Flat Universe with Hyperbolic Voids

TL;DR

This paper investigates how matter inhomogeneities, especially voids, can induce hyperbolic geodesic flow in a flat universe, affecting cosmic structure analysis and the interpretation of CMB data.

Contribution

It derives an averaged Jacobi equation showing voids can cause hyperbolicity regardless of the universe's overall curvature, highlighting a geometric effect on cosmological observations.

Findings

Voids induce hyperbolicity in geodesic flow.

Energy independence of geometric effects.

Implications for CMB ellipticity analysis.

Abstract

The properties of geodesics flow are studied in a Friedmann-Robertson-Walker metric perturbed due to the inhomogeneities of matter. The basic, averaged Jacobi equation is derived, which reveals that the low density regions (voids) are able to induce hyperbolicity, even if the global curvature of the Universe is zero or slightly positive. It is shown that the energy independence is a characteristic property of these geometric effects. The importance of these conclusions is determined by the temperature independent ellipticity of excursion sets and regions of different randomness found in Kolmogorov CMB maps.