CMB observables and reheat temperature as a window to models of inflation and freeze-in dark matter production

TL;DR

This work introduces a systematic approach to using CMB observables $n_s$, $A_s$, and $r$ to discriminate between inflationary models while treating reheating as a bridge to particle-physics scenarios such as freeze-in dark matter (DM). By expressing the independent parameters of α-attractor potentials (E-, T-, P-models) in terms of the CMB quantities, and enforcing a standard reheating description with EOS $w$ and dissipation rate $Γ$, the reheating temperature $T_{re}$ is uniquely fixed, enabling sharp, model-dependent predictions for $n_s(k_*)$ and consistency tests with current and future data. The framework is applied to UV-freeze-in DM production, showing how $T_{re}$ acts as a portal to constrain DM parameters $(\Lambda_{DM}, m_{DM})$ via the DM relic abundance and EFT validity, with detailed results for prototype operators of dimensions $d=1,2,6,10$ and a Higgs-portal example. The analysis indicates that ACT data can yield stronger discrimination among the considered models than Planck alone, and that improved CMB accuracy will tighten the allowed DM parameter space by further constraining $T_{re}$; extensions to hidden sectors, non-perturbative reheating, and gravitational-wave probes offer promising future directions.

Abstract

A systematic approach is presented for using CMB observables and reheating temperature for discriminating between various models of inflation and certain freeze-in dark matter scenarios. It is applied to several classes of $α$-attractor models as an illustrative example. In the first step, all independent parameters of the inflationary potential are expressed in terms of the CMB observables (the three parameters - by the scalar spectral index $n_s$, scalar amplitude $A_s$ and the tensor-to-scalar amplitude ratio $r$). For a standard reheating mechanism characterized by the inflaton equation of state parameter $w$ and its effective dissipation rate $Γ$ the reheating temperature is uniquely fixed in terms of the CMB observables measured for some pivot scale $k_*$. There are striking consequences of this fact. The model independent bounds on the reheating temperature, the BBN lower bound and the upper bound of the order of the GUT/Planck scale, translate themselves for each class of models into very narrow ranges of the allowed values of the spectral index $n_s(k_*)$, providing their strong tests by the present and future CMB data. The recent tension between Planck and DESI-ACT results has strong impact on our conclusions. Furthermore, given a class of inflaton models satisfying those tests, the reheating temperature is an interesting portal to link the CMB observables to the particle physics scenarios that are sensitive to it. As an example, non-thermal dark matter (DM) production mechanisms are discussed. One obtains then a consistency check between theories of inflation and DM production. If the future precision of the CMB data will constrain the reheating temperature beyond the model independent bounds, further constraints on the DM production will follow.

Figures (12)

• Figure 1: A schematic evolution of comoving Hubble radius $aH$ as a function of the scale factor $a$. The blue line is for $r(k_*)=0.04$ and $w =0$; the green line is for $r(k_*)=10^{-6}$ and $w =1/2$; the red line is for $r(k_*)=10^{-10}$ and $w =0$; the obtained reheating temperatures are 10 GeV, $10^6$ GeV and $10^{12}$ GeV, respectively. The horizontal dotted line corresponds to the comoving wavenumber value $k_*=a_0\times 0.05\,$Mpc$^{-1}$.
• Figure 2: Correlation between $n_s$ and $r$ for three $\alpha$-attractor models (E, T, and P) and two values of the exponent $n$ (1 and 10). Colorful curves correspond to fixed values of the reheat temperature $T_\times$, while black curves represent fixed values of the number of e-folds $N_k$.
• Figure 3: Correlation between $n_s$ and $r$ as a function of the reheat temperature $T_\times$ in the case of E-model for several values of the exponent $n$. Results for $n=2$ do not depend on $T_\times$ and are represented by the black curve. The experimental $1\sigma$ and $2\sigma$ allowed regions from Planck, BK15 and BAOPlanck:2018vygBICEP2:2018kqh are shown. Future sensitivity reaches of LiteBIRD, CMB-S4, and SOLiteBIRD:2022cntCMB-S4:2016pleSimonsObservatory:2018koc experiments are also indicated.
• Figure 4: Correlation between $n_s$ and $r$ as a function of the reheat temperature $T_\times$ in the case of E-model for several values of the exponent $n$. Results for $n=2$ do not depend on $T_\times$ and are represented by the black curve. The experimental $1\sigma$ and $2\sigma$ allowed regions from Planck, BK15 and BAOPlanck:2018vygBICEP2:2018kqh are shown. Future sensitivity reaches of LiteBIRD, CMB-S4, and SOLiteBIRD:2022cntCMB-S4:2016pleSimonsObservatory:2018koc experiments are also indicated.
• Figure 5: Correlation between scalar spectral index $n_s$ and its running $\alpha_s$, following from eq. \ref{['eq:alphaS_n_r_ns']}, in the case of E- and P-model for two values of the exponent $n=1,10$ for fixed reheat tempearature $T_\times$ (color coding as in figures \ref{['fig:ns-r_Tx-Nk']}-\ref{['fig:nsrPlotTPmodels']}). As the curves in different colours partially overlap, the end of some of them is denoted by the dot of the same clour. The absence of a dot in a given color means that the corresponding curve ends outside the plot.