Late time anisotropy as an imprint of cosmological backreaction

Backreaction effects of the large-scale structure on the background dynamics have been claimed to lead to a renormalization of the background dynamics that may account for the late time acceleration of the cosmic expansion. This article emphasizes that generically the averaged flow is locally anisotropic, a property that can be related to observation. Focusing on perturbation theory, the spatially averaged shear, that characterizes the anisotropy of the flow, is computed. It is shown that this shear arising from backreaction differs from a homogeneous shear: its time evolution is different, and its amplitude is completely determined by the cosmological parameters and the matter power spectrum. It ranges within 2% and 37% at a redshift of order 0.5 so that the isotropy of the Hubble flow may allow us to constrain the backreaction approach to dark energy.

Figure 1

Comparison of the matter APM power spectrum $P_{\delta }$ (dashed line) and the $\Lambda \mathrm{CDM}$ power spectum (solid line) assuming $({\Omega }_{\mathrm{m}0},{\Omega }_{\Lambda 0})=(0.27,0.73)$ and a spectral index $n_s=0.96$.

Figure 2

Dependence of the window function $W$ on the UV cutoff scales $k_{\mathrm{UV}}$, assuming the APM (thin lines) or an inflationary (thick lines) power spectrum. The solid line refers to a sharp cutoff and the dashed line to a Gaussian regularization.

Figure 3

Dependence of the anisotropy $\Sigma$ as a function of the redshift $z$ assuming UV cutoff $k_{\mathrm{UV}}=0.1$, 0.5, $1{\mathrm{Mpc}}^{-1}$ (from left to right) and assuming the APM power spectrum with ${\Omega }_{\Lambda 0}=0.73$. We plot both the solution using Eq. (64) (solid lines) and the solution using Eq. (65) (dashed lines).

Figure 4

Value $z_{\max }$ of the position of the peak of $\Sigma$ as a function of ${\Omega }_{\Lambda 0}$. Such a peak exists only if the condition of Eq. (71) is satisfied; that is, for ${\Omega }_{\Lambda 0}>0.44$.

Figure 5

Dependence of $\Sigma (z)$ on the value of ${\Omega }_{\Lambda 0}$ for an UV cutoff $k_{\mathrm{UV}}=0.5{\mathrm{Mpc}}^{-1}$. The position of the peak corresponds to the value of $z_{\max }$ depicted in Fig. 4. ${\Omega }_{\Lambda 0}$ ranges from 0.2 to 0.9 by steps of 0.1 (with the addition of the curve correspondent to ${\Omega }_{\Lambda 0}=0.73$). The dashed curves do not satisfy the condition of Eq. (71) and have no maximum. The thick curve is the one which corresponds to ${\Omega }_{\Lambda 0}=0.73$.

Figure 6

Amplitude of the peak $\Sigma (z_{\max })$ as a function of ${\Omega }_{\Lambda 0}$. From bottom to top, $k_{\mathrm{UV}}=0.1$, 0.5, $1{\mathrm{Mpc}}^{-1}$, and we have used the two regularization schemes [Eq. (64) (solid lines) and Eq. (65) (dashed lines)]. It decreases with ${\Omega }_{\Lambda 0}$.

Figure 7

Dependence of $\tilde{A}$ on the cosmological parameters, normalized to its value for ${\Omega }_{\Lambda 0}=0.73$.