Fuzzy Dark Matter candidates from string theory

Published for SISSA by Springer Received: November Revised: March Accepted: April Published: May 29, 28, 22, 17, 2021 2022 2022 2022 Michele Cicoli,a,b Veronica Guidetti,c Nicole Righic and Alexander Westphalc a Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, Bologna 40126, Italy b INFN, Sezione di Bologna, viale Berti Pichat 6/2, Bologna 40127, Italy c Deutches Electronen-Synchrotron, DESY, Notkestraße 85, Hamburg 22607, Germany E-mail: , , , Abstract: String theory has been claimed to give rise to natural fuzzy dark matter candidates in the form of ultralight axions. In this paper we revisit this claim by a detailed study of how moduli stabilisation affects the masses and decay constants of different axion fields which arise in type IIB flux compactifications. We find that obtaining a considerable contribution to the observed dark matter abundance without tuning the axion initial misalignment angle is not a generic feature of 4D string models since it requires a mild violation of the Sf . MP bound, where S is the instanton action and f the axion decay constant. Our analysis singles out C4 -axions, C2 -axions and thraxions as the best candidates to realise fuzzy dark matter in string theory. For all these ultralight axions we provide predictions which can be confronted with present and forthcoming observations. Keywords: Compactification and String Models, Cosmology of Theories beyond the SM, Superstring Vacua ArXiv ePrint: 2110.02964 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP05(2022)107 JHEP05(2022)107 Fuzzy Dark Matter candidates from string theory Contents 1 Introduction 1 2 String origin of ultralight axionic DM candidates 2.1 Closed string axions 2.2 Open string axions 4 6 9 10 11 20 27 4 Overall predictions and comparison with experimental constraints 30 5 Conclusions 34 A Closed string axions: Sf computations A.1 C0 axion A.2 B2 axion A.3 C2 axion A.4 C4 axions 36 36 37 38 38 B Open string axions calculations 39 C Additional corrections for C4 axions C.1 Non-vanishing 2-form fluxes C.2 Ample divisors C.3 Poly-instantons 41 41 42 43 D Anharmonicity and isocurvature bounds 44 1 Introduction Despite long model building efforts, the origin and nature of dark matter remains one of the biggest puzzles in Physics and astronomy. In recent years, Cold Dark Matter (CDM) has been pointed out as the best class of models that is able to reproduce large scale structure formation of the universe. In these models, dark matter is made out of weakly interacting non-relativistic particles with a small initial velocity dispersion relation inherited from interactions in the early universe that do not erase structures on galactic and sub-galactic scales. Among the various models, the combination of cosmic acceleration measurement –1– JHEP05(2022)107 3 FDM from closed string axions 3.1 LVS: FDM from C4 axions 3.2 LVS: FDM from C2 axions 3.3 FDM from thraxions: KKLT & LVS? –2– JHEP05(2022)107 and the CMB evidence for a flat universe led to the choice of ΛCDM model which is nowadays considered as the ‘Standard Model’ of cosmology. Despite its success in explaining the large scale structure of the universe, ΛCDM was believed to suffer from some problems related to galaxy formation [1] that may be actually explained with unaccounted baryonic feedback mechanisms or to new exotic dark matter physics on small scales [2–6] but a final and exhaustive solution is still lacking. Regardless of the veracity of small-scale problems, Weakly Interacting Massive Particles (WIMPs) having mass ∼ O(100) GeV that were considered the most promising CDM candidates have continuously eluded whatever kind of experimental measurement as collider searches and direct/indirect detection experiments. These concerns about ΛCDM and WIMPs led to the study of alternative DM models. Among those, in recent years the idea of bosonic ultralight CDM, also called Fuzzy Dark Matter (FDM), has been proposed [7–10]. In one of its prominent versions, DM is made of ultralight axion-like particles that form halos as Bose-Einstein condensates. In this theory each axionic particle can develop structures on the scale of de Broglie wavelength thanks to gravitational interactions. This is an ensemble effect which is given by the mean properties of every single axion field. A prominent soliton, i.e. a state where self-gravity is balanced by the effective pressure arising from the uncertainty principle, develops at the centre of every bound halo. The soliton properties depend on the axion mass but usually its extension is assumed to be much smaller than the galaxy or galaxy cluster size. In the original proposal, an axion having mass around 10−22 eV and decay constant f ∼ 1016÷17 GeV was pointed out as the best candidate to represent the dominant part of CDM in the universe since the wave nature of such a particle can suppress kpc scale cusps in DM halos and reduce the abundance of low mass halos [8, 9, 11]. Recent studies put severe constraints on the vanilla FDM model without self-interφ2 actions where the usual cosine axionic potential is approximated as 1 − cos(φ/f ) ∼ 2f 2. Various analyses of Lyman-α forest, satellite galaxies formation, dwarf galaxies, the Milky Way core and Black Hole superradiance [12–19] leave as the only viable mass windows mφ ∼ 10−24 eV and mφ ∼ 10−15 eV, although certain of these bounds could be relaxed and open a window near 10−21 eV also. These experimental bounds imply that FDM cannot solve the alleged small-scale problems affecting ΛCDM as the Jeans mass (representing the lower bound on DM halos mass production) rapidly decreases at increasing ultralight boson masses [17]. Nevertheless, even in this case, these problems can be solved by baryonic physics and a better understanding of galaxy formations may allow us to discriminate between standard CDM and FDM models. Indeed, it was proven that small-mass halos suppression in the FDM model causes a delay in the onset of Cosmic Dawn and the Epoch of Reionization. Future experiments, such as the HERA survey, will measure the neutral hydrogen (HI) 21 cm line power spectrum at high statistical significance across a broad range of redshifts [14, 17] and their findings may be able to discriminate between standard WIMP and FDM scenarios. Since experimental bounds and simulations strongly constrain the original FDM model with negligible self-interaction, many extensions of it have been studied. It was shown that for large initial misalignment angles ALPs self-interactions can affect the baryonic structure and accelerate star formation in the early universe or induce oscillon formation that can give rise to detectable low frequency stochastic gravitational –3– JHEP05(2022)107 waves [20]. Other authors suggest that FDM may not represent the entirety of DM [21] or that FDM may not be given by a single component, being made out of multiple ultralight ALPs [ (...truncated)