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

TL;DR

This paper explores how modifications in the Barrow entropy framework influence inflationary parameters, primordial black hole formation, and gravitational waves, suggesting potential detectability of PBHs and associated signals with upcoming observational missions.

Contribution

It derives modified inflationary parameters and PBH predictions within the Barrow entropy model, connecting theoretical modifications to observable signatures and dark matter contributions.

Findings

PBHs of about 10^{-12} solar masses can constitute up to one-third of dark matter.

Primordial gravitational wave peaks are around 10^{-3} Hz, detectable by future missions.

PBHs evolve with accretion, increasing mass and decreasing temperature, making them observable today.

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.