Testing backreaction effects with observational Hubble parameter data

Authors：Cao Shu Lei; Teng Huan Yu; Wan Hao Yi; Yu Hao Ran; Zhang Tong Jie^*

Source：European Physical Journal C, 2018, 78(2): 170.

DOI：10.1140/epjc/s10052-018-5616-4

The spatially averaged inhomogeneous Universe includes a kinematical backreaction term Q(D) that is relate to the averaged spatial Ricci scalar < R >(D) in the framework of general relativity. Under the assumption that Q(D) and < R >(D) obey the scaling laws of the volume scale factor a(D), 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 kappa(D)(t) is employed. However, we doubt the validity of the prescription for kappa(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(D0)(m) = 0.25(-0.03)(+0.03), n = 0.02(-0.66)(+0.69), and H-D0 = 70.54(-3.97)(+4.24) km s(-1) Mpc(-1), the evolutions of parameters are explored. Second, in template metric context, by marginalizing over H-D0 as a prior of uniform distribution, we obtain the best-fit values of n = -1.22(-0.41)(+0.68) and Omega(D0)(m) = 0.12(-0.02)(+0.04). Moreover, we utilize three different Gaussian priors of H-D0, which result in different best-fits of n, but almost the same best-fit value of Omega(D0)(m) similar to 0.12. Also, the absolute constraints without marginalization of parameter are obtained: n = -1.1(-0.50)(+0.58) and Omega(D0)(m) = 0.13 +/- 0.03. With these constraints, the evolutions of the effective deceleration parameter q(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(D) is insufficient and should be improved.

• Institution
  德州学院; 上海交通大学; 北京师范大学; 中国科学院国家天文台