Path integral measure and cosmological constant

TL;DR

This paper demonstrates that properly accounting for the path integral measure and UV cutoff in quantum gravity calculations reduces the vacuum energy's sensitivity to high-energy scales, offering new insights into the cosmological constant problem.

Contribution

It shows that including the correct measure and UV cutoff in quantum gravity calculations changes the vacuum energy sensitivity from quartic and quadratic to logarithmic, impacting the cosmological constant problem.

Findings

Vacuum energy sensitivity becomes logarithmic with proper measure and cutoff.

Results hold for matter fields on spherical backgrounds.

No supersymmetric assumptions are needed for these results.

Abstract

Considering (euclidean) quantum gravity in the Einstein-Hilbert truncation, we calculate the one-loop effective action $\Gamma^{1l}_{\rm grav}$ using a spherical background. Usually, this calculation is performed resorting to proper-time regularization within the heat kernel expansion and gives rise to quartically and quadratically UV-sensitive contributions to the vacuum energy $\rho_{\rm vac}=\frac{\Lambda_{\rm cc}}{8\pi G}$, with $\Lambda_{\rm cc}$ and $G$ cosmological and Newton constant, respectively. We show that, if the measure in the path integral that defines $\Gamma^{1l}_{\rm grav}$ is correctly taken into account, and the physical UV cutoff $\Lambda_{\rm cut}$ properly introduced, $\rho_{\rm vac}$ presents only a (mild) logarithmic sensitivity to $\Lambda_{\rm cut}$. We also consider a free scalar field and a free Dirac field on a spherical gravitational background, and find that the same holds true even in the presence of matter. These results are found without resorting to any supersymmetric embedding of the theory, and shed new light on the cosmological constant problem.