Constraints on a new post-general relativity cosmological parameter

A new cosmological variable is introduced to characterize the degree of departure from Einstein's general relativity with a cosmological constant. The new parameter, pi, 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, pi 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, pi measures the scalar shear fluctuation in a dark-energy component. In the context of a vanilla, cosmological constant-dominated universe, a nonzero pi signals a departure from general relativity or a fluctuating cosmological constant. Using a phenomenological model for the time evolution pi=pi(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 temperature anisotropies limit the overall normalization constant to be -0.4 < 0.1 at the 95% confidence level. Existing measurements of the cross-correlations of the cosmic microwave background with large-scale structure further limit pi(0)>-0.2 at the 95% CL. In the future, integrated Sachs-Wolfe and weak lensing measurements can more tightly constrain pi(0), providing a valuable clue to the nature of dark energy and the validity of general relativity.