Primordial black holes from modified supergravity

Abstract

The modified supergravity approach is applied to describe a formation of Primordial Black Holes (PBHs) after Starobinsky inflation. Our approach naturally leads to the two-(scalar)-field attractor-type double inflation, whose first stage is driven by scalaron and whose second stage is driven by another scalar field which belongs to a supergravity multiplet. The scalar potential and the kinetic terms are derived, the vacua are studied, and the inflationary dynamics of those two scalars is investigated. We numerically compute the power spectra and we find the ultra-slow-roll regime leading to an enhancement (peak) in the scalar power spectrum. This leads to an efficient formation of PBHs. We estimate the masses of PBHs and we find their density fraction (as part of Dark Matter). We show that our modified supergravity models are in agreement with inflationary observables, while they predict the PBH masses in a range between $$10^{16}$$ 10 16 g and $$10^{20}$$ 10 20 g. In this sense, modified supergravity provides a natural top-down approach for explaining and unifying the origin of inflation and the PBHs Dark Matter.

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

“…where we have added the Friedmann equation at the end. Our results for double inflation and PBH formation in the two special cases: the one with δ = 0 (called the γ model) and the one with γ = 0 (called the δ model) are given below, in accordance with the work in [67]. Every term in Equations ( 47) and ( 48) is well motivated, as follows: (i) the first term in F comes from the pure (standard) supergravity, (ii) the first term in N describes the R 2 supergravity, (iii) the second ζ-term in N is required for stabilization of the R 2 supergravity and of its scalar potential, and (iv) the remaining γ-and δ-terms are introduced for PBH formation.…”

“…It is also straightforward to derive the equations of motion in our two-field model in the FLRW universe, when keeping only time dependence. We find [67]…”

“…It is straightforward (but tedious) to obtain the scalar part of the Lagrangian in Einstein frame. It takes the form of Equation ( 5) indeed [67],…”

“…In the former case, n s is within 2σ (CL), whereas in the latter case, n s is within 3σ but outside 2σ (CL). Let us now compare the specific models studied in the preceding subsections in order to tune their parameters to the best fit with the CMB observations, and then compare those models with the available observational constrains on PBH and DM [67,75]. We also want to estimate the PBH-to-DM density fractions in the γ-models and in the δ-models.…”

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].…”