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Register a new userThe Observed Growth of Massive Galaxy Clusters III: Testing General Relativity on Cosmological Scales
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This is the third of a series of papers in which we derive simultaneous constraints on cosmological parameters and X-ray scaling relations using observations of the growth of massive, X-ray flux-selected galaxy clusters. Our data set consists of 238 clusters drawn from the ROSAT All-Sky Survey, and incorporates extensive follow-up observations using the Chandra X-ray Observatory. Here we present improved constraints on departures from General Relativity (GR) on cosmological scales, using the growth index, gamma, to parameterize the linear growth rate of cosmic structure. Using the method of Mantz et al. (2009a), we simultaneously and self-consistently model the growth of X-ray luminous clusters and their observable-mass scaling relations, accounting for survey biases, parameter degeneracies and systematic uncertainties. We combine the cluster growth data with gas mass fraction, SNIa, BAO and CMB data. This combination leads to a tight correlation between gamma and sigma_8. Consistency with GR requires gamma~0.55. Under the assumption of self-similar evolution and constant scatter in the scaling relations, and for a flat LCDM model, we measure gamma(sigma_8/0.8)^6.8=0.55+0.13-0.10, with 0.79<sigma_8<0.89. Relaxing the assumptions on the scaling relations by introducing two additional parameters to model possible evolution in the normalization and scatter of the luminosity-mass relation, we obtain consistent constraints on gamma that are only ~20% weaker than those above. Allowing the dark energy equation of state, w, to take any constant value, we simultaneously constrain the growth and expansion histories, and find no evidence for departures from either GR or LCDM. Our results represent the most robust consistency test of GR on cosmological scales to date. (Abridged)
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(Abridged) This is the first of a series of papers in which we derive simultaneous constraints on cosmological parameters and X-ray scaling relations using observations of the growth of massive, X-ray flux-selected galaxy clusters. Our data set consists of 238 clusters drawn from the ROSAT All-Sky Survey, and incorporates extensive follow-up observations using the Chandra X-ray Observatory. Here we describe and implement a new statistical framework required to self-consistently produce simultaneous constraints on cosmology and scaling relations from such data, and present results on models of dark energy. In spatially flat models with a constant dark energy equation of state, w, the cluster data yield Omega_m=0.23 +- 0.04, sigma_8=0.82 +- 0.05, and w=-1.01 +- 0.20, marginalizing over conservative allowances for systematic uncertainties. These constraints agree well and are competitive with independent data in the form of cosmic microwave background (CMB) anisotropies, type Ia supernovae (SNIa), cluster gas mass fractions (fgas), baryon acoustic oscillations (BAO), galaxy redshift surveys, and cosmic shear. The combination of our data with current CMB, SNIa, fgas, and BAO data yields Omega_m=0.27 +- 0.02, sigma_8=0.79 +- 0.03, and w=-0.96 +- 0.06 for flat, constant w models. For evolving w models, marginalizing over transition redshifts in the range 0.05-1, we constrain the equation of state at late and early times to be respectively w_0=-0.88 +- 0.21 and w_et=-1.05 +0.20 -0.36. The combined data provide constraints equivalent to a DETF FoM of 15.5. Our results highlight the power of X-ray studies to constrain cosmology. However, the new statistical framework we apply to this task is equally applicable to cluster studies at other wavelengths.
The apparent sizes and brightnesses of galaxies are correlated in a dipolar pattern around matter overdensities in redshift space, appearing larger on their near side and smaller on their far side. The opposite effect occurs for galaxies around an underdense region. These patterns of apparent magnification induce dipole and higher multipole terms in the cross-correlation of galaxy number density fluctuations with galaxy size/brightness (which is sensitive to the convergence field). This provides a means of directly measuring peculiar velocity statistics at low and intermediate redshift, with several advantages for performing cosmological tests of GR. In particular, it does not depend on empirically-calibrated scaling relations like the Tully-Fisher and Fundamental Plane methods. We show that the next generation of spectroscopic galaxy redshift surveys will be able to measure the Doppler magnification effect with sufficient signal-to-noise to test GR on large scales. We illustrate this with forecasts for the constraints that can be achieved on parametrised deviations from GR for forthcoming low-redshift galaxy surveys with DESI and SKA2. Although the cross-correlation statistic considered has a lower signal to noise than RSD, it will be a useful probe of GR since it is sensitive to different systematics.
We test general relativity (GR) at the effective redshift $bar{z} sim 1.5$ by estimating the statistic $E_G$, a probe of gravity, on cosmological scales $19 - 190,h^{-1}{rm Mpc}$. This is the highest-redshift and largest-scale estimation of $E_G$ so far. We use the quasar sample with redshifts $0.8 < z < 2.2$ from Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 (DR16) as the large-scale structure (LSS) tracer, for which the angular power spectrum $C_ell^{qq}$ and the redshift-space distortion (RSD) parameter $beta$ are estimated. By cross correlating with the $textit{Planck}$ 2018 cosmic microwave background (CMB) lensing map, we detect the angular cross-power spectrum $C_ell^{kappa q}$ signal at $12,sigma$ significance. Both jackknife resampling and simulations are used to estimate the covariance matrix (CM) of $E_G$ at $5$ bins covering different scales, with the later preferred for its better constraints on the covariances. We find $E_G$ estimates agree with the GR prediction at $1,sigma$ level over all these scales. With the CM estimated with $300$ simulations, we report a best-fit scale-averaged estimate of $E_G(bar{z})=0.30pm 0.05$, which is in line with the GR prediction $E_G^{rm GR}(bar{z})=0.33$ with $textit{Planck}$ 2018 CMB+BAO matter density fraction $Omega_{rm m}=0.31$. The statistical errors of $E_G$ with future LSS surveys at similar redshifts will be reduced by an order of magnitude, which makes it possible to constrain modified gravity models.
We test General Relativity (GR) using current cosmological data: the cosmic microwave background (CMB) from WMAP5 (Komatsu et al. 2009), the integrated Sachs-Wolfe (ISW) effect from the cross-correlation of the CMB with six galaxy catalogs (Giannantonio et al. 2008), a compilation of supernovae Type Ia (SNe) including the latest SDSS SNe (Kessler et al. 2009), and part of the weak lensing (WL) data from CFHTLS (Fu et al. 2008, Kilbinger et al. 2009) that probe linear and mildly non-linear scales. We first test a model where the effective Newtons constant, mu, and the ratio of the two gravitational potentials, eta, transit from the GR value to another constant at late times; in this case, we find that standard GR is fully consistent with the combined data. The strongest constraint comes from the ISW effect which would arise from this gravitational transition; the observed ISW signal imposes a tight constraint on a combination of mu and eta that characterizes the lensing potential. Next, we consider four pixels in time and space for each function mu and eta, and perform a Principal Component Analysis (PCA) finding that seven of the resulting eight eigenmodes are consistent with GR within the errors. Only one eigenmode shows a 2-sigma deviation from the GR prediction, which is likely to be due to a systematic effect. However, the detection of such a deviation demonstrates the power of our time- and scale-dependent PCA methodology when combining observations of structure formation and expansion history to test GR.
The next generation of weak lensing surveys will trace the evolution of matter perturbations and gravitational potentials from the matter dominated epoch until today. Along with constraining the dynamics of dark energy, they will probe the relations between matter overdensities, local curvature, and the Newtonian potential. We work with two functions of time and scale to account for any modifications of these relations in the linear regime from those in the LCDM model. We perform a Principal Component Analysis (PCA) to find the eigenmodes and eigenvalues of these functions for surveys like DES and LSST. This paper builds on and significantly extends the PCA analysis of Zhao et al. (2009) in several ways. In particular, we consider the impact of some of the systematic effects expected in weak lensing surveys. We also present the PCA in terms of other choices of the two functions needed to parameterize modified growth on linear scales, and discuss their merits. We analyze the degeneracy between the modified growth functions and other cosmological parameters, paying special attention to the effective equation of state w(z). Finally, we demonstrate the utility of the PCA as an efficient data compression stage which enables one to easily derive constraints on parameters of specific models without recalculating Fisher matrices from scratch.
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