The Cosmological Consistency Relation in a Universe with Structure

Abstract

In this short paper we determine the effects of structure on the cosmological consistency relation which is valid in a perfect Friedmann Universe. We show that within $\Lambda$CDM the consistency relation is violated by about 1.5% for redshifts $z\simeq 2$ and this violation raises up to 2% at $z\simeq 5$ and 3% at $z\simeq 10$ after which it settles at about 2.7% for $z>10$. This effect of cosmic structure on the distance redshift relation is also very sensitive to the determination of the dark energy equation of state via cosmic distances. It actually leads to an apparent unphysical behavior of $w(z)$ which even diverges at $z\sim 2.5$ and which we also discuss here.