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Cosmic Inflation From Regular Black Holes

Kensuke Sueto, Riku Yoshimoto, Pablo A. Cano

Abstract

We study braneworld cosmology in quasi-topological gravity (QTG) with an infinite tower of higher-curvature terms, focusing on the case in which the bulk admits regular black hole solutions. We derive the $\mathbb{Z}_2$-symmetric junction conditions for a FLRW brane moving in a static, spherically symmetric bulk geometry, and obtain the corresponding modified Friedmann equations for the scale factor. We prove that, in the small scale factor regime, the brane generically approaches a de Sitter phase characterized solely by the length scale $\sqrtα$ of the higher-derivative terms, while the standard Einstein-gravity braneworld dynamics is recovered in the low-energy regime. We further provide a universal estimate for the number of e-folds of the de Sitter phase in terms of the ratio between the black hole scale and the scale of new physics $r_g/\sqrtα$. The inflationary regime is fully independent of the brane matter content and hence avoids the problem of trans-Planckian matter densities. Numerical integrations for explicit regular bulk solutions (Dymnikova-like and Hayward black holes) confirm these estimates and illustrate how the bulk black hole sector controls the onset and termination of inflation. This framework leverages the powerful properties of QTGs, defined only in $D\ge 5$, to study consequences for a four-dimensional universe.

Cosmic Inflation From Regular Black Holes

Abstract

We study braneworld cosmology in quasi-topological gravity (QTG) with an infinite tower of higher-curvature terms, focusing on the case in which the bulk admits regular black hole solutions. We derive the -symmetric junction conditions for a FLRW brane moving in a static, spherically symmetric bulk geometry, and obtain the corresponding modified Friedmann equations for the scale factor. We prove that, in the small scale factor regime, the brane generically approaches a de Sitter phase characterized solely by the length scale of the higher-derivative terms, while the standard Einstein-gravity braneworld dynamics is recovered in the low-energy regime. We further provide a universal estimate for the number of e-folds of the de Sitter phase in terms of the ratio between the black hole scale and the scale of new physics . The inflationary regime is fully independent of the brane matter content and hence avoids the problem of trans-Planckian matter densities. Numerical integrations for explicit regular bulk solutions (Dymnikova-like and Hayward black holes) confirm these estimates and illustrate how the bulk black hole sector controls the onset and termination of inflation. This framework leverages the powerful properties of QTGs, defined only in , to study consequences for a four-dimensional universe.

Paper Structure

This paper contains 14 sections, 72 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Bulk theory: Birkhoff-QTG and regular black hole solutions
  3. Definition of Birkhoff-QTG
  4. Black hole solutions
  5. Braneworld cosmology with regular black holes
  6. Junction conditions and effective Friedmann equation
  7. Einstein gravity
  8. Dymnikova-like scenario
  9. Hayward scenario
  10. Universality of de Sitter inflation and the number of e-folds
  11. Conclusion and discussion
  12. Derivation of modified Friedmann equation for concrete models
  13. Dymnikova-like scenario
  14. Hayward scenario

Figures (1)

  • Figure 1: Scale factor $a$ and indicator $F=\sqrt{\tilde{H}^2+\frac{1}{\tilde{a}^2}}$ for parameters $D=5$, $\tilde{M}=10^9$, $\tilde{\sigma}=10^{-2}$, $\tilde{\Lambda}=-10^{-9}$, and $\tilde{\rho}=\frac{1}{\tilde{a}^4}$. We start the evolution at a given time $\tilde{t}=0$ for which $\tilde{a}(0)=100$ and solve for the evolution of the scale factor backwards in time. The blue curves represent the Dymnikova-like braneworld scenario, the orange lines represent the Hayward braneworld scenario, and the green dashed curves represent an Einstein-gravity limit. While all the curves coincide at late times, they disagree for earlier times: Einstein gravity predicts a singularity in the past, and the other two models a de Sitter phase with a bounce.