Voids as a precision probe of dark energy

The shapes of cosmic voids, as measured in spectroscopic galaxy redshift surveys, constitute a promising new probe of dark energy (DE). We forecast constraints on the DE equation of state and its variation from current and future surveys and find that the promise of void shape measurements compares favorably to that of standard methods such as supernovae and cluster counts even for currently available data. Owing to the complementary nature of the constraints, void shape measurements improve the Dark Energy Task Force figure of merit by 2 orders of magnitude for a future large scale experiment such as EUCLID when combined with other probes of dark energy available on a similar time scale. Modeling several observational and theoretical systematics has only moderate effects on these forecasts. We discuss additional systematics which will require further study using simulations.

Figure 1

Left panel: the derivative of the growth function with respect to the dark energy parameters $w_0$ and $w_a$. The growth function shown has been normalized to unity at a redshift of 0.01. Right panel: the theoretical distribution of the largest ellipticity $ϵ$ as a function of $\sigma (R,z)$ for ${\delta }_{\mathrm{lin}}=-2.81$.

Figure 2

Setting the minimum size of voids: the dashed red curve shows the $R_{\min }^{V\mathrm{inc}}$, while the solid thin (thick) curves show (twice) the average separation of observed galaxies for a SDSS DR7–like survey (left) and a EUCLID-like survey (right). At a particular redshift, we only consider voids with sizes larger than both these scales.

Figure 3

Comparison of forecasts on one $\sigma$ constraints on the CPL parameters with standard probes using the identification $R_{\mathrm{Smooth}}=R_{\mathrm{Void}}/4$, $A=1$, and ${\sigma }_{ϵ}=0.1$: for data from the near future (left panels) and futuristic data (right panels). PLANCK and HST priors were used in all of these forecasts. For reference, we show the current constraints [40] in the thick green contours, and forecasted constraints from clusters $(\mathrm{\text{number counts and power spectrum}})+\mathrm{\text{PLANCK}}$ taken from 79.

Figure 4

Effects of shot noise: sensitivity of one sigma constraints to the efficiency of the void finder: degradation of constraints due to low efficiency of the void finder with the constraints shown in Fig. 3 assuming high efficiency from the near future (left panel) and futuristic data (right panel). HST and PLANCK constraints were used in all these plots.

Figure 5

Impact of bias: degraded constraints on voids due to marginalization over a linear scale independent bias compared to constraints shown in Fig. 3 for data from the near future (left panel) and futuristic data (right panel). HST and PLANCK priors were considered for all of these plots.

Figure 6

Sensitivity of Fisher constraints with respect to the prescription of void selection: comparison of the constraints (red open circles) from voids shown in Fig. 3 with other prescriptions. PLANCK and HST priors were used in all these plots. The other prescriptions lead to better constraints.

Figure 7

Sensitivity of Fisher constraints with ${\sigma }_{ϵ}$: comparison of constraints from voids (open red circles) with ${\sigma }_{ϵ}=0.1$ shown in Fig. 3 with pessimistically degraded constraints from voids due to a larger ${\sigma }_{ϵ}=0.4$ for data in the near future (left panel) and in the far future (right panel). Despite the degradation, the constraints are still interesting. HST and PLANCK priors were used in all the plots.

Figure 8

Comparison of the distribution of ellipticity $e$ (prolateness $p$) in the left (right) panel according to Doroshkevich formula with the distribution obtained from generalized excursion set formalism described for different values of $\nu =\frac{\delta }{\sigma }$.

Figure 9

A comparison of evolution of the axes ratios $\alpha$ and $\beta$ of the void ellipsoid computed using the linear tide approximation of Bond and Myers [64] (blue dots), the nonlinear tide approximation (magenta dots) against the ratios computed using Zeldovich approximation for different values of the axes ratio $\beta$.