Holographic inflation and slow-roll inflation within R\'enyi entropic framework in the light of ACT DR6

TL;DR

This paper investigates holographic and slow-roll inflation models within the Rényi entropic framework, finding that ACT DR6 data disfavor holographic inflation but support certain slow-roll inflation scenarios.

Contribution

It demonstrates the viability of slow-roll inflation with power-law potentials in the Rényi entropic framework, contrasting with the exclusion of holographic inflation by observational data.

Findings

Holographic inflation is ruled out by ACT DR6 data.

Slow-roll inflation with $V_{0}\phi^{n}$ for n=0.2, 0.3 is favored by ACT DR6.

The Rényi entropic framework supports slow-roll inflation models.

Abstract

Based on the R\'enyi entropy, R\'enyi holographic dark energy has been proposed to explain the current accelerated expansion of the universe. In this paper, we analyze holographic inflation and slow-roll inflation within the framework of RHDE. Our results show that holographic inflation is ruled out by ACT DR6, while the slow-roll inflation with the power-law potential $V_{0}\phi^{n}$ is favored by ACT DR6 for the cases $n=0.2$ and $0.3$, with $N$ in the range of $50$ to $55$. These findings suggest that RHDE provides a viable framework for slow-roll inflation while disfavoring the holographic inflation scenario.