Logarithmically Divergent Vacuum Energy in Effective Field Theory

TL;DR

This paper demonstrates that in effective field theories, the vacuum energy divergence is typically only logarithmic due to Lorentz invariance constraints, contrasting with the quartic divergence traditionally expected.

Contribution

The study introduces a Monte Carlo approach to show that Lorentz invariance limits vacuum energy divergence to a logarithmic scale in effective field theories.

Findings

Vacuum energy divergence is unlikely to be faster than logarithmic.

Monte Carlo simulations produce a Gaussian distribution centered at zero.

The width of the distribution grows logarithmically with the cutoff.

Abstract

The vacuum energy density due to a single quantum field diverges quarticly with the ultraviolet cutoff $\Lambda$, in wild disagreement with the value implied by cosmological observations. We show that in effective field theories containing bosons and fermions the requirement of a Lorentz invariant vacuum makes any divergence faster than logarithmic exponentially unlikely. We show this by generating an ensemble of mass spectra by Monte Carlo, and find that the probability distribution function for the vacuum energy is a gaussian centered on zero with a width that grows only logarithmically with the ultraviolet cutoff.