Conformal transformations and the beginning of the Universe

TL;DR

This paper explores the properties of consecutive universes with positive cosmological constants, revealing constraints on their matter content, dualities in Einstein's equations, and the near-critical nature of their initial and final states, suggesting a radiation-dominated beginning.

Contribution

It demonstrates that such universes are limited to specific matter classes, exhibit duality with the Einstein universe, and are nearly critical, providing insights into the universe's initial conditions.

Findings

Universes can only contain four classes of perfect fluids.

The field equations show duality with the Einstein universe.

Both universes are nearly critical and radiation-dominated.

Abstract

We show that two consecutive Universes with positive cosmological constants filled with perfect fluids and conformal to the positive-spatial-curvature FLRW metric by an analytic conformal transformation have the following features implied by the Einstein equations: a) the fluids can only belong to 4 classes (radiation, dust and two other classes with negative pressures corresponding to a gas of strings and a gas of domain walls), b) the field equations on both sides of the future/eternity hypersurface exhibit certain duality with the Einstein Universe at the background, and c) both eons (one at the end, and the other at the beginning) are almost critical, so that the future eon is dominated by radiation and resembles the beginning of our Universe.