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 .