Cosmic Microwave Background Anisotropies

CMB Anisotropies in Lava-Void Cosmology

By C. Rich 

To incorporate cosmic microwave background (CMB) anisotropies into Lava-Void Cosmology while preserving the unified relativistic viscous fluid framework, the temperature and polarization fluctuations observed in the CMB are interpreted as the frozen imprint of primordial density perturbations, seeded by multifractal turbulent intermittency during the bounce and viscous quasi-de Sitter (inflationary) phase, evolved through linear perturbation growth in the post-reheating radiation- and matter-dominated epochs. At recombination (when effective fluid coupling weakens due to dilution), these perturbations manifest as acoustic oscillations in the tightly coupled relativistic (photon-like) and clustered (baryon-like) components of the fluid, projecting onto the last scattering surface.

This mechanism aligns with the model’s core ontology: a single fluid exhibits density-dependent behavior, where high-Reynolds turbulence at early times generates nearly scale-invariant scalar perturbations (via anomalous scaling in structure functions), while viscous clustering provides an effective baryon acoustic loading for oscillations. The relativistic excitations dominate the energy density during the plasma era, mimicking photons, with Thomson-like scattering emergent from vortex interactions. Recombination occurs naturally as density drops below a transition threshold, reducing effective opacity and freezing anisotropies. This yields consistency with Planck observations (power spectrum, acoustic peaks, damping tail) and DESI baryon acoustic oscillations (BAO) without separate species, extending the radiation-phase treatment from Big Bang nucleosynthesis.

The approach reproduces the empirical successes of the standard model’s acoustic physics while offering potential distinguishability through turbulence-induced features (e.g., slight deviations in non-Gaussianity or peak ratios).

Mathematical Formulation

The background evolution follows the modified Friedmann equations with density-dependent pressure and viscosity, as previously extended:
\[ H^2 = \frac{8\pi G}{3} \rho \]
\[ \dot{\rho} + 3H(\rho + p_{eff}) = 0, \quad p_{eff} = p(\rho) – 3\xi(\rho)H \]

The key addition is the chiral (axial) current for effective left-minus-right vorticity:
\[ J^\mu_5 = n_5 u^\mu + \xi \omega^\mu + \xi_B B^\mu \]

For perturbations, employ gauge-invariant linear scalar perturbation theory in a viscous imperfect fluid. Key perturbed equations (in Fourier space, for comoving curvature perturbation \( \mathcal{R} \)):

Continuity and Euler equations for density contrast \( \delta = \delta\rho/\rho \):
\[ \dot{\delta} = -3H(c_s^2 – w)\delta – (1 + w)(\theta + 3\dot{\Phi}) \]
\[ \dot{\theta} = -H(1 – 3w)\theta + c_s^2 k^2 \delta + k^2 \Psi – 3\xi H k^2 \left(\frac{\theta}{\rho}\right) \]

Poisson equation:
\[ k^2 \Phi = -4\pi G \rho \left(1 + \frac{3\xi H}{c_s^2}\right) \delta \]

Where:
* \( \theta \) is the divergence of peculiar velocity.
* \( \Psi, \Phi \) are Bardeen potentials.
* \( w = p/\rho \) and \( c_s^2 = \dot{p}/\dot{\rho} \) is the adiabatic sound speed.
* \( \omega^\mu = \frac{1}{2} \epsilon^{\mu\nu\rho\sigma} u_\nu \partial_\rho u_\sigma \) represents the vorticity.

Acoustic Oscillations & Primordial Power Spectrum

During the tight-coupling era, the effective sound speed is:
\[ c_s \approx \frac{1}{\sqrt{3(1+R)}} \]

Acoustic oscillations arise with frequency \( \omega = kc_s \), leading to peaks in the power spectrum at multipoles:
\[ l_n \approx n\pi \frac{d_A(z_{rec})}{r_s(z_{rec})} \]

Primordial power spectrum from turbulence:
\[ P_{\mathcal{R}}(k) \propto k^{n_s-4}, \quad n_s – 1 \approx -2\epsilon + \eta_{turb} \]

Temperature anisotropy:
\[ \frac{\Delta T}{T}(\hat{n}) = \left[ \Phi + \Psi + \frac{1}{4} \delta_\gamma + \mathbf{v}_b \cdot \hat{n} \right]_{LSS} + \int ISW \]
with Doppler and integrated Sachs-Wolfe (ISW) terms.
Polarization (E-modes dominant, B-modes from tensors if present) arises from quadrupole anisotropy at scattering, computed via Boltzmann hierarchy extended to viscous fluids.

Existing numerical frameworks (e.g., extending CLASS or CAMB with viscous modules) can integrate these equations forward from turbulent initial conditions, constraining parameters for agreement with Planck C_ℓ (acoustic scale θ_* ≈ 0.0104 rad, peak spacing, damping) and polarization (EE, TE correlations). Residual viscosity may subtly shift peak heights or introduce scale-dependent damping, offering testable predictions.

This extension completes the treatment of CMB physics within the fluid paradigm, bridging early primordial seeds to late-time observables while maintaining unification across epochs.

C. Rich