Cosmic acceleration in the nonlocal approach to the cosmological constant problem

Abstract

We have recently constructed a manifestly local formulation of a nonlocal approach to the cosmological constant problem which can treat with quantum effects from both matter and gravitational fields. In this formulation, it has been explicitly shown that the effective cosmological constant is radiatively stable even in the presence of the gravitational loop effects. Since we are naturally led to add the R 2 term and the corresponding topological action to an original action, we make use of this formulation to account for the late-time acceleration of expansion of the universe in case of the open universes with infinite space-time volume. We will see that when the "scalaron", which exists in the R 2 gravity as an extra scalar field, has a tiny mass of the order of magnitude O(1meV ), we can explain the current value of the cosmological constant in a consistent manner.

Gravitational quantum effects and nonlocal approach to the cosmological constant problem

“…It is straightforward to show that this is not indeed the case explicitly when the mass of the scalaron is around 1meV . The detail will be explained in a separate publication when we treat with the cosmic acceleration on the basis of the present formalism [24]. The variation of the total action with respect to the 3-form Bµνρ produces…”

“…It is worthwhile to point out that constructing of a model accounting for the inflation in the present context is a nontrivial task since the vacuum energy density decouples from the gravitational equation and the residual cosmological constant is in general believed to be small in large and/or old universes. In a future publication, we will report this study [24].…”

More on Weinberg’s no-go theorem in quantum gravity

“…The Weinberg theorem also lays a cornerstone on recent developments of nonlocal approaches to the cosmological constant problem where the operation of taking the spacetime average of physical quantities plays a critical role, and as a result the effective cosmological constant is expressed in terms of the space-time average of the trace of the energy-momentum tensor [3][4][5][6][7][8][9][10][11][12][13][14]. 1 In the nonlocal approaches, one has to evaluate quantum effects of both matter and gravitational fields properly.…”