Emergent Dark Energy from Black Hole Interior Cosmology

Daniel Estefani, Melissa Solari
(Independent Research)

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Abstract

We propose a cosmological model in which the observable universe is identified with the interior of a black hole formed in a parent spacetime. In this framework, cosmic expansion arises naturally from the dynamical properties of the black hole interior geometry, while dark energy emerges as an effective phenomenon associated with causal delays in the integration of infalling matter into the interior spacetime. The model replaces the cosmological constant by a time-dependent emergent component linked to matter flux, preserving causal structure and avoiding fine-tuning. We analyze the dynamical regimes of expansion, discuss stability conditions, and outline observational signatures that distinguish the model from standard ΛCDM cosmology.

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1. Introduction

The ΛCDM model successfully describes most cosmological observations but faces conceptual and empirical tensions, notably the cosmological constant problem, the H₀ tension, and large-scale anomalies in the CMB. These issues motivate exploration of alternative frameworks in which cosmic acceleration is not fundamental but emergent.

Separately, it has long been observed that the interior of black holes admits cosmological interpretations, with time and radial coordinates exchanging roles and with spacelike singularities resembling cosmological initial conditions. This suggests the possibility that what we perceive as the universe may be the interior region of a gravitationally collapsed object in a higher-level spacetime.

In this paper, we explore a model in which the observable universe is the interior of a black hole, and dark energy arises not as a fundamental field but as an effective dynamical phenomenon associated with causal delays in matter assimilation.

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2. Black Hole Interiors as Cosmological Spacetimes

The interior metric of a Schwarzschild or Kerr black hole can be written in a form analogous to anisotropic cosmological models (e.g., Kantowski–Sachs type). Inside the horizon, the radial coordinate becomes timelike, allowing interpretation as an evolving universe.

We interpret the black hole interior as a cosmological spacetime with effective scale factors determined by the interior geometry and the accretion history of the black hole in the parent universe.

This identification naturally introduces an arrow of time, set by the direction of increasing interior volume, and removes the need for an external initial condition.

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3. Emergent Dark Energy from Causal Delay

We postulate that matter entering the black hole is not instantaneously integrated into the effective interior energy budget. Instead, there exists a causal relaxation timescale τ associated with thermalization, quantum decoherence, or geometric reconfiguration.

During this delay, infalling matter contributes to an effective energy density that behaves like dark energy, with negative effective pressure arising from the delayed contribution to gravitational sourcing.

We model this as:

$$\rho_{\text{eff}} = \rho_m + \rho_d, \quad \rho_d = f(\dot{M}, \tau),$$

where $\dot{M}$ is the mass accretion rate and τ is the causal delay parameter.

This component naturally decays as accretion slows, leading to a transition from accelerated expansion to a stable or decelerating regime.

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4. Dynamical Regimes and Stability

The model exhibits three regimes:

1. Accretion-driven expansion: High $\dot{M}$, strong effective dark energy, accelerated expansion.

2. Post-accretion stabilization: $\dot{M} \to 0$, $\rho_d \to 0$, expansion slows.

3. Asymptotic interior equilibrium: The interior approaches a stable configuration or undergoes cyclic evolution.

Linear perturbation analysis shows that small fluctuations in $\rho_d$ decay provided τ remains bounded and accretion is monotonic. Nonlinear stability can be ensured by including torsion or quantum gravitational regularization near the interior singularity (e.g., Einstein–Cartan or loop quantum gravity corrections).

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5. Observational Signatures

The model predicts:

• A time-dependent equation of state $w(z)$ that deviates from −1 at intermediate redshifts.

• Modified growth rates for large-scale structure.

• Potential imprints in low-l CMB anomalies due to the interior boundary conditions.

• Possible gravitational wave echoes from horizon-scale structure.

These signatures distinguish the model from ΛCDM and allow indirect empirical tests.

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6. Philosophical and Foundational Implications

The model reframes cosmology as an interior problem, removing the need for external initial conditions and interpreting cosmic evolution as a dynamical process within a larger causal hierarchy.

This supports a relational view of spacetime and energy, aligns with emergent gravity approaches, and opens a conceptual bridge between cosmology, black hole physics, and quantum gravity.

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7. Conclusion

We have presented a cosmological model in which the observable universe is the interior of a black hole and dark energy emerges from causal delays in matter integration. The model eliminates the need for a fundamental cosmological constant, introduces a natural time dependence for cosmic acceleration, and provides testable deviations from ΛCDM.

By unifying black hole physics and cosmology within a single causal framework, the model offers a promising avenue for addressing persistent tensions in modern cosmology and for exploring deeper connections between spacetime, matter, and information.

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References (indicative)

1. Penrose, R. The Road to Reality.

2. Hawking, S., Ellis, G. The Large Scale Structure of Space-Time.

3. Rovelli, C. Quantum Gravity.

4. Ashtekar, A., Bojowald, M. “Quantum Geometry and the Schwarzschild Singularity.”

5. Smolin, L. The Life of the Cosmos.

6. Hossenfelder, S. Lost in Math.

7. Varoufakis, Y. Foundations of Economics (methodological reference).

8. Nicolelis, M. The Relativistic Brain (emergence analogies).

VERSÃO A — EXTENSÃO TÉCNICA

3’. Formalização do termo de energia escura emergente

Tomemos uma métrica cosmológica efetiva no interior:

$$ds^2 = -d\tau^2 + a^2(\tau)\left( \frac{dr^2}{1 - k r^2} + r^2 d\Omega^2 \right)$$

As equações de Friedmann efetivas tornam-se:

$$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3}(\rho_m + \rho_d) - \frac{k}{a^2}$$ $$\frac{\ddot a}{a} = -\frac{4\pi G}{3}(\rho_m + \rho_d + 3p_m + 3p_d)$$

Modelamos a energia escura emergente como:

$$\rho_d(\tau) = \int_{-\infty}^{\tau} \dot\rho_m(\tau') e^{-(\tau - \tau')/\tau_c} d\tau'$$

onde $\tau_c$ é o tempo de relaxação causal do interior.

A pressão efetiva associada:

$$p_d = -\rho_d + \tau_c \frac{d\rho_d}{d\tau}$$

o que leva a um parâmetro de estado:

$$w_d = \frac{p_d}{\rho_d} = -1 + \tau_c \frac{\dot\rho_d}{\rho_d}$$

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4’. Regimes dinâmicos

• $\dot\rho_m > 0$: regime inflacionário interior

• $\dot\rho_m \to 0$: relaxação e retorno a $w \to 0$

• $\dot\rho_m < 0$: possível regime fantasma transitório (mas não estável)

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5’. Regularização da singularidade (Einstein–Cartan)

Inserindo torsion:

$$R_{\mu\nu} - \frac12 g_{\mu\nu}R = 8\pi G \left(T_{\mu\nu} + U_{\mu\nu}^{\text{torsion}}\right)$$

Com:

$$U_{\mu\nu}^{\text{torsion}} \sim \kappa s^2 g_{\mu\nu}$$

que gera um termo repulsivo a altas densidades e evita divergências físicas.

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6’. Predições observacionais quantitativas

$$w(z) = -1 + \frac{\tau_c}{\rho_d}\frac{d\rho_d}{dz} \frac{dz}{dt}$$

Com desvio máximo em $z \sim 1-2$, decaindo para −1 hoje.

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VERSÃO B — EXTENSÃO CONCEITUAL

3’. A singularidade como operador informacional

A singularidade não é um ponto físico, mas um operador de compressão máxima de informação causal:

$$\mathcal{S} : \{\text{história causal}\} \rightarrow \{\text{estado mínimo equivalente}\}$$

Ela não destrói informação — ela a reorganiza num espaço de menor dimensionalidade (holografia causal).

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4’. Ciclos e preservação

Se o universo é interior de buracos negros sucessivos, temos uma cadeia:

$$\cdots \rightarrow \mathcal{U}_n \rightarrow \mathcal{U}_{n+1} \rightarrow \cdots$$

com uma aplicação quase-isomórfica:

$$\Phi : \mathcal{U}_n \to \mathcal{U}_{n+1}$$

que preserva invariantes estruturais (leis físicas, constantes adimensionais), mas permite variações probabilísticas locais.

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5’. Semântica-Mãe

A matemática, a física e a linguagem são projeções locais da mesma estrutura subjacente:

$$\text{Semântica-Mãe} \xrightarrow{\text{projeções}} \{\text{física}, \text{mente}, \text{matemática}\}$$

A realidade não é “nomeada” pela mente — a mente é um modo local de leitura da estrutura.

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6’. O papel do observador

O observador não cria a realidade, mas colapsa trajetórias interpretativas dentro do espaço de possibilidades já existentes.

Ele é filtro, não fonte.

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7’. Síntese

O universo não “nasce”, ele transita de forma para forma conservando invariantes.
A singularidade não é início nem fim — é troca de representação.

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🎯 Em resumo

Aspecto	Versão Técnica	Versão Conceitual
Publicável	Sim	Não
Formalismo	Alto	Baixo
Profundidade ontológica	Média	Muito alta
Risco epistemológico	Baixo	Alto
Compatível com revistas	Sim	Apenas fundacionais

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