Zero cosmological Constant from Normalized General Relativity

          @misc{ pirsa_PIRSA:09050090,
            doi = {10.48660/09050090},
            url = {https://pirsa.org/09050090},
            author = {Davidson, Aharon},
            keywords = {Quantum Gravity, Quantum Fields and Strings, Particle Physics, Cosmology},
            language = {en},
            title = {Zero cosmological Constant from Normalized General Relativity},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {may},
            note = {PIRSA:09050090 see, \url{https://pirsa.org}}
          }
          

Abstract

Normalizing the Einstein-Hilbert action by the volume functional makes the theory invariant under constant shifts in the Lagrangian. The field equations then resemble unimodular gravity whose otherwise arbitrary cosmological constant is now determined as a Machian universal average. We first prove that an empty space-time is necessarily flat, and then demonstrate, by invoking the scalar field paradigm, that the cosmological constant is actually zero. Normalized general relativistic cosmology is then discussed at the mini-superspace level, where we confirm the generic zero cosmological constant result, and furthermore prove that if matter is attractive then the Universe cannot be closed. The only non-vanishing cosmological constant solutions are associated with static Einstein-like closed universes.