Holographic inflation and slow-roll inflation within Rényi entropic framework in the light of ACT DR6

Abstract

Based on the Rényi entropy, Rényi 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 Rényi holographic dark energy (RHDE) using ACT DR6. Our results show that holographic inflation is ruled out by the data, while slow-roll inflation with power-law potentials for $n=\frac{1}{2}$ and $n=\frac{1}{3}$ is viable for a suitable choice of $N$ and $C$. We also analyze the inflationary attractor and confirm its existence. In addition, we compute the primordial power spectrum and find it falls well within the observational bounds. Thus, slow-roll inflation is favored in RHDE, but holographic inflation is not.