Constraining the quintessential $\alpha$-attractor inflation through dynamical horizon exit method

Abstract

In the present paper, we perform a sub-Planckian quantum mode analysis of linear cosmological perturbation in the inflaton field over a classical quasi de-Siter metric background by dynamical horizon exit (DHE) method. In this way, we probe the inflationary regime of a quintessential $\alpha$-attractor model by analysing the COBE/Planck normalized power spectra, spectral indices, tensor to scalar ratio, number of e-folds, running of the spectral index and inflationary Hubble parameter in $k$-space. We compare our results with ordinary $\alpha$-attractor $E$ and $T$ models and with that of Planck-2018 results. Our estimated values of $n_s$ and $r$ lie within $68\%$ CL with respect to Planck data for $k=0.001-0.009$ Mpc${}^{-1}$ for all values of $\alpha$. The $\alpha$ values, obtained in our calculations satisfy various post inflationary constraints regarding preheating and reheating, reported in current literature. We observe that quintessence sets an upper bound of $\alpha =4.3$ and thereby restricts the model from becoming of the power law type, making it more efficacious than ordinary $\alpha$-attractors in explaining both inflation and dark energy. A striking observation in our analyses is that, unlike in our previous study, we find a continuous values of $\alpha$ within $\frac{1}{10}\le \alpha \le 4.3$ for the specified $k$ range. At the end, we have shown that the model parameters constrained in this work give a very small vacuum density $\sim 10^{-117}-10^{-115}{M}_P^4$ which is an essential criterion for current and future dark energy observations of the universe.

46 pages, 20 figures, 2 tables

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