Divergent Integrals, The Riemann Zeta Function, and The Vacuum

Abstract

This paper presents a new theoretical estimate for the vacuum energy density by summing the contributions of all quantum fields' vacuum states which turns out to match the predictions of current cosmological models and all observational data to date. The basis for this estimate is the recent results on the analytical solution to improper integral of divergent power functions using the Riemann Zeta function.