The Universe Originating from an Empty Planck-Size Torus

TL;DR

This paper proposes a model where the universe starts as an empty Planck-sized three-torus, driven by Casimir energies, and evolves to match current observations, including the cosmic microwave background anomaly.

Contribution

It introduces a pre-inflationary model based on Casimir energies in a three-torus topology, linking initial conditions to present-day universe size and CMB anomalies.

Findings

Universe can reach several Hubble radii today

Model explains low-multipole CMB anomaly

Derived relation between universe size, inflation, and reheating

Abstract

We consider a Universe with a three-torus topology which before inflation is devoid of any matter or radiation. Its pre-inflationary evolution is driven solely by Casimir energies of the existing fields, with a radiation-like equation of state. We show that, quite strikingly, with the appropriate number of fermions and bosons in the theory, such a Universe evolving from Planck size at Planck time has the correct critical energy density today. Moreover, assuming typical parameters for inflation and reheating, the three-torus Universe can be several Hubble radii across at present time, which is precisely the size hinted by the anomaly in the cosmic microwave background observed at low multipole moments. We derive a relation between the size of the Universe, the number of e-folds of inflation, and the energy density decrease during reheating, which we then use to determine the parameter values consistent with the anomaly and the lower bound on the size of the Universe from Planck.