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

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 ${10}^{-3}\mathrm{H}\mathrm{z}$, 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 $1\mathrm{/}3$ to $-1\mathrm{/}3$, 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.