Generating PBHs and small-scale GWs in two-field models of inflation

Abstract

Primordial black holes (PBHs) generated by gravitational collapse of large primordial overdensities can be a fraction of the observed dark matter. In this paper, we introduce a mechanism to produce a large peak in the primordial power spectrum (PPS) in two-field inflationary models characterized by two stages of inflation based on a large non-canonical kinetic coupling. This mechanism is generic to several two-field inflationary models, due to a temporary tachyonic instability of the isocurvature perturbations at the transition between the two stages of inflation. We numerically compute the primordial perturbations from largest scales to the small scales corresponding to that of PBHs using an extension of BINGO (BI-spectra and Non-Gaussianity Operator). Moreover we numerically compute the stochastic background of gravitational waves (SBGW) produced by second order scalar perturbations within frequencies ranging from nano-Hz to KHz that covers the observational scales corresponding to Pulsar Timing Arrays, Square Kilometer Array to that of Einstein telescope. We discuss the prospect of its detection by these proposed and upcoming gravitational waves experiments.

Multi-Field versus Single-Field in the Supergravity Models of Inflation and Primordial Black Holes

“…All that becomes even more important for multi-field models of inflation, PBH, and DM, where SUSY and supergravity can serve as the guiding fundamental principle for discrimination of phenomenological models. We find that it is the case for the effective two-field models derived from the modified (Starobinsky) supergravity by starting from the manifestly supersymmetric Lagrangian (46). After (Taylor) expanding its potentials N and F in powers of the scalar curvature superfield R, and keeping only the few leading terms, we arrived at our models defined by Equations ( 47) and (48), whose scalar part is described by Equations ( 50) and (51).…”

“…They reduce to the the standard Einstein supergravity action in the special case of N = 0 and F = −3R. In other words, Equations (45) or (46) is the most general extension of the (R + R 2 ) gravity. Though an F-type term (except a constant) can be rewritten as the D-type term in Equations ( 45) and ( 46), we keep both of them because they represent different modifications of the standard (pure) supergravity.…”

“…Relaxing fine-tuning and making PBH production more natural are the basic reasons for considering multi-field models of inflation and PBH. For instance, PBH production may be a generic feature of two-field inflation with a sharp turn of inflationary trajectory [46]. The required growth of primordial fluctuations can be achieved by tachyonic instabilities, like in the waterfall phase of hybrid inflation [47,48].…”

The multi-field, rapid-turn inflationary solution

“…Rapidly turning trajectories in multi-dimensional field spaces have been of much recent interest: they can yield inflation and quintessence in potentials satisfying the de-Sitter conjecture [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], and they can form primordial black holes [18][19][20][21]. Rapidly turning inflation models are also profound in their own right, as they can exhibit dynamics very different from single-field inflation while being phenomenologically viable [14,15,[22][23][24][25][26][27][28].…”

Scalaron–Higgs inflation reloaded: Higgs-dependent scalaron mass and primordial black hole dark matter

“…The production of PBHs in multi-field inflation has recently been realized in a variety of models, see e.g. [42,[52][53][54][55][56][57][58]. The formation of PBHs by an effective single-field ultraslow roll mechanism has also been investigated in a finetuned RG-analysis of the scalaron-Higgs model [31].…”