Ricci Focusing Degeneracy between Dynamical Dark Energy and Matter Inhomogeneity

Abstract

The influence of dynamical (phantom) dark energy on light propagation within the framework of the Zeldovich-Kantowsky-Dyer-Roeder (ZKDR) approximation is discussed. This effect is considered in terms of the redshift-dependent parameter $α(z)$ of the ZKDR model, which is defined as the ratio of the mean matter density (baryonic matter, dark matter, and dark energy in the form of a cosmological constant) to the total density, including its fluctuations. We demonstrate that the observational manifestations of $α(z)$ admit two equivalent interpretations in the framework of both (1) a dynamical dark energy model, and (2) a model considering weak gravitational lensing in a universe with a cosmological constant. Thus, a degeneracy arises between these two physical scenarios. Finally, a simple statistical test, independent of cosmological probes, is proposed for breaking this degeneracy and testing the dynamical nature of dark energy. The test is based on the expected isotropy of dynamical dark energy at a fixed redshift, in contrast to stochastic inhomogeneities in the matter distribution induced by weak gravitational lensing.