Confronting General Relativity with Further Cosmological Data

TL;DR

This work develops a model-independent, redshift- and scale-bin framework to test deviations from general relativity using cosmological data. It introduces decorrelated post-GR variables $\mathcal{G}$ and $\mathcal{V}$ that encode the sum of metric potentials and the growth of structure, respectively, and employs an extensive MCMC analysis with current data (including Tg and gg measurements) to constrain them. The study finds GR is consistent in most bins, with CFHTLS data alone producing apparent but likely systematic deviations that vanish when using COSMOS data; Tg and gg data tighten high-$k$ constraints on growth-related deviations. It further forecasts that next-generation surveys like BigBOSS, combined with Planck and JDEM, can improve constraints on the post-GR parameters by factors of 10–100 across the $z$–$k$ plane, enabling precise, time- and scale-dependent tests of gravity.

Abstract

Deviations from general relativity in order to explain cosmic acceleration generically have both time and scale dependent signatures in cosmological data. We extend our previous work by investigating model independent gravitational deviations in bins of redshift and length scale, by incorporating further cosmological probes such as temperature-galaxy and galaxy-galaxy cross-correlations, and by examining correlations between deviations. Markov Chain Monte Carlo likelihood analysis of the model independent parameters fitting current data indicates that at low redshift general relativity deviates from the best fit at the 99% confidence level. We trace this to two different properties of the CFHTLS weak lensing data set and demonstrate that COSMOS weak lensing data does not show such deviation. Upcoming galaxy survey data will greatly improve the ability to test time and scale dependent extensions to gravity and we calculate the constraints that the BigBOSS galaxy redshift survey could enable.

Figures (11)

• Figure 1: 1D marginalized probability of the post-GR parameter $\varpi$ in the redshift bin $1<z<2$. The narrower, dashed (black) distribution fixes the other post-GR parameter $\mu=1$, making it more difficult to fit the data (consistent with GR) by compensating one parameter with another. The wider, solid (red) distribution includes a simultaneous fit for $\mu$. All other cosmological parameters, including $\varpi$ and $\mu$ in the lower and higher redshift bins, are marginalized over.
• Figure 2: 2D joint probability contours at 95% cl between the post-GR functions $\varpi$ and $\mu$, for three independent redshift bins. Values within the redshift bins are consistent with each other and with GR (denoted by the cross at (0,0)). The solid, black curve, motivated by a modified Poisson equation, closely follows the degeneracy direction, and suggests a more insightful parametrization using variables along and perpendicular to the curve.
• Figure 3: 68% and 95% confidence limit contours for ${\mathcal{V}}-1$ and ${\mathcal{G}}-1$ are given for $2\times2$ binning in redshift and $k$ space, using WMAP7 Jarosik:2010iu, Union2 amanullah, and CFHTLS Fu:2007qq data. The diagonal, dot-dashed line denotes values of ${\mathcal{V}}$ and ${\mathcal{G}}$ for which $\mu=0$ and gravity vanishes (see Eq. \ref{['eq:mudef']}). The x's denote GR values.
• Figure 4: The square of the aperture mass (see Eq. 5 of Fu:2007qq) is plotted for different cosmological models in comparison to data from the CFHTLS survey. The solid, black curve shows the results from the $\Lambda$CDM concordance model in GR. One can match the small angle behavior by suppressing growth through decreasing the gravitational coupling ${\mathcal{G}}$, but increasing growth by increasing $\Omega_m$. Exploring the larger angular scales, the dashed, red curve shows the effect of changing ${\mathcal{G}}(k>0.01\,\text{Mpc}^{-1};z<1)$ while compensating $\Omega_m$. The dot-dashed, green curve shows the case for ${\mathcal{G}}(k>0.1~\text{Mpc}^{-1}; z<1)$ as taken in Fig. 8 of Zhao:2010dz. Because this parametrization divides $k$ bins in the midst of the scales probed by the data, this curve fits better the (possibly spurious) bump in $\langle M^2_{ap}\rangle$ seen in the data between $60~\text{arcmin}<\theta<180~\text{arcmin}$. Data is taken from Table B2 of Fu:2007qq.
• Figure 5: A view of the data in Fig. \ref{['fig:zhaomap']} with a log scale in $\theta$ to zoom in on small angles. The theory curves use bins divided at $k_{\rm bin}=0.01\text{Mpc}^{-1}$, and each is generated with identical background cosmology parameters, fixing the amplitude of the primordial scalar perturbations, so that different post-GR parameter values give different values of $\sigma_8$. Labeled values of ${\mathcal{V}}-1$ are set in the high $k$ -- high $z$ bin. Values of ${\mathcal{G}}-1$ in the high $k$ -- low $z$ bin are then given by the approximate degeneracy relation ${\mathcal{G}}-1=-0.2({\mathcal{V}}-1)+0.06$. All other post-GR parameters are set to zero. To fit the rise at small angles, much steeper than in GR, requires very negative ${\mathcal{V}}$ and hence low $\sigma_8$. Even raising the primordial perturbation amplitude (dashed red curve) cannot bring $\sigma_8$ into the usual range. Values of $\chi^2$ reported in the legend are calculated naively assuming a diagonal covariance matrix using the error bars shown. The four smallest-scale data points are excluded from the $\chi^2$ calculation.