Precision Cosmography With Stacked Voids

Abstract

We present a purely geometrical method for probing the expansion history of the Universe from the observation of the shape of stacked voids in spectroscopic redshift surveys. Our method is an Alcock-Paczyński test based on the average sphericity of voids posited on the local isotropy of the Universe. It works by comparing the temporal extent of cosmic voids along the line of sight with their angular, spatial extent. We describe the algorithm that we use to detect and stack voids in redshift shells on the light cone and test it on mock light cones produced from N -body simulations. We establish a robust statistical model for estimating the average stretching of voids in redshift space and quantify the contamination by peculiar velocities. Finally, assuming that the void statistics that we derive from N -body simulations is preserved when considering galaxy surveys, we assess the capability of this approach to constrain dark energy parameters. We report this assessment in terms of the figure of merit (FoM) of the dark energy task force and in particular of the proposed EUCLID mission which is particularly suited for this technique since it is a spectroscopic survey. The FoM due to stacked voids from the EUCLID wide survey may double that of all other dark energy probes derived from EUCLID data alone (combined with Planck priors). In particular, voids seem to outperform Baryon Acoustic Oscillations by an order of magnitude. This result is consistent with simple estimates based on mode-counting. The Alcock-Paczyński test based on stacked voids may be a significant addition to the portfolio of major dark energy probes and its potentialities must be studied in detail.

Observational probes of cosmic acceleration

“…A naive estimate for the error on the mean ellipticity of voids with rms ellipticity ǫ rms in a survey volume V is σǭ ∼ ǫ rms (f V / 4 3 πR 3 ) −1/2 ≈ 6 × 10 −4 (ǫ rms /0.3)(f V /1 h −3 Gpc 3 ) −1/2 (R/10 h −1 Mpc) −3/2 , if the galaxy density is high enough to make the shot noise contribution to the ellipticity scatter negligible on scale R. Peculiar velocities have a small, though not negligible, impact on void sizes and shapes (Little et al, 1991;Ryden and Melott, 1996;Lavaux and Wandelt, 2012), so one can hope that the uncertainty in this impact will be small, but this hope has yet to be tested. Assuming statistical errors only, Lavaux and Wandelt (2012) estimate that a void-based AP constraint from a Euclid-like redshift survey would provide several times better dark energy constraints than the BAO measurement from the same data set, mainly because the scale of voids is so much smaller than the BAO scale. Sutter et al (2012) have recently applied the AP test to a void catalog constructed from the SDSS DR7 redshift surveys, though with this sample the statistical errors are too large to yield a significant detection of the predicted effect.…”

Cosmological Constraints From the Redshift Dependence of the Alcock–paczynski Effect: Application to the SDSS-Iii Boss Dr12 Galaxies

“…The effect depends on both redshift and underlying cosmology, and is rather difficult to model accurately (Jennings et al 2011). Ryden (1995) and Lavaux & Wandelt (2012) proposed another method using the apparent stretching of voids. This approach has the advantage that the void regions are easier to model compared with dense regions, but has limitations in that it utilizes only low density regions of the LSS and requires large samples.…”

A Cosmic Void Catalog of SDSS DR12 BOSS Galaxies

“…The size and shape distribution of voids, their intrinsic structure, and their counts can provide insights into the growth of structure (Jennings et al 2013) and dark energy (Lee & Park 2009;Biswas et al 2010;Bos et al 2012;Pisani et al 2015). Moreover, the Alcock-Paczyński test (Alcock & Paczynski 1979) can be applied to "stacked" voids to probe the expansion history of the universe (Ryden 1995;Lavaux & Wandelt 2012;Sutter et al 2012a). Voids can also be correlated with the cosmic microwave background (Bennett et al 2013) to study the integrated Sachs-Wolfe effect (Thompson & Vishniac 1987;Granett et al 2008;Planck Collaboration et al 2014).…”