Testing backreaction effects with observational Hubble parameter data

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.