Quantum Cosmology of Classically Constrained Gravity

TL;DR

This paper explores novel solutions in a classically constrained gravity model, revealing mechanisms for universe creation, stability conditions, and implications for inflation, differing from standard General Relativity.

Contribution

It introduces new cosmological solutions in constrained gravity, including universe creation from nothing and stability analysis, expanding understanding beyond classical GR.

Findings

A spatially-flat de Sitter universe can be created from nothing with zero total energy.

Positive cosmological constant solutions are unstable and can transition to inflationary states.

Negative cosmological constant solutions are stable and do not transition to inflation.

Abstract

In hep-th/0506040 we discussed a classically constrained model of gravity. This theory contains known solutions of General Relativity (GR), and admits solutions that are absent in GR. Here we study cosmological implications of some of these new solutions. We show that a spatially-flat de Sitter universe can be created from ``nothing''. This universe has boundaries, and its total energy equals to zero. Although the probability to create such a universe is exponentially suppressed, it favors initial conditions suitable for inflation. Then we discuss a finite-energy solution with a nonzero cosmological constant and zero space-time curvature. There is no tunneling suppression to fluctuate into this state. We show that for a positive cosmological constant this state is unstable -- it can rapidly transition to a de Sitter universe providing a new unsuppressed channel for inflation. For a negative cosmological constant the space-time flat solutions is stable.