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Cosmological Bounce Relics: Black Holes, Gravitational Waves, and Dark Matter

Enrique Gaztanaga

Abstract

We propose a new mechanism for generating cosmological relics -- black holes, gravitational waves (GWs), and possibly dark matter (DM) -- in a bouncing Universe. Relics arise through two channels: (i) compact objects and GWs produced during pre-bounce collapse that remain super-horizon and re-enter after the bounce, and (ii) dark-matter halos formed during collapse that exit the horizon and collapse into black holes upon re-entry. Unlike inflationary primordial black holes, these relic black holes originate from nonlinear structure formation during collapse. We derive the particle horizon and horizon-crossing conditions in bouncing cosmology and show that perturbations or compact objects larger than 90 m survive the bounce. The resulting population of relic black holes and GWs spans a wide mass range, offering a unified origin for dark matter, gravitational-wave backgrounds, and the early growth of supermassive black holes and galaxies.

Cosmological Bounce Relics: Black Holes, Gravitational Waves, and Dark Matter

Abstract

We propose a new mechanism for generating cosmological relics -- black holes, gravitational waves (GWs), and possibly dark matter (DM) -- in a bouncing Universe. Relics arise through two channels: (i) compact objects and GWs produced during pre-bounce collapse that remain super-horizon and re-enter after the bounce, and (ii) dark-matter halos formed during collapse that exit the horizon and collapse into black holes upon re-entry. Unlike inflationary primordial black holes, these relic black holes originate from nonlinear structure formation during collapse. We derive the particle horizon and horizon-crossing conditions in bouncing cosmology and show that perturbations or compact objects larger than 90 m survive the bounce. The resulting population of relic black holes and GWs spans a wide mass range, offering a unified origin for dark matter, gravitational-wave backgrounds, and the early growth of supermassive black holes and galaxies.
Paper Structure (12 sections, 24 equations, 2 figures)

This paper contains 12 sections, 24 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Dark Matter Halo Virialization
  3. Press–Schechter formalism
  4. A Cosmological Bounce Solution
  5. Bounce Inflation and Particle Horizon
  6. Horizon Crossing
  7. What does it mean to “cross the horizon”?
  8. Bounce DM and GW relics
  9. Discussion and Conclusions
  10. The FLRW* cloud perturbation
  11. The Black Hole Universe (BHU)
  12. Junction for $P \ne 0$ and $\Lambda \ne 0$

Figures (2)

  • Figure 1: Configuration of a spherical collapse perturbation. We consider three spherically symmetric regions: (1) an outer background with radius $>r$ and mean density $\bar{\rho}$; (2) an inner region of radius $R<r$ with higher density $\rho = \bar{\rho}(1+\delta)$; and (3) an intermediate near-vacuum layer separating them. This can represent a collapsing overdensity of size $R$ within a larger universe of size $r$, or analogously, our finite Universe of radius $R$ embedded in a larger space.
  • Figure 2: Particle horizon versus perturbation scale in a bounce cosmology. The blue dashed curve shows the comoving particle horizon in a bounce scenario with an analytic $\cosh$-inflationary phase; the red curve includes transition from matter domination to the stiff ground state. The black dotted line shows the physical scale $a\,\lambda$ of a perturbation. The green dotted line marks the minimum scale that becomes superhorizon (Eqs. \ref{['eq:lambda_min']}–\ref{['eq:rHmin']}). The pink region shows times when the mode is superhorizon, while the white region denotes subhorizon scales. During collapse (left to center), the horizon shrinks and all $\lambda > 90$ m modes become superhorizon; after the bounce (center to right), the horizon grows and such modes re-enter.