Probing the imprint of interacting dark energy on very large scales

The observed galaxy power spectrum acquires relativistic corrections from light-cone effects, and these corrections grow on very large scales. Future galaxy surveys in optical, infrared and radio bands will probe increasingly large wavelength modes and reach higher redshifts. In order to exploit the new data on large scales, an accurate analysis requires inclusion of the relativistic effects. This is especially the case for primordial non-Gaussianity and for extending tests of dark energy models to horizon scales. Here we investigate the latter, focusing on models where the dark energy interacts nongravitationally with dark matter. Interaction in the dark sector can also lead to large-scale deviations in the power spectrum. If the relativistic effects are ignored, the imprint of interacting dark energy will be incorrectly identified and thus lead to a bias in constraints on interacting dark energy on very large scales.

Figure 1

Evolution of the IDE effective equation of state parameters $w_{x,\text{eff}}$, for the $w\mathrm{CDM}$ equation of state parameters $w_x=-0.8$ (left panel) and $w_x=-1.1$ (right panel). Solid lines correspond to model 1 (27), while dashed lines correspond to model 2 (30), and the $w_x$ line denotes $\mathrm{\Gamma }=0=\xi$.

Figure 2

Ratios of the matter density parameters (left) and Hubble rates (right) for $iw\mathrm{CDM}$ relative to those of $w\mathrm{CDM}$: with $w_x=-0.8$ (top panels) and $w_x=-1.1$ (bottom panels). Line styles are as in Fig. 1.

Figure 3

The ratio of the matter overdensity and gravitational potential growth functions, at $a_0=1$ (or $z=0$), with $w_x=-0.8$. Solid lines correspond to model 1 (27) and dashed lines to model 2 (30). The $\mathrm{\Lambda }\mathrm{CDM}$ case (dashed black line) and the Hubble horizon (solid black line) are also shown.

Figure 4

Observed galaxy power spectrum $P_{\mathrm{g}}^{\text{obs}}$ (solid lines) and the standard power spectrum $P_{\mathrm{g}}^{\text{std}}$ (dashed lines) along the line of sight ($\mu =1$), at $z=0$: for $w_x=-0.8$ (top); and for $w_x=-1.1$ (bottom). The corresponding ratios of the power spectra are given on the right panels.

Figure 5

Ratios of the observed galaxy power spectrum $P_{\mathrm{g}}^{\text{obs}}$ to the standard power spectrum $P_{\mathrm{g}}^{\text{std}}$ along the line of sight ($\mu =1$), at $z=1$: for $w_x=-0.8$ (left) and $w_x=-1.1$ (right).

Figure 6

Ratios of ${\tilde{P}}_{\mathrm{g}}^{\text{obs}}$, which is $P_{\mathrm{g}}^{\text{obs}}$ with the correlation between ${\mathrm{\Delta }}_{\mathrm{g}}^{\text{std}}$ and ${\mathrm{\Delta }}_{\mathrm{g}}^{\text{GR}}$ subtracted, to the standard power spectrum $P_{\mathrm{g}}^{\text{std}}$, along the line of sight ($\mu =1$). Top panels have $z=0$, for $w_x=-0.8$ (top left) and $w_x=-1.1$ (top right). Similarly for $z=1$ in the bottom panels.