# The Cosmological Consistency Relation in a Universe with Structure

## TL;DR

This paper investigates how cosmic structures affect the cosmological consistency relation in a $\Lambda$CDM universe, revealing small violations at high redshifts and implications for dark energy measurements.

## Contribution

It quantifies the impact of cosmic structures on the consistency relation and explores resulting unphysical behaviors in dark energy parameter estimations.

## Key findings

- Consistency relation violated by about 1.5% at z~2
- Violation increases to 3% at z~10
- Unphysical divergence in dark energy equation of state at z~2.5

## 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.