Abstract
In cosmological framework, Noether symmetry technique has revealed a useful tool in order to examine exact solutions. In this work, we first introduce the Jordan-frame Lagrangian and apply the conformal transformation in order to obtain the Lagrangian equivalent to Einstein-frame form. We then analyze the dynamics of the field in the cosmological alpha-attractors using the Noether symmetry approach by focusing on the single field scenario in the Einstein-frame form. We show that with a Noether symmetry the corresponding dynamical system can be completely integrated and the potential exhibited by the symmetry can be exactly obtained. With the proper choice of parameters, the behavior of the scale factor displays an exponential (de Sitter) behavior at the present epoch. Moreover, we discover that the Hubble parameters strongly depends on the initial values of parameters exhibited by the Noether symmetry. Interestingly, it can retardedly evolve and becomes a constant in the present epoch in all cases.
Highlights
In modern cosmology, the mechanism of cosmic inflation seems conceivable
We first introduce the Jordan-frame Lagrangian and apply the conformal transformation in order to obtain the Lagrangian equivalent to Einstein-frame form
Notice that the Hubble parameters strongly depends on the initail values of F0, u0, A and Σ0 exhibited by the Noether symmetry
Summary
The mechanism of cosmic inflation seems conceivable. Inflation marks nowadays an inevitable ingredient when studying very early evolution of the universe. The reason stems from the fact that it solves most of the puzzles that plague the standard Big Bang theory, and simultaneously is consistent with recent observational data In other words, it gives sensible explanations for the horizon, flatness, and relic abundant problems, and provides us primordial density perturbation as seeds of the formation for a large-scale structure in the universe. Recent observational data much flavors large field inflationary models with plateau-like inflaton potentials. A model with plateau potentials was proposed by the authors of Refs.[1, 2] It describes a potential which is exponentially approaching a positive constant for super-Planckian values of the inflaton field. The cosmological α-attractors incorporate most of the existing inflationary models with plateau-like potentials including the Starobinsky model and some generalized versions of the Higgs inflation.
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