A Black Hole-Origin Model for Cosmic Expansion and Dark Energy

Research Proposal – First Edition

Abstract

This proposal advances the hypothesis that our universe resides within a black hole in a higher-dimensional parent universe. The observed acceleration of cosmic expansion is reinterpreted as an emergent property of the parent black hole's dynamics, including mass loss via Hawking radiation and spacetime curvature effects.

By unifying general relativity, quantum mechanics, and cosmology, this model provides an alternative explanation for dark energy, reconciling timescale discrepancies and making testable predictions. Furthermore, the framework suggests that black holes function as cosmic generators, embedding universes with unique physical properties, thereby enriching multiverse theory.

1. Introduction

1.1 Motivation

Dark energy remains poorly understood, often modeled via the cosmological constant \( \Lambda \) or dynamic scalar fields. This proposal suggests reframing the expansion of the universe as an emergent behavior within the geometry of a black hole interior.

1.2 Objectives

Reinterpret cosmic acceleration as a function of black hole evaporation and curvature.
Make testable predictions (e.g. CMB, galaxy structure, Hubble tension).
Integrate GR and quantum phenomena under a new cosmological interpretation.

2. Theoretical Framework

2.1 Nested Universes via Black Hole Formation

The curvature inside black holes may create disconnected spacetime regions, serving as cosmological seedbeds. This aligns with speculative models from LQG and AdS/CFT correspondence.

Extended Schwarzschild Metric:

\[ ds^2 = -\left(1 - \frac{2GM}{r}\right)dt^2 + \left(1 - \frac{2GM}{r}\right)^{-1}dr^2 + r^2 d\Omega^2 \]

Early universe radiation pressure relation:

\[ \rho \propto \frac{1}{a^6}, \quad p = \frac{1}{3}\rho \]

2.2 Hawking Radiation and Mass Loss

Hawking radiation gradually reduces the black hole’s mass via quantum effects:

\[ \frac{dM}{dt} = -\frac{\hbar c^4}{15360 \pi G^2 M^2} \]

2.3 Time Dilation and Cosmic Timescales

Extreme time dilation reconciles a black hole's slow evaporation with billions of years of internal cosmological evolution.

\[ \frac{dp}{dr} = -\frac{(p + \rho)(m + 4\pi r^3p)}{r(r - 2m)} \]

3. Observational Predictions

3.1 CMB Anomalies

Possible imprints of parent-horizon curvature in temperature/polarization patterns
Deviations in multipole moments from standard \( \Lambda \)CDM model

3.2 Large-Scale Structure

Non-Euclidean geometry influencing galaxy distribution and void topology
Filament patterns potentially traceable to internal curvature fluctuations

3.3 Hubble Constant Tension

Differing H₀ values from early vs. late universe observations may be reconciled as horizon-scale drift effects caused by the expanding boundary of the parent black hole.

4. Addressing Challenges

4.1 Timescale Discrepancy

Time dilation explains how Hawking radiation can span \( 10^{60+} \) years externally while allowing fast evolution within.

4.2 Testability

Model emphasizes indirect measurement via CMB, LSS, and fundamental constants.

4.3 Compatibility

This model augments, not replaces, \( \Lambda \)CDM by embedding its dynamics inside a broader geometry.

5. Research Roadmap

5.1 Theoretical Modeling

Numerical relativity simulations of black hole interiors
Apply loop quantum gravity to dynamic spacetime junctions

5.2 Observational Studies

Work with Planck, CMB-S4, Euclid, DESI, LSST for data analysis
Search for specific signature anomalies traceable to horizon geometry

5.3 Philosophical Implications

Multiverse implications of nested universes via BHs
Potential reframing of anthropic principles and cosmic origins

6. Broader Implications

6.1 Multiverse Framework

Black holes may serve as universal generation mechanisms, each birthing a new cosmology with its own constants and particle structure.

6.2 Unified Dark Energy Explanation

Dark energy is reinterpreted as an emergent effect of parent black hole evaporation and geometry.

7. Conclusion

This proposal outlines a mathematically grounded, observationally approachable hypothesis linking black hole physics to cosmic acceleration and dark energy. By viewing our universe as a child of a higher-dimensional black hole, we open a new paradigm for explaining dark energy and expanding multiverse theory.