Super-Acceleration from Massless, Minimally Coupled $\phi^4$

TL;DR

This paper derives the propagator for a massless, minimally coupled scalar in de Sitter space and shows that quantum effects lead to super-acceleration and violation of energy conditions, revealing observable de Sitter symmetry breaking.

Contribution

It provides a simple propagator form and computes the renormalized stress tensor for a scalar phi^4 theory, demonstrating super-acceleration and de Sitter invariance breaking.

Findings

Scalar field induces super-acceleration in de Sitter space.

De Sitter invariance is broken by scalar self-interactions.

Weak energy condition is violated on cosmological scales.

Abstract

We derive a simple form for the propagator of a massless, minimally coupled scalar in a locally de Sitter geometry of arbitrary spacetime dimension. We then employ it to compute the fully renormalized stress tensor at one and two loop orders for a massless, minimally coupled phi^4 theory which is released in Bunch-Davies vacuum at t=0 in co-moving coordinates. In this system the uncertainty principle elevates the scalar above the minimum of its potential, resulting in a phase of super-acceleration. With the non-derivative self-interaction the scalar's breaking of de Sitter invariance becomes observable. It is also worth noting that the weak energy condition is violated on cosmological scales. An interesting subsidiary result is that canceling overlapping divergences in the stress tensor requires a conformal counterterm which has no effect on purely scalar diagrams.