Growth of curvature perturbations for PBH formation & detectable GWs in non-minimal curvaton scenario revisited

Abstract

AbstractWe revisit the growth of curvature perturbations in non-minimal curvaton scenario with a non-trivial field metricλ(ϕ) whereϕis an inflaton field, and incorporate the effect from the non-uniform onset of curvaton's oscillation in terms of an axion-like potential. The field metricλ(ϕ) plays a central role in the enhancement of curvaton field perturbation δχ, serving as an effective friction term which can be either positive or negative, depending on the first derivativeλ,ϕ. Our analysis reveals thatδχundergoes the superhorizon growth when the conditionηeff≡ -2 √2ϵMPlλ,ϕ/λ< -3 is satisfied. This is analogous to the mechanism responsible for the amplification of curvature perturbations in the context of ultra-slow-roll inflation, namely the growing modes dominate curvature perturbations. As a case study, we examine the impact of a Gaussian dip inλ(ϕ) and conduct a thorough investigation of both the analytical and numerical aspects of the inflationary dynamics. Our findings indicate that the enhancement of curvaton perturbations during inflation is not solely determined by the depth of the dip inλ(ϕ). Rather, the first derivativeλ,ϕalso plays a significant role, a feature that has not been previously highlighted in the literature. Utilizing theδ𝒩 formalism, we derive analytical expressions for both the final curvature power spectrum and the non-linear parameterfNLin terms of an axion-like curvaton's potential leading to the non-uniform curvaton's oscillation. Additionally, the resulting primordial black hole abundance and scalar-induced gravitational waves are calculated, which provide observational windows for PBHs.