New Prospects for Solving the Cosmological Constant Problem - 2009

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.

The currently accelerating Hubble expansion is in accord with the old heuristic prediction, from causal set theory, of a fluctuating and ever-present cosmological "constant''. More recently, a phenomenological model based on certain of the ideas behind the prediction has been devised, but it remains incomplete. I will review these developments and also mention a possible consequence for the dimensionality of spacetime.

I will give account of a work in progress in which I attempt to modify the metric-manifold structure of GR in the infra-red. The proposed modification does not contain any massive parameter as it is effective at length scales comparable with the inverse (extrinsic) curvature. The guiding line for this modification is an "ultra-strong" equivalence principle, according to which even semi-classical gravitational effects (i.e. particle production) are definitely banned from a sufficiently small free-falling elevator. Some cosmological consequences of this modification will be discussed.