Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Primordial Black Hole Formation in Rastall Gravity: Shifted Collapse Threshold and Exponential Abundance Sensitivity

Mayukh R. Gangopadhyay

Abstract

Primordial black holes formed in the early universe are compelling candidates for dark matter. We investigate their production in Rastall gravity, a modification of general relativity that introduces a non-minimal coupling between matter and geometry through the non-conservation of the energy-momentum tensor. Analyz- ing cosmological perturbations during radiation domination, we demonstrate that the Rastall parameter fundamentally alters the collapse dynamics, modifying the growth of density fluctuations, the critical threshold for black hole formation, and the fluctuation amplitude at horizon crossing. Current cosmological constraints from Big Bang Nucleosynthesis, the cosmic microwave background, and large-scale structure restrict the Rastall parameter to small values, yet within this allowed range PBH production can be altered by orders of magnitude compared to general relativity. Our results establish primordial black holes as novel probes of modified gravity.

Primordial Black Hole Formation in Rastall Gravity: Shifted Collapse Threshold and Exponential Abundance Sensitivity

Abstract

Primordial black holes formed in the early universe are compelling candidates for dark matter. We investigate their production in Rastall gravity, a modification of general relativity that introduces a non-minimal coupling between matter and geometry through the non-conservation of the energy-momentum tensor. Analyz- ing cosmological perturbations during radiation domination, we demonstrate that the Rastall parameter fundamentally alters the collapse dynamics, modifying the growth of density fluctuations, the critical threshold for black hole formation, and the fluctuation amplitude at horizon crossing. Current cosmological constraints from Big Bang Nucleosynthesis, the cosmic microwave background, and large-scale structure restrict the Rastall parameter to small values, yet within this allowed range PBH production can be altered by orders of magnitude compared to general relativity. Our results establish primordial black holes as novel probes of modified gravity.
Paper Structure (16 sections, 53 equations, 3 figures)

This paper contains 16 sections, 53 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Rastall Gravity: Fundamentals and Background Evolution
  3. Scalar Perturbations and Density Contrast Evolution
  4. Derivation of the Master Equation for Density Contrast
  5. Solution During Radiation Domination
  6. Super-horizon solution ($x \ll 1$)
  7. Horizon crossing ($x = 1$)
  8. PBH Formation Criterion in Rastall Gravity
  9. Critical Density Threshold for Collapse
  10. Approach 1: Jeans scale modification
  11. Approach 2: Spherical collapse model
  12. Variance of Density Fluctuations
  13. PBH Abundance
  14. Primordial Black Hole Abundance
  15. Implications for PBH Dark Matter Scenarios
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Critical density threshold $\delta_c(\lambda)$ as a function of the Rastall parameter $\lambda$. The solid line shows GR case, while the shaded region indicates the range of variation for different perturbation profiles based on numerical simulations.
  • Figure 2: Different profile dependences for critical density contrast.
  • Figure 3: Enhancement factor for different values of A.