Noether symmetry approach in the cosmological alpha-attractors

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 analyse the dynamics of the field in the cosmological alpha-attractors using the Noether sysmetry approach by focusing on the single field scenario in the Einstein-frame form. We show that with a Noether symmetry the coresponding 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.

v2: 8 pages, 5 figures, texts modified reflecting comments from the referees, version accepted by Nucl.Phys.B

References in corpus (13)

• The Standard Model Higgs boson as the inflaton
• The Unity of Cosmological Attractors
• Cosmology with Nilpotent Superfields
• The Minimal Volkov - Akulov - Starobinsky Supergravity
• Planck, LHC, and $\alpha$-attractors
• On sgoldstino-less supergravity models of inflation
• Inflation and Uplifting with Nilpotent Superfields
• Does the first chaotic inflation model in supergravity provide the best fit to the Planck data?
• Scalar-Tensor Gravity Cosmology: Noether symmetries and analytical solutions
• Inflation in no-scale supergravity
• Minimal Composite Inflation
• Nonminimal coupling and inflationary attractors
• O'Hanlon actions by Noether symmetry

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