Zero Cosmological Constant from Normalized General Relativity

Abstract

Normalizing the Einstein-Hilbert action by the volume functional makes the theory invariant under constant shifts in the Lagrangian. The associated field equations then resemble unimodular gravity whose otherwise arbitrary cosmological constant is now determined as a Machian universal average. We prove that an empty space-time is necessarily Ricci tensor flat, and demonstrate the vanishing of the cosmological constant within the scalar field paradigm. The cosmological analysis, carried out at the mini-superspace level, reveals a vanishing cosmological constant for a Universe which cannot be closed as long as gravity is attractive. Finally, we give an example of a normalized theory of gravity which does give rise to a non-zero cosmological constant.

5 PRD pages;

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• Normalized General Relativity: Non-closed Universe and Zero Cosmological Constant
• String Theory, the Dark Sector and the Hierarchy Problem
• Vacuum energy sequestering and conformal symmetry
• Metamorphosis of the Cosmological Constant and 5D Origin of the Fiducial Metric
• Dark Energy and Inflation with Volume Normalized Action
• Note About Canonical Formalism for Normalized Gravity And Vacuum Energy Sequestering Model
• Mach like principle from conserved charges
• A note on dark matter and dark energy
• Nonlocal Galileons and Self-Acceleration
• Exploring the self-tuning of the cosmological constant from Planck mass variation