Predicting spatial curvature $\Omega_K$ in globally $CPT$-symmetric universes

TL;DR

This paper extends the $CPT$-symmetric universe model by analyzing constraints on spatial curvature, finding specific permissible values of $ ext{Omega}_K$ that align with observational data.

Contribution

It introduces end-of-universe symmetric conditions into the $CPT$-symmetric model, constraining allowed curvature values based on mode compatibility.

Findings

Allowed curvature values are $ ext{Omega}_K otin ext{integers}$, specifically $ ext{Omega}_K o ext{discrete set}$.

Constrained curvature values are consistent with Planck observations.

The model links symmetry conditions to observable spatial curvature constraints.

Abstract

Boyle and Turok's $CPT$-symmetric universe model posits that the universe was symmetric at the Big Bang, addressing numerous problems in both cosmology and the Standard Model of particle physics. We extend this model by incorporating the symmetric conditions at the end of the Universe, which impose constraints on the allowed perturbation modes. These constrained modes conflict with the integer wave vectors required by the global spatial geometry in a closed universe. To resolve this conflict, only specific values of curvature are permissible, and in particular the curvature density is constrained to be $\Omega_K \in \{-0.014, -0.009, -0.003, \ldots\}$, consistent with Planck observations.