can be seen that the potential is almost at at high eld values ensuring slow roll. The slow roll parameters and with this potential are: = 1 2 MP2 l 1 dVe Ve dA 2 = = MP2 l V1e dd2AV2e = " 4 3 4 3 h 1 + exp h 2 exp 1 + exp 1 and thus slow roll is satis ed. In ation ends when ' 1. We would now like to get estimates for the values of A at the beginning and end of in ation which will be needed to get the power spectrum. This can be done by looking at the number of times the universe expanded by e times its own size, also called the number of e-folds N . It is obtained as follows: N = 1 Z Aini Ve dA MP2 l Aend Ve0 3 4 " = exp exp where Ve0 = ddVAe , Aini is the value of A at the beginning of in ation and Aend is the value of A at the end of the in ation. { 6 { 0.2 0 0 Inflationary Potential 1 2 To get Aend, we make use of the fact that slow roll in ation ends when eq. (3.12), which gives: Using eq. (3.15) in eq. (3.14) for N = 601 we get exp exp Looking at gure 2, we see that eld values are consistent with slow-roll and its end. With N xed at 60 and the eld value at the start of in ation xed, we can get the scalar power spectrum (PS), the tensor to scalar ratio (r) and the spectral index (ns) as 1In principle N could be any number greater than around 50 to solve atness and horizon problems. 60 e-folds solves the baryon asymmetry problem if in ationary energy scales are O[1016] GeV [31]. Lower in ationary energy scales would need more e-folds and vice versa. However, the number of e-folds cannot be much larger than 60. { 7 { follows: 0.966 0.965 0.964 n Number of ef-olds (N) scalar ratio lie within Planck bounds. later for energy density calculations. where Ve0 is the derivative of Ve with respect to A and both Ve and Ve0 are calculated at the Aini. The values of r and ns are well within the Plank bounds [ 2 ] of ns = 0:9677 0:0060 at 1 level and r < 0:11 at 95% con dence level. Since there is no reason for N to be precisely 60, we look at the in ationary parameters over a range of N from 55 to 65 (see gure 3 and 4). We see that in the entire region of N , the spectral index and the tensor to We can use WMAP7 constraint for Ps [3] to relate 2 and 2 which will be needed Ps = (2:430 0:091) Having multiple scalar elds can give rise to multi- eld e ects which can cause signi cant iso-curvature uctuations. The presence of isocurvature uctuations has been studied in detail in [32{34]. Following them, we expand the elds to rst order i = 'i(t) + i(x ) { 8 { (3.19) (3.20) (3.21) (3.22) HJEP1(207)8 0.0036 0.0034 where " is the turn-rate vector in the eld space: "i = ^_i + ijk ^j '_ k with ijk being the connection in the eld space for the eld space metric Gij . We also de ne the mass-squared matrix for the gauge invariant linearized perturbations [32]: Mji = Gij Dj Dk V e Riklj '_ k'_ l where Di is the covariant derivative in the eld space w.r.t. eld 'i and Riklj is the Riemann tensor in eld space. These together are used to get a parameter ss which is used to calculate the mass-square of the isocurvature uctuations s2 as follows: 2 1 Since 22 21 , in ation occurs along the h 0 direction, thereby making s^1 and s^2 zero. We are left with remaining two scalars q and x which have symmetric couplings 2 and 2 . For such a case, ss very suppressed isocurvature fraction of iso with Planck data [ 2 ]. 1 ( O(10 6)) which means [34] s2=H2 ' 0 giving a O(10 5). The results are hence consistent ss = s^is^j Mji MP2 l V e At the end of in ation, the universe is too dilute for anything to be present. Unless the universe is somehow repopulated by particles, it remains empty. It is at this juncture that the energy density till now stored in the in aton starts to disperse as the in aton particles annihilate or decay into other particles including those of the standard model. This phase of the universe after in ation where in aton annihilates into other relativistic particles is called reheating [35]. If the in aton decays or annihilates into bosons, parametric resonance production of bosons triggers e cient reheating [36, 37] (see also [38, 39]) and at the end of it, the universe becomes radiation dominated. allows us to identify two distinct regions [40] marked by Acr = q 2 MP l : The conformal transformation and the rede nition of elds done in the previous section In ation occurs in the second region where A > Acr which can also be written as (q2 + x2)1=2 > Acr. Much below MP l, the in ationary potential in eq. (3.11) can be approximated by a quadratic potential well: A Ve = ' Ve = ( (q2 + x2)1=2 for A < Acr; q 32 MP l log 2 for A > Acr: 2 MP4 l "1 This is a simple harmonic potential in which the in aton oscillates rapidly with frequency !. This makes the oscillations coherent, the phase being the same at all points in space. Since the potential is a simple harmonic one near the minimum, the average energy density obeys the relation A = hA_ 2i and thus obeys the equation _A + 3H A = 0 which yields a 1=a3 evolution for the average energy density. This means that during this period the in aton behaves as non-relativistic matter. A matter dominated universe has the following characteristics with respect to the scale factor and Hubble's constant: The equation of motion for A during this phase is which gives on solving for ! H: H(t) = a / t2=3; a_(t) a(t) = 2 3t : A + 3HA_ + dA dVe = 0; A = A0(t) cos(!t); (4.1) (4.2) (4.3) (4.4) (4.5) (4.6) (4.7) where The quadratic phase ends when the amplitude of the oscillations A0 crosses Acr which gives us the crossing time as tcr = 2!2 . In [35] it was shown that reheating occurs when the eld oscillates in a quadratic potential well. Therefore in the present scenario, reheating starts when the potential gets approximated by eq. (4.3) and ends when the amplitude A0 crosses Acr at time tcr. The inert doublet can decay into the W and Z bosons through the kinetic coupling terms and into the Higgs boson through the potential in the Lagrangian. The resultant particles don't have a physical mass at this time but an e ective mass arising due to the in aton oscillations. If the oscillation frequency ! is much larger than the expansion rate H, the amplitude can be taken to be constant over one oscillation period. This allows us to write down e ective mass terms for the vector and scalar bosons. When A q 32 MP l but still above Acr, (q2 + x2) in terms of q and x to get: 2 MP2 l . Using this we can expand the log term in the de nition of A is 4gp26 M2P l A W 2. This gives an e ective mass for W bosons to be: The coupling of the inert doublet to W bosons is g42 (q2 + x2)W 2 which in terms of A 2 MP l jAj: 2 (4.8) (4.9) (4.10) (4.11) The other vector boson e ective masses can be related by the Weinberg angle. The coupling to Higgs is through 3;4;5. This gives us an e ective mass term for the Higgs boson: m2h = p 1 6 3 + 4 2 MP l jAj: 2 In writing the Higgs e ective mass, we have taken equal contributions of q and x in A. Note that eq. (4.9) is not an equation for vacuum expectation value as it is not calculated at the minimum of the potential. It just describes the transformation between q and x on one hand and A on the other in a particular regime mentioned above the equation that follows from eq. (3.8). The masses in eqs. (4.10) and (4.11) are therefore not usual masses obtained from spontaneous symmetry breaking but are just e ective masses coming out of their interactions with the in aton elds when written in terms of the transformed eld A. The weak coupling g is large which makes the vector bosons non-relativistic. They will decay and annihilate to other relativistic fermions to reheat the universe. If either of 3 and 4 is large, the produced Higgs too will be non-relativistic and it will decay into fermions through Yukawa interactions which will add to the relativistic energy density. The inert doublet gives a cold dark matter candidate which means the combination of its couplings to Higgs becomes of the order of 1 [41]. We choose a case where 3 1 is the dominant coupling when compared to 4 and 5 which are taken to be very small just for the sake of brevity. This enables us to remove the 4 term from the e ective mass of Higgs in eq. (4.11). At low number densities of the produced W and Higgs bosons (nW and nh respectively) their decay to fermions is the dominant channel to produce relativistic particles. If the number density of the bosons becomes large, their production rate will become exponential due to parametric resonancne. During the resonance phase, the W bosons will mostly annihilate to produce fermions. Their decays will become sub-dominant channels of fermion production. Higgs on the other hand can only produce fermions through decays. Following [40] (see also [42, 43]), the production of W bosons in the linear and resonance regions is: weak coupling constant. Making the corresponding changes for the production of Higgs, we have: d(nha3) dt 8 > > = < 2P3 !K23a3; (linear); > >: 2a3!Qnh: (resonance): K1 = K2 = " " g2MP2 l r K1 and K2 have dimensions of energy and are dependent on the respective mass terms with: where ti are instants when the in aton A = 0. In aton can decay into W and Higgs bosons only in the vicinity of A = 0 when the e ective masses of these bosons are much less than the in aton e ective mass !. W bosons decay into fermions with a decay rate given by: while their annihilation cross section is given by: W W g4 2Nl + 2NqNc 16 8 hm2W i 10 g 4 16 2hm2W i : W = 4g2 is the (4.13) (4.14) (4.15) (4.16) (4.17) Parametric resonance production of W bosons can start only when their decay rate in eq. (4.16) falls below their production rate through parametric resonance in eq. (4.12). Comparing them, we nd that resonance production of W bosons can start only when A0 < 2 0:5625 Production of relativistic particles through decay of W takes place very slowly and would reheat the universe long after the resonance period would have ended [40] while production of relativistic particles through annihilation is a much faster process and can yield enough relativistic particles to reheat the universe. Annihilation can occur only when the number density of W bosons is large. This makes the occurrence of parametric resonance necessary allowing us to put a lower bound on 2 When W is produced through resonance, its number density increases exponentially and the dominant channel for production of fermions is by annihilations of W bosons following eq. (4.17). We need to check these conditions for fermion production via Higgs as well. The decay rate of Higgs into fermions is given by the Yukawa couplings: In eq. (4.20), only the coupling to top is important as it is large while the coupling for other fermions is very small. The top quark can later decay or annihilate into other fermions. Comparing eq. (4.20) to resonance production rate of Higgs in eq. (4.13), we nd that Higgs production enters the resonance regime only after: A0 < Comparing eq. (4.21)2 to eq. (4.18), we see that if 3 . 0:006, Higgs production will enter the resonance regime around the same time as W boson. For even a small amount of resonance production in Higgs to occur, 3 cannot be greater than 0:41 2 . Since the inert doublet is a dark matter candidate with large couplings, Higgs production will not enter resonance regime till long after the end of the quadratic phase of the potential. The production rate of Higgs remains small and its decay to fermions is at a much lower rate than the annihilation of gauge bosons. During parametric resonance production of gauge bosons, almost all the W bosons get converted to fermions giving a complete transfer of energy density from W bosons to relativisitc fermions which can be obtained by solving the following equation [40] d( a4) dt = 2a4q hm2W i 4Q2!2 W W ; (4.22) 2The eq. (4.21) contains only 3 in the denominator instead of full 3 + 4=2 because of our choice of large 3. The fact that Higgs won't be produced via resonance stands even if 4 is used. 2 & 1 60 h = y 2 16 hmhi: which after integration gives = 10 where tp is the time when the parametric resonance starts given by the condition in eq. (4.18) and tcr is the end of reheating. During this conversion, almost all the W bosons get converted to fermions so that the only remaining particles by the time reheating ends are the fermions apart from the inert doublet particles. Putting in the numbers, we get: At this time, energy density in A is: (4.24) In the non-relativistic limit where vrel 1, we can re-write eq. (5.1) as jCM vrel = 1 We can now obtain the reheating temperature from the energy density in relativistic particles: 5 Dark matter where g is the number of degrees of freedom in the relativistic plasma. The end of reheating marks the end of the quadratic oscillations phase of the re-arranged eld A. Since now, A is the same as (q2 + x2)1=2 and the Jordan and Einstein frames have become equivalent, we can come back to using the physical Jordan frame. The in aton eld no longer has an e ective mass !. Rather things go back to the original inert doublet potential given in eq. (2.2) with the inert doublet having a mass of m2. In the beginning, the inert doublet obtains a thermal equilibrium with the rest of the relativistic plasma and evolves as radiation. Later, as the temperatures fall and the inert doublet becomes non-relativistic, its evolution is given by the Boltzmann equation. It freezes-out as a cold relic and thus becomes a candidate for cold dark matter. We will use the observed relic abundance of dark matter dm h2 = 0:12 [12] to calculate certain parameters in the model. The interactions of the neutral scalar part of the inert doublet are its annihilations into the vector bosons and Higgs. There are no decays of any of the inert doublet components as they are prevented by the Z2 symmetry. At the tree level, there are 4-point interactions (see gure 5). The scattering cross-section for these processes is: jCM vrel = 32 m22 (1 + vr2el=4) processes X jMj2: The amplitude Pprocesses jMj2 for the neutral scalar component of actual dark matter candidate is: where g and g0 are the weak couplings to the vector bosons. Apart from these 4-point interactions, there are trilinear couplings as well which include the annihilation of a pair of inert doublet particles via the gauge boson or the Higgs channel into SM particles as shown in gure 6. The gauge boson mediated diagrams are momentum dependent. Their contribution is small compared to the one shown in gure 5. Most of the thermal equilibrium evolution of the dark matter particles occur above the EW symmetry breaking scale where the Higgs mediated diagram of gure 6 are not present. To calculate the freeze-out temperature and the relic abundance, we need to solve the Boltzmann equation. Assuming only s-wave annihilations, one can obtain the xf = mTf2 3 3We use m2 as the mass of the neutral scalar component of 2 because there are no mass corrections which occur only after EW symmetry breaking. 0.2 0.1 2h 0.15 ) Ω ( e c n a d n u b a c i l e R 0.05 0 0 λ3=1 λ3=0.9 λ3=0.8 λ3=0.7 λ3=0.6 λ3=0.5 g g1s=2 g dmh2 to ; (5.4) (5.5) (5.6) (5.7) HJEP1(207)8 500 1000 1500 2000 2500 Mass of dark matter (m) Tf = xf m2 = 1:89 TeV; m2 = 65:7 GeV: This calculation has been done using a xed set of values for 3 , 4 and 5 with 3 1 and 4; 5 1. In principle, 3 can vary between 0:5 to 1 while still keeping 4 and 5 very small. The e ect of varying 3 on the mass of the dark matter candidate is shown in gure 7 where the solid horizontal line shows the value of the relic abundance obtained from Planck 2015 [12] and is equal to 0.12. Note that m2 is the dark matter mass till EW symmetry breaks which occurs around the same time as freeze-out. After the symmetry black band is the Planck 2015 result. at freeze-out where Tf is the freeze-out temperature, and the relic abundance where mP is the Planck mass (not the reduced Planck mass which we have denoted as MP l), g and g are the number of degrees of freedom in the plasma and the entropic number of degrees of freedom respectively and h vi is taken from eq. (5.2). Planck 2015 data for the relic abundance can now be used to get estimates for the mass of the dark matter and its freeze-out temperature. We obtain: 1 0.9 breaks, dark matter mass will get a small correction of order 100 GeV. The table 1 gives the values of dark matter mass satisfying the relic abundance constraint for various values of 3 . The corresponding freeze-out temperatures are a little below the EW symmetry breaking scale suggesting that we include the Higgs mediated diagrams in gure 6 in the calculations. However, their contribution to the calculations are very small and any changes that they bring about in dark matter masses are beyond the second decimal place. 6 Conclusion Explaining in ation and dark matter remain two challenges for any theory beyond the standard model of particle physics. The inert doublet model has been studied extensively in the literature in the context of generating neutrino masses and mixing as well as dark matter. The doublet is called inert because of a Z2 charge assignment which forbids all Yukawa couplings of this doublet with the standard model fermions. This is done to avoid all undesirable avor violations in the model. In this work we showed that the inert doublet coupled non-minimally to gravity could act both as the in aton driving slow-roll in ation as well as the cold dark matter of the universe. We obtained a Starobinsky like potential from the model and showed that both slow-roll parameters ; 1. We calculated the scalar power spectrum, the tensor to scalar ratio and the spectral index in our model and showed them to be well within the observed limits from Planck. After successfully reheating the universe, the inert doublet attains thermal equilibrium and eventually freezes-out as a cold dark matter. We obtained bounds on the couplings of the scalar potential from reheating and dark matter constraints and showed that the Planck bound on relic abundance can be satis ed for neutral scalar component mass of the inert doublet of around 1.3 to 2 TeV. Acknowledgments The authors would like to thank the Department of Atomic Energy (DAE) Neutrino Project under the XII plan of Harish-Chandra Research Institute. This project has received funding from the European Union's Horizon 2020 research and innovation programme InvisiblesPlus RISE under the Marie Sklodowska-Curie grant agreement No 690575. This project has received funding from the European Union's Horizon 2020 research and innovation programme Elusives ITN under the Marie Sklodowska- Curie grant agreement No 674896. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. [1] A.H. Guth, The in ationary universe: a possible solution to the horizon and atness problems, Phys. Rev. D 23 (1981) 347 [INSPIRE]. HJEP1(207)8 Astron. Astrophys. 594 (2016) A20 [arXiv:1502.02114] [INSPIRE]. 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Sandhya Choubey, Abhass Kumar. Inflation and dark matter in the inert doublet model, Journal of High Energy Physics, 2017, 80, DOI: 10.1007/JHEP11(2017)080