Multi-graviton theory, a latticized dimension, and the cosmological constant

TL;DR

This paper constructs a multi-graviton model with a latticized extra dimension, showing it can produce a small positive vacuum energy that potentially explains dark energy in the universe.

Contribution

It introduces a novel multi-graviton theory with a latticized dimension, connecting it to Kaluza-Klein models and analyzing vacuum energy implications.

Findings

Vacuum energy can be positive in 6, 10,... dimensions.

Vacuum energy can be arbitrarily small by parameter choice.

Model offers a potential explanation for the small positive dark energy.

Abstract

Beginning with the Pauli-Fierz theory, we construct a model for multi-graviton theory. Couplings between gravitons belonging to nearest-neighbor ``theory spaces'' lead to a discrete mass spectrum. Our model coincides with the Kaluza-Klein theory whose fifth dimension is latticized. We evaluate one-loop vacuum energy in models with a circular latticized extra dimension as well as with compact continuous dimensions. We find that the vacuum energy can take a positive value, if the dimension of the continuous space time is $6, 10,...$. Moreover, since the amount of the vacuum energy can be an arbitrary small value according to the choice of parameters in the model, our models is useful to explain the small positive dark energy in the present universe.