The dark universe after reheating in string inflation

Published for SISSA by Springer Received: August 16, 2022 Revised: November 20, 2022 Accepted: November 30, 2022 Published: December 13, 2022 Michele Cicoli,a,b Kuver Sinhac and Robert Wiley Dealc a Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, 40126 Bologna, Italy b INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy c Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, U.S.A. E-mail: , , Abstract: We study the production of dark matter and dark radiation after reheating in string inflation models where the Calabi-Yau has a fibred structure and the visible sector lives on D3 branes. We show how the interplay between different physical constraints from inflation, reheating, supersymmetry breaking and dark radiation, leads to distinct predictions for the nature of dark matter. In particular, in Fibre Inflation dark matter can only be primordial black holes or an open string QCD axion with an intermediate scale decay constant since WIMPs are always too heavy and ultralight closed string axions cannot behave as fuzzy dark matter due to strong isocurvature bounds. On the other hand, Kähler moduli inflation can allow for non-thermal WIMP dark matter at the TeV-scale. Keywords: Axions and ALPs, Models for Dark Matter, String Models, Supergravity Models ArXiv ePrint: 2208.01017 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP12(2022)068 JHEP12(2022)068 The dark universe after reheating in string inflation Contents 1 2 Non-thermal dark matter 3 3 Fibred Calabi-Yau models 4 4 Moduli decays and dark radiation 4.1 Canonical normalization 4.2 Decays to closed string axions 4.3 Decays to open string axions 4.4 Decays to Higgses 4.5 Dark radiation predictions 6 6 8 8 11 13 5 String inflation and dark matter 5.1 Kähler moduli inflation 5.2 Fibre inflation 16 16 21 6 Conclusions 23 1 Introduction Recent advances in string phenomenology in type IIB compactifications have progressed in two complementary directions: (i) Constructing specific compactifications that are phenomenologically promising: typically, these constructions incorporate moduli stabilization, have chiral matter, are broadly able to accommodate the gauge groups and matter content of the Minimal Supersymmetric Standard Model (MSSM) [1–6], and have at least a somewhat welldefined inflationary and reheating sector [7–9]; (ii) Proceeding along statistical lines, by drawing statistical conclusions about the distribution of important phenomenological quantities like the scale of supersymmetry breaking and the axion decay constant, from the ensemble of type IIB flux vacua [10– 17]. Amongst various classes of models in the first direction, type IIB Large Volume flux compactifications are particularly well-developed. Two main inflationary scenarios emerge in this context: Kähler moduli inflation (KMI) [18, 19] and Fibre Inflation (FI) [20– 22]. KMI is a small-field model where inflation is driven by a blow-up mode with a non-perturbative scalar potential. The Hubble scale during inflation is relatively low, –1– JHEP12(2022)068 1 Introduction –2– JHEP12(2022)068 HI ∼ 5 × 108 GeV, and the tensor-to-scalar ratio is unobservable r ' 10−10 . On the other hand, FI is a large field model characterized by HI ' 5 × 1013 GeV and r ' 0.007 [23], where the inflaton is a fibration bulk modulus with a perturbative scalar potential. In these constructions the visible sector can live on either D7-branes wrapping 4-cycles in the geometric regime, or D3-branes at singularities. In the first case, the soft terms are around the gravitino mass, M1/2 ∼ m0 ∼ m3/2 , while in the second case the visible sector can be sequestered from the sources of supersymmetry breaking in the bulk, resulting in soft terms which can be hierarchically smaller than the gravitino mass [24, 25]. Two limits can arise: a so-called local limit with a split-SUSY spectrum featuring M1/2  m0  m3/2 , and an ultralocal limit with a more standard MSSM-like spectrum with M1/2 ∼ m0  m3/2 . Reheating via the decay of the modulus with the smallest decay width has already been studied in both KMI and FI for several D-brane configurations which can realize an MSSM-like sector together with additional hidden sectors. In particular, reheating for KMI in the simplest Swiss-cheese LVS models has been studied in [26–28] for D3-branes in the ultralocal limit, in [29] for D3-branes in the local limit, and in [30, 31] for D7-branes. On the other hand, reheating for FI with the MSSM on D3-branes has been studied in [32], and in [33] for the D7-brane case. Each of these references analyzed in detail the constraints arising from the requirement to avoid an excessive production of ultra-light bulk axions that behave as dark radiation. Moreover [34–37] studied the implications for non-thermal neutralino dark matter for KMI with the MSSM on D3-branes in the ultralocal limit. The constraints on the nature of dark matter for KMI with the visible sector on D7-branes has instead been analyzed in [38] for superheavy WIMPs and in [39] for the QCD axion realized as a closed string mode. The largest production of dark radiation from the decay of the lightest modulus has been found in [32] for FI with the MSSM on D3-branes. This result relies on a particular expression of the moduli-dependence of the Giudice-Masiero contribution to the Kähler potential which determines an effective decoupling of the lightest modulus from the Higgs degrees of freedom. In this paper we will revisit this result by considering a more general moduli-dependence of the Giudice-Masiero term that allows to considerably reduce the production of dark radiation. In doing so, we shall follow the results of [40] which constrained the form of the Kähler potential by analogy with explicit toroidal computations. We will then study the associated production of dark matter after reheating in FI. We will find that WIMPs are always overproduced, requiring a mechanism of R-parity breaking to make them unstable. In this case, a very promising dark matter candidate is instead the QCD axion realized as the phase of a charged open string field. The axion decay constant is around fQCD ' 5 × 1010 GeV, which can avoid isocurvature bounds and lead to dark matter in a rather natural way. We will extend our analysis also to fibred Calabi-Yau compactifications with KMI and the MSSM on D3-branes. The best case scenario to avoid dark radiation overproduction with the minimal tuning of the coefficient of the GiudiceMasiero interaction among the moduli and the Higges, is the ultralocal limit. In this case, we will find that dark matter can be TeV-scale non-thermal neutralinos which are produced from the inflaton decay and then undergo annihilation. 2 Non-thermal dark matter Before focusing on string models, we first briefly review non-thermal dark matter (DM) produced by heavy scalar decay [41, 42]. The lightest mo (...truncated)