Testing backreaction effects with observational Hubble parameter data

Abstract

The spatially averaged inhomogeneous Universe includes a kinematical backreaction term QD that is relate to the averaged spatial Ricci scalar ⟨ R⟩ D in the framework of general relativity. Under the assumption that QD and ⟨ R⟩ D obey the scaling laws of the volume scale factor aD, a direct coupling between them with a scaling index n is remarkable. 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 κD(t) is employed. However, we doubt the validity of the prescription for κD, 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 ΩmD0=0.25-0.03+0.03, n=0.02-0.66+0.69, and HD0=70.54-3.97+4.24kms-1Mpc-1, the evolutions of parameters are explored. Second, in template metric context, by marginalizing over HD0 as a prior of uniform distribution, we obtain the best-fit values of n=-1.22-0.41+0.68 and ΩmD0=0.12-0.02+0.04. Moreover, we utilize three different Gaussian priors of HD0, which result in different best-fits of n, but almost the same best-fit value of ΩmD0∼0.12. Also, the absolute constraints without marginalization of parameter are obtained: n=-1.1-0.50+0.58 and ΩmD0=0.13±0.03. With these constraints, the evolutions of the effective deceleration parameter qD 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 κD is insufficient and should be improved.