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arXiv · 2401.15451

Constant-roll inflation and primordial black holes within Barrow entropic framework

Qihong Huang·Li-Yang Chen·He Huang·Bing Xu·Kaituo Zhang
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Abstract

In this paper, starting from the modified Einstein field equations, we derive the modified scalar spectral index $n_{s}$ and the modified tensor-to-scalar ratio $r$ in Barrow entropy model, calculate their values for the power-law, periodic, and hilltop potential models, constrain the model parameter $\delta$ and the potential parameter using Planck 2018 data, and find that increasing $\delta$ causes a significant decrease in $r$. Then, we calculate the primordial curvature perturbation power spectra, primordial black hole (PBH) abundance, and scalar induced gravitational waves (SIGWs) for these models, finding PBH mass of approximately $10^{-12} M_{\odot}$, PBH abundance nearly $0.98$, and the peak frequencies of SIGWs on the order $10^{-3} \mathrm{Hz}$, indicating that these models not only generate sufficient PBHs which can contribute one-third of the dark matter content but could also be detected by next-generation missions such as LISA, Taiji, and TianQin. Subsequently, we analyze the evolution of PBHs and find that when the effective equation of state parameter evolves from $1/3$ to $-1/3$, the accretion mass increases to approximately $10^{2}M_{i}$, while the temperature of the PBHs decreases from $10^{4}K$ to $10^{2}K$, suggesting that PBHs exist and are detectable today.

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Qihong Huang, Li-Yang Chen, He Huang, Bing Xu, Kaituo Zhang. 2024-01-27. Constant-roll inflation and primordial black holes within Barrow entropic framework. https://doi.org/10.1016/j.dark.2025.102072

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