# Testing backreaction effects with observational Hubble parameter data

## TL;DR

This study uses observational Hubble parameter data to test backreaction models of the universe's accelerated expansion, comparing standard and evolving curvature metrics, and finds backreaction can explain acceleration without dark energy.

## Contribution

It applies observational data to constrain backreaction cosmology models and assesses the validity of the evolving curvature prescription in describing late-time universe acceleration.

## Key findings

- Backreaction models can account for cosmic acceleration without dark energy.
- Constraints on model parameters depend on the choice of priors and metrics.
- The evolving curvature prescription needs improvement based on observational constraints.

## Abstract

In order to explore the generic properties of a backreaction model for explaining the accelerated expansion of the Universe, we exploit two metrics to describe the late time Universe. Since the standard FLRW metric cannot precisely describe the late time Universe on small scales, the template metric with an evolving curvature parameter $\kappa_{\mathcal{D}}(t)$ is employed. However, we doubt the validity of the prescription for $\kappa_{\mathcal{D}}$, which motivates us apply observational Hubble parameter data (OHD) to constrain parameters in dust cosmology. First, for FLRW metric, by getting best-fit constraints of $\Omega^{{\mathcal{D}}_0}_m = 0.25^{+0.03}_{-0.03}$, $n = 0.02^{+0.69}_{-0.66}$, and $H_{\mathcal{D}_0} = 70.54^{+4.24}_{-3.97}\ {\rm km \ s^{-1} \ Mpc^{-1}}$, the evolutions of parameters are explored. Second, in template metric context, by marginalizing over $H_{\mathcal{D}_0}$ as a prior of uniform distribution, we obtain the best-fit values of $n=-1.22^{+0.68}_{-0.41}$ and ${{\Omega}_{m}^{\mathcal{D}_{0}}}=0.12^{+0.04}_{-0.02}$. Moreover, we utilize three different Gaussian priors of $H_{\mathcal{D}_0}$, which result in different best-fits of $n$, but almost the same best-fit value of ${{\Omega}_{m}^{\mathcal{D}_{0}}}\sim0.12$. Also, the absolute constraints without marginalization of parameter are obtained: $n=-1.1^{+0.58}_{-0.50}$ and ${{\Omega}_{m}^{\mathcal{D}_{0}}}=0.13\pm0.03$. With these constraints, the evolutions of the effective deceleration parameter $q^{\mathcal{D}}$ indicate that the backreaction can account for the accelerated expansion of the Universe without involving extra dark energy component in the scaling solution context. Nevertheless, the results also verify that the prescription of $\kappa_{\mathcal{D}}$ is insufficient and should be improved.