Inflationary models constrained by reheating

The study of reheating in inflationary models is crucial for understanding the early universe and gaining insights into inflationary dynamics and parameters. The reheating temperature $T_{re}$ and the duration of the reheating phase, quantified by the number of $e$-folds $N_{re}$, have significant implications for particle production, thermalization, and the primordial power spectrum. The duration of reheating affects particle abundance, including dark matter, and shapes the primordial power spectrum and cosmic microwave background anisotropies. By combining cosmological observations and theoretical considerations, we can constrain both $T_{re}$ and $N_{re}$, which in turn constrain the spectral index $n_s$, tensor-to-scalar ratio $r$, and inflation model parameters. Utilizing consistency relations among observables, such as $n_s$ and $r$, provides additional constraints on inflationary models and determines bounds for other observables like the running of the scalar spectral index. These bounds 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 observed quantities. We present equations for the conditions of instantaneous reheating, establish consistency relations, and explore the generalized $\alpha$-attractor model using cosmological data.