Varying $$\boldsymbol{\Lambda}$$ Theory Revisited

Abstract

We revisit the variable $$\Lambda$$ theory recently developed by Alexander et al. [1, 2]. We implement it to explain the current expansion of the Universe. The varying $$\Lambda$$ theory reduces one degree of freedom. The varying $$\Lambda$$ term (cosmological term) follows the energy density of the Universe. We consider such a theory which does not respect self-dual symmetry. The Bianchi identity enforces the $$\Lambda$$ term to be a constant for a theory without torsion. However, torsion can incorporate a varying $$\Lambda$$ term in the action. We consider a form of the action which has such a varying $$\Lambda$$ term, and the presence of only nonrelativistic matter energy density. We fit the luminosity distance according to the model and compare it with that in the $$\Lambda\textrm{{CDM}}$$ model and find their close behavior. However, we find a current value of matter energy density $$\rho_{m0}$$ larger than the critical energy density. Using the supernova data from Union 2.1 compilation, we further consider a different set of parameters, for which $${\kappa\rho_{m0}}/{3H_{0}^{2}}$$ becomes close to unity but, however, greater. For this set of parameters, we find a negative value in the effective equation of state, however, the model has a very different pattern of the Hubble parameter from the standard scenario.