PBH-Driven Cosmic Acceleration Phase

• PBH-driven cosmic acceleration is a mechanism where repulsive effects from primordial black holes replace conventional inflaton fields to drive rapid cosmic expansion.
• It utilizes the Swiss Cheese cosmological model by embedding PBHs within an FLRW background, which modifies the Friedmann equations to include effective negative pressure.
• Distinct PBH mass regimes yield different cosmic phases, from inflation via ultra-light PBHs to early dark energy from intermediate masses, with supermassive, charged PBHs influencing late-time acceleration.

A PBH-driven cosmic acceleration phase describes epochs of accelerated universal expansion induced by a cosmological population of primordial black holes (PBHs), where repulsive effects—either from regular black hole metrics with de Sitter-like cores or from electromagnetic interactions—replace the conventional inflaton field or cosmological constant in driving expansion. Central to this mechanism is the "Swiss Cheese" cosmological model, in which spherically symmetric PBHs are embedded within a homogeneous and isotropic FLRW universe, yielding effective modifications to Friedmann equations and thus the acceleration dynamics. Recent studies explore both ultra-light PBHs responsible for inflation and heavier PBHs that contribute an early dark energy (EDE) component relevant to the Hubble tension, as well as the role of supermassive, electrically charged PBHs in late-time acceleration (Dialektopoulos et al., 25 Feb 2025, Dialektopoulos et al., 22 Nov 2025, Frampton, 2022).

1. Swiss Cheese Construction and Spacetime Embedding

PBH-driven cosmic acceleration fundamentally relies on the Swiss Cheese cosmological framework, an extension of the Einstein–Straus model where spherical "vacuoles" containing PBH interiors are excised from an FLRW background. The PBH interiors are described by static, spherically symmetric metrics (e.g., Hayward, Bardeen, Dymnikova, Schwarzschild–de Sitter):

• FLRW exterior:

$$ds^2_F = -dt^2 + a^2(t)\left[\frac{dr^2}{1-kr^2} + r^2 d\Omega^2\right]$$

• Interior metric:

$$ds^2_S = -F(R)\,dT^2 + F(R)^{-1} dR^2 + R^2 d\Omega^2$$

• Examples include Hayward:

$$F_H(R) = 1 - \frac{2G_N\,m\,R^2}{R^3 + 2G_N\,m\,L^2}$$

Matching these metrics at the vacuole boundary ($R = a\,r_\Sigma$) via the Darmois–Israel junction conditions ensures continuity of both the induced metric ($\gamma_{\alpha\beta}$) and extrinsic curvature ($K_{\alpha\beta}$), resulting in generalized dynamical equations for the cosmological scale factor (Dialektopoulos et al., 25 Feb 2025, Dialektopoulos et al., 22 Nov 2025).

2. Effective Friedmann Equations and Repulsive Core Dynamics

Embedding regular metric PBHs modifies the traditional Friedmann equations, yielding effective density and pressure terms. For the Hayward core,

• Effective Hubble rate:

$$H^2 + \frac{k}{a^2} = \frac{2G_N\,m}{R^3 + 2G_N\,m\,L^2}$$

which recasts into:

$$H^2 + \frac{k}{a^2} = \frac{8\pi G_N}{3}\left[\rho^{-1} + \frac{8\pi G_N L^2}{3}\right]^{-1}$$

with exterior matter density $\rho = 3m/(4\pi R^3)$. The repulsive core introduces an effective component $\rho_{\rm PBH}$, analogous to a fluid with negative pressure.

• Effective acceleration:

$$\frac{\ddot a}{a} = 4\pi G_N \rho \frac{16\pi G_N L^2 \rho - 3}{(8\pi G_N L^2 \rho + 3)^2}$$

Acceleration occurs for $\rho > \rho_c$, where $\rho_c = \frac{3}{16\pi G_N L^2}$.

Such repulsive cores generate a quasi-de Sitter expansion ($H \rightarrow 1/L$) at high density, achieving accelerated expansion without invoking a scalar field inflaton (Dialektopoulos et al., 25 Feb 2025).

3. PBH Mass Windows: Inflation and Early Dark Energy

Distinct cosmic acceleration phases are achieved for specific PBH mass and abundance regimes:

• Ultra-light PBHs ($m < 5 \times 10^8$ g): Dominate the energy content prior to Big Bang nucleosynthesis, triggering an inflationary phase with scale factor evolution $a(t) = a_i \exp(t/L)$ and e-fold number $N_{\rm inf} \gg 50-60$. Inflation naturally concludes as $\rho$ falls below the critical density or PBHs evaporate; Hawking radiation reheats the universe at $$T_{\rm reh} \sim [30/(\pi^2 g_*)]^{1/4}/(L^{1/2} G_N^{1/4})$$ (Dialektopoulos et al., 25 Feb 2025, Dialektopoulos et al., 22 Nov 2025).
• Intermediate PBHs ($m \sim 10^{12}$ g): With abundances $0.107 < \Omega^{\rm eq}_{\rm PBH}<0.5$ near matter-radiation equality, these generate a transient EDE component—modifying the expansion rate during recombination, which alleviates the Hubble $H_0$ tension by $\Delta H_0 \sim 0.5-1$ km s$^{-1}$ Mpc$^{-1}$ (Dialektopoulos et al., 25 Feb 2025, Dialektopoulos et al., 22 Nov 2025).

The table summarizes the parameter windows:

PBH Mass Regime	Phenomenology	Observational Signature
$m<5\times 10^8$g	PBH-driven inflation	Stochastic GW, Hawking reheating
$m\sim10^{12}$g	Early Dark Energy	CMB, LSS modifications, $H_0$ shift

4. Electromagnetic Self-Repulsion and Supermassive PBHs

An orthogonal PBH-driven acceleration mechanism arises from the electromagnetic properties of highly charged PBHs. If all PBHs carry electric charge $Q$ that grows quadratically with mass ($Q(M) = 4\times 10^{2p+8}$ C for $M = 10^p M_\odot$), Coulomb repulsion can dominate gravitational attraction for $M \gtrsim 10^{12} M_\odot$ (Frampton, 2022).

• For supermassive PBHs, this yields an effective negative pressure in the Friedmann equations.
• The effective equation-of-state parameter $w_{\rm eff}$, determined from the ratio of EM self-energy density to DM density, drives cosmic acceleration when $w_{\rm eff} < -1/3$.
• The required abundance is compatible with current supernova Ia, CMB, and LSS constraints given the low number density and large mean separation ($\sim$ Mpc scale).

5. Observational Constraints and Signatures

Robustness of the PBH-driven acceleration scenario is contingent on several parameter constraints and observational tests:

• Evaporation timescale must satisfy $t_{\rm evap} < t_{\rm BBN}$ for inflationary PBHs.
• EDE component must peak at $\Omega_{\rm EDE}(t_{\rm eq}) \sim 0.1-0.5$ but remain subdominant at last scattering ($\Omega_{\rm EDE}(t_{\rm LS}) < 0.015$), constrained by CMB and large-scale-structure data.
• For charged PBHs, sufficient smoothness and low number density avoid constraints from lensing and small-scale structure (Frampton, 2022).
• Signatures include modifications to CMB anisotropies, gravitational-wave backgrounds, and $\gamma$-ray/cosmic-ray signals from evaporation.

6. Extensions, Open Questions, and Model Viability

Current models invoke regular black hole solutions from quantum gravity (Hayward, Bardeen, Dymnikova metrics) and charged PBH populations, dispensing with scalar field inflatons and fine-tuning. Open theoretical and observational challenges comprise:

• The dynamics of PBH clustering and evaporation beyond the idealized vacuole model (Szekeres-type inhomogeneity).
• The generation and spectrum of perturbations during PBH-driven inflation.
• Forecasts for gravitational-wave observatories sensitive to early PBH-dominated eras.
• The possible roles of repulsive PBHs in late-time dark-energy phenomenology.

Further numerical simulations and quantum-gravity motivated regular PBH models are anticipated to clarify the predictions and observational viability of the PBH-driven cosmic acceleration scenario (Dialektopoulos et al., 25 Feb 2025, Dialektopoulos et al., 22 Nov 2025).