Probing modifications of General Relativity using current cosmological observations

TL;DR

This work tests General Relativity against current cosmological observations by parameterizing deviations in linear perturbations with μ(a,k) and η(a,k) (or Σ(a,k)). It deploys two approaches: a simple redshift-transition model (X_I) and a scale- and redshift-resolved PCA (X_II) within a Boltzmann framework, using CMB (WMAP5), ISW cross-correlations, SNe, and CFHTLS weak lensing data. The main finding is that GR remains consistent with the data, with the ISW signal providing the strongest constraint on the lensing potential evolution, and seven of eight PCA modes aligning with GR; a single 2σ deviation is traced to a known WL systematic rather than new physics. The results underscore the value of flexible, scale-dependent parametrizations to leverage the full information content of structure growth and expansion history, and they point to future surveys (DES, Pan-STARRS, LSST, Euclid) as capable of tightening these tests further.

Abstract

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 Newton's 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.

Figures (10)

• Figure 1: Imprints of modified gravity parametrized by $\mathcal{X}_{\rm I}$ on the weak lensing aperture mass dispersion (panels $A_1, A_2$), relative difference in $M_{\rm ap}^{1/2}$ with respect to GR ($B_1, B_2$), and relative difference in $\Delta$ with respect to GR ($C_1, C_2$). The model parameters are shown in the legend of panel ($A_1$). The shaded regions in panels ($A_1,A_2,B_1,B_2$) are excluded from our analysis. The data with error bars over-plotted in panels ($A_1, A_2$) are taken from the CFHTLS survey.
• Figure 2: Imprints of modified gravity parametrized by $\mathcal{X}_{\rm I}$ on the CMB TT power spectra for different threshold redshift $z_s$ and different transition width $\Delta{z}$. Different models are distinguished by different line styles and colors, as shown in panel ($A_1$) of Fig. \ref{['fig:WL_imprint']}. The data points with error bars are taken from the WMAP 5-year survey.
• Figure 3: 68% and 95% C.L. contour plots for $\{\mu_0,~\eta_0\}$ and $\{\mu_0,~\Sigma_0\}$ for two different threshold redshifts: $z_s=1$ (upper panels) and $z_s=2$ (lower panels). In both cases the transition width is fixed to $\Delta{z}=0.05$. From outside in, the shaded regions in cyan, yellow and blue illustrate the contours derived from the data of CFHTLS+CMB shift parameters, CFHTLS+WMAP5 and CFHTLS+WMAP5+ISW, respectively. For the contours shaded in the same color, the light and dark regions show the 68% and 95% C.L. contour respectively. In all cases, the SNe data are combined, and the priors of cosmic age, BBN and HST are applied. The star denotes the GR values.
• Figure 4: 68% and 95% C.L. contour plots for $\{\mu_0,~\eta_0\}$ and $\{\mu_0,~\Sigma_0\}$ for two different threshold redshifts: $z_s=1$ (upper panels) and $z_s=2$ (lower panels). In both cases the transition width is fixed to $\Delta{z}=0.05$. From outside in, the shaded regions in yellow and blue illustrate the contours derived from the data of WMAP5 and WMAP5+ISW, respectively. For the contours shaded in the same color, the light and dark regions show the 68% and 95% C.L. contour respectively. In all cases, the SNe data are combined, and the priors of cosmic age, BBN and HST are applied. The star denotes the GR values.
• Figure 5: 68% (dark shaded) and 95% C.L. (light shaded) contour plots for $\{\mu_0,\Sigma_0\}$ and $\{\mu_0,\eta_0\}$ for two different threshold redshifts: $z_s=1$ (upper panels) and $z_s=2$ (lower panels). All the constraints are from the combined data of ISW, WMAP5 and CFHTLS. To obtain the front, green contours, the transition width is fixed to $\Delta{z}=0.05$, while the blue contours on the back layers show the case of a floating $\Delta{z}$, which is marginalized over. The dashed curves show the covered contour edges. The star illustrates the GR values.