Dark energy model with very large-scale inhomogeneity

Abstract

We consider a dynamical model for dark energy based on an ultralight mass scalar field with very large-scale inhomogeneities. This model may cause observable impacts on the anisotropic properties of the cosmic microwave background (CMB) intensity and luminosity distance. We formulate the model as the cosmological perturbations of the superhorizon scales, focusing on the local region of our universe. Moreover, we investigated the characteristic properties of the late-time evolution of inhomogeneous dark energy. Our numerical solutions show that the model can mimic the standard ΛCDM cosmology while including spatially dependent dark energy with flexible ranges of the model parameters. We put a constraint on the amplitude of these inhomogeneities of the dark energy on very large scales with the observations of the CMB anisotropies. We also discuss their influence on the estimation of the luminosity distance.

Large-scale structure with superhorizon isocurvature dark energy

“…II B, and keep them to the order of 1 To clarify the difference of the notations between this paper and the previous work Ref. [24], we note that in this paper, V (n) 1 is equivalent with the V 1(m) defined in Sec. II A of Ref.…”

“…As assumed in the previous works [23,24], we consider the model that the ultralight scalar field is varying at a very large spatial scale, much longer than the Hubble length in the present universe. Thus, they create large-scale inhomogeneities of the dark energy on superhorizon scales and break the cosmological principle, but the violation is small within the horizon of our universe at present.…”

“…Next, we will introduce the equations that the sh-mode, which were given in Ref. [24], and a review with more details of this part is given in Appendix A. The sh-mode of O(κ 0 1 ) follows equations…”

“…The evolution of the superhorizon modes is investigated in Ref. [24] using both an analytic method and a numerical method based on the above equations. We remark some of the results.…”

“…Motivated by the model, in the present paper, we will consider the dark energy model of a scalar field with inhomogeneities on scales larger than the current horizon scale assuming the spatial curvature K is set to K = 0 . In the following, we will first review the previous studies [24] to introduce this model, and then find the equations governing the terms of perturbations relevant to the LSS, the solutions for the evolution of the perturbations, and the formulation for the power spectrum based on these solutions.…”