Constraining the quintessential <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e2043" altimg="si18.svg"><mml:mi mathvariant="bold-italic">α</mml:mi></mml:math>-attractor inflation through dynamical horizon exit method

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