Cosmological black holes in the inflationary epoch

Abstract

We investigate the evolution of black holes present during the inflationary epoch, assuming they are dynamically coupled to the cosmological background through a generalized McVittie geometry, such that their gravitational mass scales with the cosmic scale factor. Adopting Starobinsky's $\mathcal{R}^2$ inflation model, we analyse the combined effects of cosmological coupling, Hawking evaporation and radiation accretion during the subsequent cosmic eras: inflation, radiation, matter, and dark energy. Requiring the black hole event horizon to remain smaller than the particle horizon at all times yields an upper bound on the mass parameter. Radiation accretion during the radiation era further constrains the parameter space to prevent runaway growth. Hawking evaporation sets a lower bound on the initial mass to ensure survival through inflation. We find that only black holes formed within a narrow initial mass range during inflation can persist to the present day, reaching a maximum mass of $M(t_0) \simeq 1.043\times10^{-3} M_\odot$.

Figures (8)

• Figure 1: Time evolution of the black hole event horizon and the particle horizon on a logarithmic scale during the matter- and dark energy–dominated epochs, for $\gamma=\gamma_2$. The vertical dashed line marks the transition between the two cosmological regimes.
• Figure 2: Mass evolution in the radiation era on a logarithmic scale. The black hole has a mass of $M=1062.35\,\text{g}$ at the end of the inflationary period, and a mass of $M(t_{\rm rm})=2.14391\times10^{-7}\,M_{\odot}$ at the end of the radiation era.
• Figure 3: Zoom-in of the early stages of the radiation-dominated epoch shown in Fig. \ref{['fig:Radiation']}. At early times, the accretion term clearly dominates the evolution.
• Figure 4: Mass evolution in the inflation era on a logarithmic scale. The black hole has a mass parameter of $\gamma=\gamma_{3}$ at the end of the inflationary period.
• Figure 5: Mass evolution in the matter era on a logarithmic scale. The black hole has a mass of $M(t_{\mathrm{f}})=1062.35\,\text{g}$ at the end of the inflationary period, and ends the matter era with a mass of $M(t_{\rm mdm})=7.53862\times10^{-4}\,M_{\odot}$.