Constant roll and primordial black holes

Abstract

The constant-roll inflation with small positive value of the constant-roll parameter β ≡φ Hφ = const. has been known to produce a slightly red-tilted curvature power spectrum compatible with the current observational constraints. In this work, we shed light on the constant-roll inflation with negative β and investigate how a stage of constant-roll inflation may realize the growth in the primordial curvature power spectrum necessary to produce a peaked spectrum of primordial black hole abundance. We first review the behavior of constant-roll models in the range of parameters − 3 2 < β < 0, which allows for a constant-roll attractor stage generating a blue-tilted curvature power spectrum without superhorizon growth. As a concrete realization, we consider a potential with two slow-roll stages, separated by the constant-roll stage, in a way that satisfies the current constraints on the power spectrum and the primordial black hole abundance. The model can produce primordial black holes as all dark matter, LIGO-Virgo events, or OGLE microlensing events. Due to the range of different scalar tilts allowed by the constant-roll potential, this construction is particularly robust and testable by future observations.

Constant-rate inflation: primordial black holes from conformal weight transitions

“…To see this, let us divide the existing models into two classes with respect to the scaling behavior of the power spectrum on scales much smaller than the (steepest) growing phase led by a negative δ < −3. We refer scenarios with an approximately constant scaling dimension |∆(N → N end )| ∼ O(1) that significantly violates the standard slow-roll conditions as the first class [5,7,9,[11][12][13][14]18], and those with |∆(N → N end )| 1 being essentially a secondary slow-roll phase as the second class [11,13,16,20]. To demonstrate the PBH scenarios in both secondary slow-rolling (SSR) and slowroll-violating (SRV) classes, we adopt the parametrization of the inflaton potential by a power-law series [12] as…”

“…That enhanced primordial density fluctuations from inflationary models with large curvature perturbations on small scales is the mainstream scenario for PBH formation. PBHs from models of inflation, with targeting masses spanning in the range of 10 −17 -10 9 M , can be realized either in the single-field [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] or multi-field [22][23][24][25][26][27][28][29][30][31][32][33][34][35] framework.…”

“…Single-field models of inflation for PBH formation ending with an effective slow-roll phase can be found in[11,13,16,20].…”

Anisotropic constant-roll inflation for the Dirac–Born–Infeld model

“…Consequently, the constant-roll inflation has been investigated extensively in Refs. [115][116][117][118][119][120][121][122][123][124][125][126][127][128][129][130][131][132][133]. It appears that the constant-roll condition has been applied to a number of cosmological models such as the non-minimal Coleman-Weinberg [119], F(R) gravity [120][121][122][123], scalar-tensor gravity [124], k-inflation [125], non-canonical scalar field [126], DBI [127], Palatini-R 2 gravity [128], Gauss-Bonnet gravity [129,130], multi scalar fields [131], non-commutative gravity [132], and f (φ)R gravity [133] models to figure out either novel (exact) inflationary solutions or cosmological consequences.…”

Gauss–Bonnet inflation with a constant rate of roll

“…The constantroll condition with small η H is compatible with the slow-roll inflation, and a special value η H = 3 amounts to the ultraslow-roll inflation [4,5], in which the potential is very flat and the inflaton almost stops rolling.The constant-roll inflationary models are discussed in more details in [6][7][8], and extended to modified theories of gravity [9][10][11][12][13][14] or two fields case [15], and using other constant-roll conditions [16][17][18]. Other developments are appeared in [19][20][21][22].…”