A Strategy for a Vanishing Cosmological Constant in the Presence of Scale Invariance Breaking

TL;DR

This paper proposes a theoretical approach where scale invariance in a noncommutative operator framework leads to a natural vanishing of the cosmological constant, even with spontaneous symmetry breaking.

Contribution

It introduces a novel mechanism linking scale invariance to the vanishing cosmological constant within an emergent quantum field theory framework.

Findings

Scale invariance implies zero cosmological constant.

Vacuum energy vanishes under the proposed condition.

Spontaneous scale invariance breaking is compatible with this mechanism.

Abstract

Recent work has shown that complex quantum field theory emerges as a statistical mechanical approximation to an underlying noncommutative operator dynamics based on a total trace action. In this dynamics, scale invariance of the trace action becomes the statement $0=Re Tr T_{\mu}^{\mu}$, with $T_{\mu \nu}$ the operator stress energy tensor, and with $Tr$ the trace over the underlying Hilbert space. We show that this condition implies the vanishing of the cosmological constant and vacuum energy in the emergent quantum field theory. However, since the scale invariance condition does not require the operator $T_{\mu}^{\mu}$ to vanish, the spontaneous breakdown of scale invariance is still permitted.