Primordial black holes from inflation with nonminimal derivative coupling

Abstract

We propose a novel enhancement mechanism of the curvature perturbations in the nonminimal derivative coupling inflation model with a coupling parameter related to the inflaton field. By considering a special form of the coupling parameter as a function of the inflaton, a period of ultraslow-roll inflation can be realized due to the gravitationally enhanced friction, and the resulting power spectrum of the curvature perturbations has a sharp peak, which is large enough to produce the primordial black holes. Under this mechanism, we can easily obtain a sharp mass spectrum of primordial black holes around specific masses such as O(10)M , O(10 −5 )M , and O(10 −12 )M , which can explain the LIGO events, the ultrashort-timescale microlensing events in OGLE data, and the most of dark matter, respectively.

Scalar induced gravitational waves in inflation with gravitationally enhanced friction

“…As discussed in Ref. [46], the strong friction conditionθ(φ)H 2 1 can be satisfied easily in the vicinity of φ c . In addition,H φ 1/5 c / √ 3 Table I in the appendix).…”

“…This constraint is obtained conservatively by parametrizing the power spectrum of curvature perturbations [20]. In [46], the Press-Schechter approach with the Gaussian window function has been used to discuss the production rate of PBHs. It has been pointed in Ref.…”

“…In Ref. [46], we demonstrated that PBHs with physically attractive masses, The PBH formation is accompanied inevitably with the production of significant GW backgrounds induced by the overly large curvature perturbations. The detection of such GW signals may serve as evidence of the GEF mechanism.…”

“…where κ −1 ≡ M pl = 2.4 × 10 18 GeV is the reduced Planck mass, g the determinant of the metric tensor g µν , R the Ricci scalar, G µν the Einstein tensor, θ a dimensionless coupling parameter, which is function of φ, and V (φ) the potential of the inflaton field. By choosing a special function form of θ(φ), i.e., θ = ω/ κ 2 φ−φc σ 2 + 1, a high-friction region can be realized at the slow-roll stage through the mechanism of the gravitationally enhanced friction (GEF) [46][47][48][49]. Here, ω, σ and φ c are constants.…”

“…II, we outline the basic formulas about the secondorder GWs and calculate the GW energy spectra associated with the PHB formation studied in Ref. [46]. In Sec.…”