Tsallis holographic dark energy for inflation

TL;DR

This paper explores a modified holographic inflation model using Tsallis entropy, deriving analytical solutions and comparing predictions with Planck data to constrain model parameters.

Contribution

It introduces a Tsallis entropy-based holographic inflation model, providing analytical solutions and connecting it with scalar field potentials.

Findings

Derived slow-roll parameters and spectral indices.

Identified parameter space consistent with Planck data.

Established correspondence between holographic energy and scalar fields.

Abstract

The application of holographic principle in very early time is studied. The consideration of the principle in the late-time evolution will be a good motivation to study its role at the time of inflation. Since the length scale is expected to be small during inflation, the resulted energy density form the holographic principle is expected to be large enough to drive inflation. The entropy of the system is the main part of the holographic principle, in which modifying entropy will leads to a modified energy density. Here, instead of the original entropy, we are going to apply a modified entropy, known as Tsallis entropy which includes quantum corrections. The length scale is assumed to be GO length scale. Finding an analytical solution for the model, the slow-roll parameters, scalar spectral index, and tensor-to-scalar ratio are calculated. Comparing the result, with Planck $r-n_s$ diagram, we could find a parametric space for the constants of the model. Then, a correspondence between the holographic dark energy and the scalar field is constructed, and the outcome potentials are investigated.