Integration of Cosmic Inflation Into Lava-Void Cosmology

Turbulent Inflation in Lava-Void Cosmology

By C. Rich

To integrate cosmic inflation into Lava-Void Cosmology while maintaining the core principle of a single relativistic viscous fluid within General Relativity, the inflationary phase can be interpreted as an emergent consequence of Planck-scale turbulence and density-dependent bulk viscosity during and immediately following the non-singular bounce.

The existing framework already replaces the Big Bang singularity with an eternal fluid undergoing phase transitions or bounces, driven by incompressibility and breaker horizons. The onset of extreme turbulence at Planck densities (Reynolds number Re > 10¹⁹) provides a natural mechanism for a temporary quasi-de Sitter expansion phase. This phase achieves the required ∼60 e-folds to resolve the horizon and flatness problems, while multifractal turbulent fluctuations seed nearly scale-invariant primordial density perturbations, consistent with the model’s treatment of quantum effects as hydrodynamic turbulence.

This approach avoids introducing new fields (e.g., an inflaton) or departing from the unified fluid ontology. Turbulence motivates an effective negative pressure contribution that dominates briefly at high densities, mimicking slow-roll inflation, before transitioning to the density-dependent Generalized Chaplygin Gas (GCG) behavior for late-universe dark matter and dark energy unification.

Mathematical Formulation

The standard Friedmann equations are augmented to include bulk viscosity, common in imperfect fluid cosmologies:

1. First Friedmann equation (constraint):

$$ \left( \frac{\dot{a}}{a} \right)^2 = H^2 = \frac{8\pi G}{3} \rho $$

2. Raychaudhuri equation (acceleration):

$$ \dot{H} + H^2 = \frac{\ddot{a}}{a} = -\frac{8\pi G}{6} \left( \rho + 3 p_{\rm eff} \right) $$

where the effective pressure is

$$p_{\rm eff} = p(\rho) – 3\xi(\rho)H$$

with $p(\rho)$ being the barotropic (GCG-like) component responsible for late-universe behavior, and $\xi(\rho)$ being the bulk viscosity coefficient.

Energy-momentum conservation yields the continuity equation in terms of the effective pressure:

$$\dot{\rho} + 3 H (\rho + p_{\text{eff}}) = 0$$

The base $p(\rho)$ follows the density-dependent GCG form implied in the framework (e.g., $p = -A / \rho^\alpha$ or a generalized interpolation yielding dust-like behavior at intermediate densities and $w \approx -1$ at low densities).

To drive inflation near the bounce:

• Specify $\xi(\rho)$ as density-dependent, motivated by the turbulence transition. For example:

  $$\xi(\rho) = \xi_0 \left( \frac{\rho}{\rho_{\rm Pl}} \right)^n \cdot \frac{1}{1 + \left( \frac{\rho}{\rho_{\rm trans}} \right)^{-m}}$$

  where $\xi_0$, $n$, $m$, and transition density $\rho_{\rm trans}$ are parameters. This ensures $\xi$ peaks near Planck/bounce densities and decays rapidly during expansion.

During the inflationary phase (high $\rho \approx \rho_{\rm bounce}$), the viscous term $-3\xi H$ dominates, rendering $p_{\rm eff} \approx -\rho$ (or slightly deviating for slow-roll exit), yielding quasi-exponential expansion ($a(t) \propto \exp(Ht)$, where $H$ is nearly constant).

tuned via parameters to $N \gtrsim 60$.

Exit occurs naturally as $\rho$ dilutes and $\xi(\rho)$ diminishes, transitioning to the standard GCG-dominated evolution (radiation/matter-like intermediately, then late acceleration).

Primordial perturbations arise from turbulent intermittency and multifractal scaling (as described in the quantum extension), providing a spectrum close to Harrison-Zel’dovich via anomalous structure functions, amplified and frozen during the rapid expansion.

This extension preserves computational verifiability: the existing numerical integration can be extended backward to the bounce, incorporating the viscous term, to confirm consistency with CMB power spectrum constraints (e.g., scalar amplitude $A_s \approx 2 \times 10^{-9}$, tilt $n_s \approx 0.96$).

Further refinement of $\xi(\rho)$ and $p(\rho)$ forms would allow quantitative predictions for tensor modes or non-Gaussianity signatures distinguishable from standard scalar-field inflation. This mechanism aligns seamlessly with the model’s emphasis on fluid dynamics across scales, resolving the identified gap in early-universe accelerated expansion.