Gravitational Bounce from the Quantum Exclusion Principle

TL;DR

This paper models how quantum principles prevent singular collapse in gravitational systems, leading to a bounce and inflation-like expansion, which predicts a small non-zero spatial curvature detectable by future surveys.

Contribution

It introduces a relativistic collapse model incorporating quantum exclusion, demonstrating a bounce that unifies black hole interiors, inflation, and dark energy phenomena.

Findings

Gravitational bounce occurs at a specific radius due to quantum effects.

The model predicts a small negative spatial curvature, -0.07 to -0.05.

Bounce confined within the initial gravitational radius, mimicking a cosmological constant.

Abstract

We investigate the fully relativistic spherical collapse model of a uniform distribution of mass $M$ with initial comoving radius $\chi_*$ and spatial curvature $k \equiv 1/\chi_k^2 \le 1/\chi_*^2$ representing an over-density or bounded perturbation within a larger background. Our model incorporates a perfect fluid with an evolving equation of state, $P = P(\rho)$, which asymptotically transitions from pressureless dust ($P = 0$) to a ground state characterized by a uniform, time-independent energy density $\rho_{\rm G}$. This transition is motivated by the quantum exclusion principle, which prevents singular collapse, as observed in supernova core-collapse explosions. We analytically demonstrate that this transition induces a gravitational bounce at a radius $R_{\rm B} = (8 \pi G \rho_{\rm G}/3)^{-1/2}$. The bounce leads to an exponential expansion phase, where $P(\rho)$ behaves effectively as an inflation potential. This model provides novel insights into black hole interiors and, when extended to a cosmological setting, predicts a small but non-zero closed spatial curvature: $ -0.07 \pm 0.02 \le \Omega_k < 0$. This lower bound follows from the requirement of $\chi_k \ge \chi_* \simeq 15.9$ Gpc to address the cosmic microwave background low quadrupole anomaly. The bounce remains confined within the initial gravitational radius $r_{\rm S} = 2GM$, which effectively acts as a cosmological constant $\Lambda$ inside $r_{\rm S}=\sqrt{3/\Lambda}$ while still appearing as a Schwarzschild black hole from an external perspective. This framework unifies the origin of inflation and dark energy, with its key observational signature being the presence of small but nonzero spatial curvature, a testable prediction for upcoming cosmological surveys.