Reheating constraints and the $H_0$ tension in Quintessential Inflation

In this work, we focus on two important aspects of modern cosmology: reheating and Hubble constant tension within the framework of a unified model, namely, quintessential inflation connecting the early inflationary era and late-time cosmic acceleration. In the context of reheating, we use instant preheating and gravitational reheating, two viable reheating mechanisms when the evolution of the universe is not affected by an oscillating regime. After obtaining the reheating temperature, we analyze the number of $e$-folds and establish its relationship with the reheating temperature. This allows us to connect, for different quintessential inflation models, the reheating temperature with the spectral index of scalar perturbations, thereby enabling us to constrain its values. In the second part of this article, we explore various alternatives to address the $H_0$ tension, a discrepancy which indicates a possible revision of the $\Lambda$CDM model. Initially, we establish that quintessential inflation alone cannot mitigate the Hubble tension by solely deviating from the concordance model at low redshifts. The introduction of a phantom fluid, capable of increasing the Hubble rate at the present time, becomes a crucial element in alleviating the Hubble tension, resulting in a deviation from the $\Lambda$CDM model only at low redshifts. On a different note, by utilizing quintessential inflation as a source of early dark energy, thereby diminishing the physical size of the sound horizon close to the baryon-photon decoupling redshift, we observe a reduction in the Hubble tension. This alternative avenue, which has the same effect of a cosmological constant changing its scale close to the recombination, sheds light on the nuanced interplay between the quintessential inflation and the Hubble tension, offering a distinct perspective on addressing this cosmological challenge.