Primordial Black Hole Formation in Supergravity

TL;DR

This work investigates primordial black hole formation within a supergravity-inspired double inflation scenario aimed at explaining MACHO-scale dark matter. A preinflation hybrid stage seeds the COBE-scale fluctuations and dynamically fixes the initial condition for a subsequent new inflation that generates large amplitude, small-scale fluctuations with a tilted spectrum ($n_s \simeq 1 - 2\kappa$). The analysis shows that if the total $e$-folds of the new inflation satisfy $N_{\rm new} \lesssim 60$, the resulting small-scale fluctuations can yield PBHs with masses $M_{\rm BH} \sim M_{\odot}$ and a required abundance, given COBE normalization of the preinflation and the derived relation $V^{3/2}/V \simeq 0.3$. The parameter constraints, including $\zeta \lesssim 0.05$, $\lambda_{\min} \le \lambda_{\max}$, and gravitino mass bounds, define a viable region where PBHs form MACHOs, with potential observational signatures in gravitational waves and dark matter phenomenology.

Abstract

We study a double inflation model (a preinflation + a new inflation) in supergravity and discuss the formation of primordial black holes which may be identified with massive compact halo objects (MACHOs) observed in the halo of our galaxy. The preinflation drives an inflaton for the new inflation close to the origin through supergravity effects and the new inflation naturally occurs. If the total e-fold number of the new inflation is smaller than $\sim 60$, both inflations produce cosmologically relevant density fluctuations. If the coherent inflaton oscillation after the preinflation continues until the beginning of the new inflation, density fluctuations on small cosmological scales can be set suitably large to produce black holes MACHOs of masses $\sim 1 M_{\odot}$ in a wide region of parameter space in the double inflation model.

Figures (1)

• Figure 1: Spectrum of the fluctuations of the gravitational potential $\Phi_k$ [ see Eq. (\ref{['eq:delta-rho-BH']})]. $k$ is the comoving wave number of the fluctuations and $L_{*}$ is the MACHO scale. The fluctuations on large scales ($k < L_{*}^{-1}$) are almost scale invariant ($\sim k^{0}$) and the spectrum is tilted ($\sim k^{-\kappa}$) on small scales ($k > L_{*}^{-1}$).