Primordial blackhole formation: Exploring chaoticpotential with a sharp step via the GLMSperspective

A sharp step on a chaotic potential can enhance primordial curvature fluctuations on smaller scales to the O(10⁻²) to form primordial black holes (PBHs). The present study discusses an inflationary potential with a sharp step that results in the formation of PBHs in four distinct mass ranges. Also this inflationary model allows the separate consideration of observable parameters nₛ and r on the CMB scale from the physics at small scales, where PBHs formation occur. In this work we computed the fractional abundance of PBHs (fPBH) using the GLMS approximation of peak theory and also the Press-Schechter (PS) formalism. In the two typical mass windows, 10⁻¹³M_ and 10⁻¹¹M_, fPBH calculated using the GLMS approximation is nearly equal to 1 and that calculated via PS is of 10⁻³. In the other two mass windows 1M_ and 6M_, fPBH obtained using GLMS approximation is 0.01 and 0.001 respectively, while fPBH calculated via PS formalism yields 10⁻⁵ and 10⁻⁶. The results obtained via GLMS approximation are found to be consistent with observational constraints. A comparative analysis of fPBH obtained using the GLMS perspective and the PS formalism is also included.