Eur. Phys. J. Plus (2024) 139: 302
https://doi.org/10.1140/epjp/s13360-024-05092-4

Regular Article

Inflationary models constrained by reheating

Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Av. Universidad s/n, 62210, Cuernavaca, MOR, Mexico

^a gabriel@icf.unam.mx

Received: 18 November 2023
Accepted: 14 March 2024
Published online: 31 March 2024

Abstract

The study of reheating in inflationary models is crucial to understand the early universe and obtain information about the dynamics and parameters of inflation. The reheating temperature $T_{\mathit{re}}$ and the duration of the reheating phase, quantified by the number of e-folds $N_{\mathit{re}}$, have significant implications for particle production, thermalisation, and the primordial power spectrum. The duration of reheating affects the abundance of particles, including dark matter, and shapes the primordial power spectrum and the anisotropies of the cosmic microwave background. By combining cosmological observations and theoretical considerations, we can constrain both $T_{\mathit{re}}$ and $N_{\mathit{re}}$, which in turn restrict the spectral index $n_s$, the tensor-to-scalar ratio r, and the parameters of the inflationary model. The use of consistency relations between observables, such as $n_s$ and r, provides additional constraints on inflationary models and determines limits for other observables, such as the running of the scalar spectral index. These limits are valuable for assessing the viability of models and can serve to specify priors in Bayesian analyses of specific models. As an example of how to proceed, we study in detail a particular case of a generalized $\alpha$-attractor model that accurately reproduces the observed quantities. We present equations for the conditions of instantaneous reheating, establish consistency relations, and explore the generalized $\alpha$-attractor model using cosmological data. We study the model defined by its potential as a given formula and, furthermore, considering its possible origin in supergravity theories, we impose constraints on the reheating temperature to avoid the overproduction of gravitinos.