An Estimate of \Lambda in Resummed Quantum Gravity in the Context of Asymptotic Safety

Abstract

We show that, by using recently developed exact resummation techniques based on the extension of the methods of Yennie, Frautschi and Suura to Feynman's formulation of Einstein's theory, we get quantum field theoretic descriptions for the UV fixed-point behaviors of the dimensionless gravitational and cosmological constants postulated by Weinberg. Connecting our work to the attendant phenomenological asymptotic safety analysis of Planck scale cosmology by Bonanno and Reuter, we estimate the value of the cosmological constant \Lambda. We find the encouraging estimate \rho_\Lambda\equiv \frac{\Lambda}{8\pi G_N} \simeq (2.4\times 10^{-3}eV)^4. While this numerical value is close to recent experimental observations, we caution the reader that the estimate involves a number of model parameters that still possess significant levels of uncertainty, such as the value of the transition time between the Planck scale cosmology era and the Friedmann-Robertson-Walker radiation dominated era, where our current understanding allows for at least two orders of magnitude in its uncertainty and this would change our estimate of \rho_\Lambda by at least four orders of magnitude. We discuss such theoretical uncertainties as well. We show why GUT and EW scale vacuum energies from spontaneous symmetry breaking are suppressed in our approach to the estimation of \rho_\Lambda. As a bonus, we show how our estimate constrains susy GUTS.