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Register a new userEuclid: Forecasts from redshift-space distortions and the Alcock-Paczynski test with cosmic voids
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Euclid will survey galaxies in a cosmological volume of unprecedented size, providing observations of more than a billion objects distributed over a third of the full sky. Approximately 20 million of these galaxies will have spectroscopy available, allowing us to map the three-dimensional large-scale structure of the Universe in great detail. This paper investigates prospects for the detection of cosmic voids therein, and the unique benefit they provide for cosmology. In particular, we study the imprints of dynamic and geometric distortions of average void shapes and their constraining power on the growth of structure and cosmological distance ratios. To this end, we make use of the Flagship mock catalog, a state-of-the-art simulation of the data expected to be observed with Euclid. We arrange the data into four adjacent redshift bins, each of which contains about 11000 voids, and estimate the void-galaxy cross-correlation function in every bin. Fitting a linear-theory model to the data, we obtain constraints on $f/b$ and $D_M H$, where $f$ is the linear growth rate of density fluctuations, $b$ the galaxy bias, $D_M$ the comoving angular diameter distance, and $H$ the Hubble rate. In addition, we marginalize over two nuisance parameters included in our model to account for unknown systematic effects in the analysis. With this approach Euclid will be able to reach a relative precision of about 4% on measurements of $f/b$ and 0.5% on $D_M H$ in each redshift bin. Better modeling or calibration of the nuisance parameters may further increase this precision to 1% and 0.4%, respectively. Our results show that the exploitation of cosmic voids in Euclid will provide competitive constraints on cosmology even as a stand-alone probe. For example, the equation-of-state parameter $w$ for dark energy will be measured with a precision of about 10%, consistent with earlier more approximate forecasts.
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Baryon acoustic oscillations (BAO), known as one of the largest cosmological objects, is now recognized as standard cosmological tool to measure geometric distances via the Alcock-Paczynski effect, by which the observed BAO exhibits characteristic anisotropies in addition to the redshift distortions. This implies that once we know the correct distances to the observed BAO, the tip points of baryon acoustic peaks in the anisotropic correlation function of galaxies, $xi(sigma,pi)$, can form a great circle (hereafter 2D BAO circle) in the $sigma$ and $pi$ plane, where $sigma$ and $pi$ are the separation of galaxy pair parallel and perpendicular to the line-of-sight, respectively. This 2D BAO circle remains unchanged under the variations of the unknown galaxy bias and/or coherent motion, while it varies transversely and radially with respect to the variations of $D_A$ and $H^{-1}$, respectively. Hereby the ratio between transverse distance $D_A$ and the radial distance $H^{-1}$ reproduces the intrinsic shape of 2D BAO circle, which is {it a priori} given by the known broadband shape of spectra. All BAO peaks of $xi(sigma,pi)$ are precisely calculated with the improved theoretical model of redshift distortion. We test this broadband Alcock--Paczynski method using BOSS--like mock catalogues. The transverse and radial distances are probed in precision of several percentage fractional errors, and the coherent motion is observed to match with the fiducial values accurately.
We apply the Alcock-Paczynski (AP) test to the stacked voids identified using the large-scale structure galaxy catalog from the Baryon Oscillation Spectroscopic Survey (BOSS). This galaxy catalog is part of the Sloan Digital Sky Survey (SDSS) Data Release 12 and is the final catalog of SDSS-III. We also use 1000 mock galaxy catalogs that match the geometry, density, and clustering properties of the BOSS sample in order to characterize the statistical uncertainties of our measurements and take into account systematic errors such as redshift space distortions. For both BOSS data and mock catalogs, we use the ZOBOV algorithm to identify voids, we stack together all voids with effective radii of 30-100Mpc/h in the redshift range 0.43-0.7, and we accurately measure the shape of the stacked voids. Our tests with the mock catalogs show that we measure the stacked void ellipticity with a statistical precision of 2.6%. We find that the stacked voids in redshift space are slightly squashed along the line of sight, which is consistent with previous studies. We repeat this measurement of stacked void shape in the BOSS data assuming several values of Omega_m within the flat LCDM model, and we compare to the mock catalogs in redshift space in order to perform the AP test. We obtain a constraint of $Omega_m = 0.38^{+0.18}_{-0.15}$ at the 68% confidence level from the AP test. We discuss the various sources of statistical and systematic noise that affect the constraining power of this method. In particular, we find that the measured ellipticity of stacked voids scales more weakly with cosmology than the standard AP prediction, leading to significantly weaker constraints. We discuss how AP constraints will improve in future surveys with larger volumes and densities.
We develop an improved Alcock-Paczynski (AP) test method that uses the redshift-space two-point correlation function (2pCF) of galaxies. Cosmological constraints can be obtained by examining the redshift dependence of the normalized 2pCF, which should not change apart from the expected small non-linear evolution. An incorrect choice of cosmology used to convert redshift to comoving distance will manifest itself as redshift-dependent 2pCF. Our method decomposes the redshift difference of the two-dimensional correlation function into the Legendre polynomials whose amplitudes are modeled by radial fitting functions. Our likelihood analysis with this 2-D fitting scheme tightens the constraints on $Omega_m$ and ${w}$ by $sim 40%$ compared to the method of Li et al. (2016, 2017, 2018) that uses one dimensional angular dependence only. We also find that the correction for the non-linear evolution in the 2pCF has a non-negligible cosmology dependence, which has been neglected in previous similar studies by Li et al.. With an accurate accounting for the non-linear systematics and use of full two-dimensional shape information of the 2pCF down to scales as small as $5~h^{-1}{rm Mpc}$ it is expected that the AP test with redshift-space galaxy clustering anisotropy can be a powerful method to constrain the expansion history of the universe.
Feasibility of the Alcock Paczynski (AP) test by stacking voids in the 21cm line intensity field is presented. We analyze the Illstris-TNG simulation to obtain the 21cm signal map. We then randomly distribute particles depending on the 21cm intensity field to find voids by using publicly available code, VIDE. As in the galaxy clustering, the shape of the stacked void in the 21cm field is squashed along the line of sight due to the peculiar velocities in redshift-space, although it becomes spherical in real-space. The redshift-space distortion for the stacked void weakly depends on redshift and we show that the dependency can be well described by the linear prediction, with the amplitude of the offset being free parameters. We find that the AP test using the stacked voids in a 21cm intensity map is feasible and the parameter estimation on $Omega_{rm m}$ and $w$ is unbiased.
We have derived estimators for the linear growth rate of density fluctuations using the cross-correlation function of voids and haloes in redshift space, both directly and in Fourier form. In linear theory, this cross-correlation contains only monopole and quadrupole terms. At scales greater than the void radius, linear theory is a good match to voids traced out by haloes in N-body simulations; small-scale random velocities are unimportant at these radii, only tending to cause small and often negligible elongation of the redshift-space cross-correlation function near its origin. By extracting the monopole and quadrupole from the cross-correlation function, we measure the linear growth rate without prior knowledge of the void profile or velocity dispersion. We recover the linear growth parameter $beta$ to 9% precision from an effective volume of 3(Gpc/h)^3 using voids with radius greater than 25Mpc/h. Smaller voids are predominantly sub-voids, which may be more sensitive to the random velocity dispersion; they introduce noise and do not help to improve the measurement. Adding velocity dispersion as a free parameter allows us to use information at radii as small as half of the void radius. The precision on $beta$ is reduced to approximately 5%. Contrary to the simple redshift-space distortion pattern in overdensities, voids show diverse shapes in redshift space, and can appear either elongated or flattened along the line of sight. This can be explained by the competing amplitudes of the local density contrast, plus the radial velocity profile and its gradient, with the latter two factors being determined by the cumulative density profile of voids. The distortion pattern is therefore determined solely by the void profile and is different for void-in-cloud and void-in-void. This diversity of redshift-space void morphology complicates measurements of the Alcock-Paczynski effect using voids.
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