Speaker
Description
I will present a unified discrete quantum cosmological framework based on the Teleparallel Equivalent of General Relativity (TEGR). By formulating gravity strictly as a gauge theory of the non-compact translation group $T(4)$, we map the continuous Weitzenböck geometry onto a simplicial Regge lattice, where spacetime torsion manifests physically as localized structural dislocations quantified by the discrete Burgers vector $b_d$. In a homogeneous and isotropic Friedmann-Robertson-Walker (FRW) minisuperspace, coarse-graining over the extensive macroscopic area $\Sigma = \sum_{\text{dis}} \Sigma_d$ and the collective translational defect $b = \sum_{\text{dis}} b_d$ demonstrates that the Burgers vector acts as the exact canonical conjugate momentum to the spatial area, $b = -24\pi G P_\Sigma$. We then establish the quantum gravitational dynamics across two complementary regimes. First, applying polymer quantization (Bohr compactification) to regularize the non-compact translational momentum via finite-difference shift operators introduces a trigonometric holonomy correction, yielding a bounded effective Friedmann equation, $H^2 = \frac{8\pi G}{3}\rho\left(1 - \frac{\rho}{\rho_c}\right)$, that averts the classical singularity at a critical density $\rho_c$. Second, in canonical quantization, the discrete finite-difference Wheeler-DeWitt equation enforces global background stationarity ($\langle \hat{H}^2 \rangle_{\text{global}} = 0$), motivating a statistical decomposition of the macroscopic FRW state into a tensor product of localized simplicial Hilbert spaces, $\mathcal{H}_{\text{tot}} = \bigotimes_{d=1}^N \mathcal{H}_d$. Evaluating the local partition function over zero-point torsion fluctuations reveals that while the mean linear defect vanishes, the local squared variance remains strictly positive. At the ultraviolet (UV) minimal area scale $l_0^2$, this variance drives a finite maximum expansion rate $H_{BB}^2 = \frac{8\pi G}{\gamma l_0^4}$ at the Quantum Bounce. Integrating the thermalized ensemble over all accessible cell scales up to the late-time infrared (IR) causal horizon $L \sim R_H$ dynamically suppresses this primordial bounce rate by the squared UV-to-IR cutoff ratio, $\langle H_d^2 \rangle_{\text{today}} = H_{BB}^2 (l_0 / L)^2 \sim 10^{-122} H_{BB}^2 \approx \Lambda / 3$. Consequently, the observed cosmological constant emerges natively—not from an ad hoc scalar potential, but as the residual macroscopic ensemble variance of discrete quantum teleparallel fluctuations.