Probing modifications of General Relativity using current cosmological
  observations
  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.
