Primordial blackhole formation: exploring chaotic potential with a sharp step via the GLMS perspective

Abstract 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 n s 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 ( f PBH ) using the GLMS approximation of peak theory and also the Press–Schechter (PS) formalism. In the two typical mass windows, 10 − 13 M ⊙ and 10 − 11 M ⊙ , f PBH 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 1 M ⊙ and 6 M ⊙ , f PBH obtained using GLMS approximation is 0.01 and 0.001 respectively, while f PBH 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 f PBH obtained using the GLMS perspective and the PS formalism is also included.