Reconstruction of potentials of hybrid inflation in the light of primordial black hole formation

Abstract

The large enhancement of the primordial power spectrum of the curvature perturbation can seed the formation of primordial black hole, that can play as a dark matter component in the Universe. In the literature, the enhanced power spectrum was calculated from the inflationary potential. However, in this paper, we show that a potential of multi scalar fields can be reconstructed from a given power spectrum which is made of a scale-invariant one on large scales and the other with a peak on small scales. In this reconstructed potential, the slow-roll of the second field in the curved trajectory is responsible for the generation of a peak in the power spectrum on small scales through the isocurvature perturbation. With multi scalar fields, the reconstructed potential may not be unique and we can find different potentials from a given power spectrum.

Potential reconstruction from general power spectrum in single-field inflation

“…(2.15), (2.18) and (2. 19) closely resemble the Hamilton-Jacobi approach to the inflationary dynamics [28], in the sense that essentially H is regarded as a function of the inflaton φ, rather than time ξ. The critical difference from the standard Hamilton-Jacobi approach is that the time derivative of φ is not related to dH/dφ but to H itself, as given in eq.…”

“…The full knowledge of the tensor power spectrum can provide a consistency check compared with the scalar power spectrum. The reconstruction programme has received renewed interests recently in the context of the primordial black holes (PBHs) and the power spectrum that allows their formation [18,19].…”

“…(2. 19). This allows, for a monotonic evolution of φ, an exact one-to-one correspondence between ξ and φ directly given the fundamental GSR function f (log ξ) inferred from eq.…”

Gravitational Waves and Primordial Black Holes from Supersymmetric Hybrid Inflation

“…Specifically, in the context of no-scale SUGRA hybrid models, a reduced value for n s can be predicted [55][56][57]. In the context of hybrid models the production of PBHs has already be studied [58][59][60][61], also with small values for n s . This PBH production obtained by an appropriate enhancement of the power spectrum of the scalar perturbations.…”

A Case Study of the Exotic Poisonous Plants found in Kottayam District, Kerala, India

“…Because of the wide range of energy scales present in hybrid inflation, from the GUT scales to the TeV scale, future GW detectors should be able to detect the stochastic background of GWs produced during preheating. In hybrid inflationary models, a peak in the primordial power spectrum of the curvature fluctuation on tiny scales leads to the development of a primordial black hole, which may serve as the universe's dark matter component [22].…”