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

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 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.