Primordial black holes and second order gravitational waves from ultra-slow-roll inflation

Abstract

The next generation of space-borne gravitational wave detectors may detect gravitational waves from extreme mass-ratio inspirals with primordial black holes. To produce primordial black holes which contribute a non-negligible abundance of dark matter and are consistent with the observations, a large enhancement in the primordial curvature power spectrum is needed. For a single field slow-roll inflation, the enhancement requires a very flat potential for the inflaton, and this will increase the number of e-folds. To avoid the problem, an ultra-slow-roll inflation at the near inflection point is required. We elaborate the conditions to successfully produce primordial black hole dark matter from single field inflation and propose a toy model with polynomial potential to realize the big enhancement of the curvature power spectrum at small scales while maintaining the consistency with the observations at large scales. The power spectrum for the second order gravitational waves generated by the large density perturbations at small scales is consistent with the current pulsar timing array observations.

Planck scale black hole dark matter from Higgs inflation

“…PBHs could then constitute part or all of the dark matter [93][94][95][96][97][98][99][100]. The recent detection of gravitational waves from black hole mergers by LIGO and Virgo [101] has rekindled the study of PBHs [102,103], with many proposed models of critical point inflation [104][105][106][107][108][109][110] that could produce PBH dark matter in the mass range observable by current or upcoming gravitational wave experiments. Such predictions are subject to stringent constraints from astrophysical observations, such as lensing and gamma-ray bursts [111][112][113].…”

$$\alpha $$-attractor from superconformal E-models in brane inflation

“…A plethora of single field inflationary models have been constructed [7] and new models continue to be proposed. For example, the recently proposed constant roll inflation [8][9][10][11][12][13] may be used to generate large density perturbation at small scales to seed the formation of primordial black holes [14][15][16][17][18]. The constraints n s = 0.965 ± 0.004 (68% C.L.)…”

Constraints on primordial curvature perturbations from primordial black hole dark matter and secondary gravitational waves

“…The solid gray line shows the induced GWs from the monochromatic power spectrum. We also show induced GWs from a inflationary model [20] by the solid blue line. The sensitivity curves from different observations are also shown [50,64,65].…”

“…Using the power law power spectrum (3.10), we calculate the µ distortion [62,63] Fig. 3, we also show the secondary GWs produced by the monochromatic power spectrum (2.32) with A ζ = 0.01, k p = 1.93 × 10 12 Mpc −1 and the inflationary model with the polynomial potential [20]. For convenience, we call the model as D-G model.…”