Geometric Birefringence and High-Multipole CMB B-Modes in Thermo-Relativistic Finsler Gravity

Geometric Birefringence and High-Multipole CMB B-Modes in Thermo-Relativistic Finsler Gravity Description / Abstract Overview This repository contains the foundational theoretical framework and analytical derivations for the polarization sector of the Thermo-Relativistic (TR) extension of spacetime, formulated strictly within the 8-dimensional tangent bundle \(TM\) of Finsler geometry. By exploiting the horizontal metricity and vertical torsion properties of the Chern-Rund linear connection, this work provides a purely geometric mechanism for breaking spatial parity invariance along photon worldlines, offering a complete, inflation-free alternative to primordial perturbation generation. Core Theoretical Breakthroughs Geometric Birefringence Operator: We derive the exact modification to the parallel transport equation of screen tetrad vectors. The mixed curvature tensor \(P^{i}_{\;jkl} = -\partial_{y^l}\Gamma^i_{jk}\) acts as an intrinsic, space-varying, and direction-dependent birefringent medium that rotates the linear polarization angle of Cosmic Microwave Background (CMB) photons. Modified Polarized Boltzmann Transport: We formalize the coupled system of radiative transport equations for the Stokes parameters (\(Q\) and \(U\)) on the unit sphere bundle \(SM\). The alignment of the active topological coupling parameter \(\alpha = \frac{1}{4\pi}\) limits the maximum amplitude of this rotation without requiring ad-hoc field tunings. High-Multipole \(B\)-Mode Plateau: Unlike standard inflationary tensor modes which decay rapidly at small angular steps, the Finslerian geometric leakage continuously shifts acoustic \(E\)-mode power into \(B\)-modes at high multipoles (\(l > 1500\)). This generates a frequency-independent power plateau that serves as a direct, testable signature for high-resolution observatories. Low-Multipole Suppression: The framework natively accounts for the anomalous large-scale power suppression observed by the Planck satellite (\(l < 10\)) as a direct consequence of the structural infrared cosmic boundary cutoff \(\Omega_{IR} \approx 14.75\%\). Context and Falsifiability This research directly addresses the active observational vectors of modern precision cosmology. By mapping the analytical running of the environmental variable \(\Lambda(v,\nu,T)\), this model presents a fully falsifiable framework primed for cross-examination against upcoming high-multipole polarization datasets from the Simons Observatory and CMB-S4.