Constraints on a New Post-General Relativity Cosmological Parameter

A new cosmological variable is introduced which characterizes the degree of departure from Einstein's General Relativity (GR) with a cosmological constant. The new parameter, \varpi, is the cosmological analog of \gamma, the parametrized post-Newtonian variable which measures the amount of spacetime curvature per unit mass. In the cosmological context, \varpi measures the difference between the Newtonian and longitudinal potentials in response to the same matter sources, as occurs in certain scalar-tensor theories of gravity. Equivalently, \varpi measures the scalar shear fluctuation in a dark energy component. In the context of a "vanilla" LCDM background cosmology, a non-zero \varpi signals a departure from GR or a fluctuating cosmological constant. Using a phenomenological model for the time evolution \varpi=\varpi_0 \rho_{DE}/\rho_{M} which depends on the ratio of energy density in the cosmological constant to the matter density at each epoch, it is shown that the observed cosmic microwave background (CMB) temperature anisotropies limit the overall normalization constant to be -0.4 < \varpi_0 < 0.1 at the 95% confidence level. Existing measurements of the cross-correlations of the CMB with large-scale structure further limit \varpi_0 > -0.2 at the 95% CL. In the future, integrated Sachs-Wolfe and weak lensing measurements can more tightly constrain \varpi_0, providing a valuable clue to the nature of dark energy and the validity of GR.