Lava-Void Cosmology: Bayesian Tests vs ΛCDM

Lava-Void Cosmology: Bayesian Tests vs ΛCDM

By C. Rich

To integrate comprehensive statistical fitting and model selection into Lava-Void Cosmology while preserving the unified relativistic viscous fluid framework, the theory undergoes rigorous quantitative evaluation through Bayesian inference, comparing its predictive power against the standard \( \Lambda \)CDM model across multiple observational probes.

The model parameters, primarily density-dependent viscosity coefficients, transition scales, and turbulent intermittency factors, are fewer and more physically motivated than those of \( \Lambda \)CDM. No separate cosmological constant, cold dark matter density, or inflaton potential is required, enabling parsimonious fitting with the potential for superior Bayesian evidence through resolution of observational tensions, particularly the Hubble constant discrepancy attributed to residence in a local underdense void.

This framework employs modified cosmological Boltzmann solvers extending CLASS or CAMB with viscous imperfect fluid modules, coupled to sampling engines for parameter estimation and model comparison. Key datasets include Planck 2018 CMB measurements with ACT and SPT polarization updates, DESI BAO and redshift-space distortion constraints, Pantheon+ and DES Type Ia supernovae, SH0ES local distance ladder constraints on \( H_0 \), and weak-lensing measurements from KiDS, DES, and HSC.

The model accommodates higher local values
\( H_0 \approx 73\text{–}74 \,{\rm km\,s^{-1}\,Mpc^{-1}} \)
through void-induced apparent acceleration, while maintaining early-universe
consistency with global values
\( H_0 \approx 67\text{–}68 \,{\rm km\,s^{-1}\,Mpc^{-1}} \).

This extension ensures empirical rigor by transforming conceptual unification into falsifiable quantitative predictions.

Mathematical Formulation

The posterior probability for model parameters \( \theta \) is

\[
P(\theta \mid d)
\propto
\mathcal{L}(d \mid \theta)\,\pi(\theta)
\]

where \( \mathcal{L} \) is the likelihood and \( \pi(\theta) \) the prior.

Core parameters (approximately 6 to 10 free, compared with \( \Lambda \)CDM’s six base parameters plus extensions) include:

• Viscosity amplitudes \( \xi_0, \eta_0 \) and exponents \( n, m \).
• Transition densities \( \rho_{\rm trans}, \rho_{\rm mat}, \rho_{\rm crit} \).
• Turbulent intermittency and multifractal exponents.
• Baryon fraction \( \Omega_b h^2 \) and void depth and scale for local \( H_0 \) adjustment.

For Gaussian likelihoods in high-signal regimes,

\[
-2 \ln \mathcal{L}
=
\chi_{\rm CMB}^2
+ \chi_{\rm BAO}^2
+ \chi_{\rm SN}^2
+ \chi_{H_0}^2
+ \chi_{\rm WL}^2
\]

For the CMB,

\[
\chi_{\rm CMB}^2
=
\left(
C_\ell^{\rm theory}
–
C_\ell^{\rm obs}
\right)^T
\mathrm{Cov}^{-1}
\left(
C_\ell^{\rm theory}
–
C_\ell^{\rm obs}
\right)
\]

BAO constraints include angular diameter distances \( D_A(z) \), Hubble rates \( H(z) \), and redshift-space distortion measurements via \( f\sigma_8(z) \).

Type Ia supernovae use standardized distance moduli

\[
\mu(z)
=
5 \log_{10}
\left(
\frac{d_L(z)}{10\,{\rm pc}}
\right)
+ M
\]

where the luminosity distance \( d_L(z) \) integrates the modified expansion history \( H(z) \).

Local measurements impose a Gaussian prior
\( H_0 = 73.04 \pm 1.04 \,{\rm km\,s^{-1}\,Mpc^{-1}} \),
reconciled through dipole or radial void profiles.

Weak-lensing observables use convergence power spectra and shear correlations \( \xi(\theta) \), sensitive to the growth function modified by viscous clustering.

Posterior exploration is performed using MCMC or nested sampling algorithms, yielding best-fit parameters, credible intervals, and marginalized constraints.

Model selection uses Bayesian evidence

\[
\mathcal{Z}
=
\int
\mathcal{L}(\theta)
\pi(\theta)
\, d\theta
\]

or information criteria such as AIC and BIC. Expected outcomes include
\( \Delta \ln \mathcal{Z} > 5 \) favoring Lava-Void Cosmology through improved treatment of the Hubble tension and small-scale structure, with comparable or reduced minimum \( \chi^2 \) across probes.

This statistical framework positions Lava-Void Cosmology as a competitive, unified alternative with enhanced explanatory power and clear falsifiability.

C. Rich