Large power spectrum and primordial black holes in the effective theory of inflation

Abstract

We study the generation of a large power spectrum, necessary for primordial black hole formation, within the effective theory of single-field inflation. The mechanisms we consider include a transition into a ghost-inflation-like phase and scenarios where an exponentially growing mode is temporarily turned on. In the cases we discuss, the enhancement in the power spectrum results from either a swift change in some effective coupling or a modification of the dispersion relation for the perturbations, while the background evolution remains unchanged and approximately de Sitter throughout inflation. The robustness of the results is guaranteed thanks to a weakly broken galileon symmetry, which protects the effective couplings against large quantum corrections. We discuss how the enhancement of the power spectrum is related to the energy scale of the operators with weakly broken galileon invariance, and study the limits imposed by strong coupling and the validity of the perturbative expansion.

Growth of power spectrum due to decrease of sound speed during inflation

“…However, whether the growth of the power spectrum due to decreasing sound speed is similar to that due to ultraslow-roll inflation and whether this growth results from the appearance of a growing term in the solution of the curvature perturbations remains unclear. Recently, it was pointed out that when the sound speed is very small the high order k 4 term in the dispersion relation will become dominant [42,43]. Although this high order term leads to a new solution of the curvature perturbations, the power spectrum is enhanced by small c s and it has a k 4 growth, which is the same as that in the case of the ultraslow-roll inflation.…”

“…the slow-roll inflation to the ultraslow-roll one, where there is a growing part and the constant part only has a k −3/2 -dependent term [42].…”

“…Since P R ∝ 1 cs , where = − Ḣ H 2 is the slow-roll parameter, with H being the Hubble parameter and Ḣ = dH/dt, and c s is the sound speed of the curvature perturbations, the enhancement of the curvature perturbations during inflation can be achieved by reducing the rolling speed of the inflaton to obtain a phase of ultraslow-roll inflation or the sound speed of the curvature perturbations [42][43][44][45][46].…”

“…the Dirac-Born-Infeld inflation [58], the multifield inflationary model [59,60], the inflationary models in modified gravity theories [61,62], and so on. Using the effective field theory of inflation, the generation of PBHs due to a small c s has been studied in [42][43][44][45]. However, whether the growth of the power spectrum due to decreasing sound speed is similar to that due to ultraslow-roll inflation and whether this growth results from the appearance of a growing term in the solution of the curvature perturbations remains unclear.…”

Induced Gravitational Waves from Multi-Sound Speed Resonances during Cosmological Inflation

“…Usually, in the standard slow-roll inflation paradigm, the sound speed of the inflaton is equal to one; but it can deviate from the unity in alternative scenarios with non-canonical kinetic term, e.g., k-inflation [50,51], Dirac-Born-Infeld inflation [52,53], effective field theory from integrating out the heavy modes [54,55] and so on. It was extensively explored in the literature that the sizable secondary GWs at small scale can be generated by various behaviors of the varying sound speed of the scalar mode [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69]. Recently, it was proposed that parametric resonances of primordial density perturbations, originated from the sound speed, with an oscillatory feature in of (conformal) time, can generate a large amplification of the abundance of induced GWs and primordial black holes (PBHs) in the early universe [7,[70][71][72].…”