Constraints on a New Post-General Relativity Cosmological Parameter

TL;DR

This work introduces a cosmological post-Newtonian parameter $\varpi$ that quantifies the slip between the Newtonian and longitudinal potentials, capturing departures from GR or dark-energy shear in a $\Lambda$CDM background. It adopts a simple phenomenological evolution $\varpi = \varpi_0 \rho_{DE}/\rho_M$ and develops practical perturbation-evolution schemes to assess cosmological observables, notably the CMB via a modified CMBfast code. The main results show that current CMB measurements constrain $-0.4 < \varpi_0 < 0.1$ (95% C.L.), strengthened by ISW cross-correlations to require $\varpi_0 > -0.2$, with future ISW and weak-lensing data capable of tightening these bounds. These constraints provide a viable pathway to test GR on cosmological scales and to probe the nature of dark energy through possible anisotropic stress.

Abstract

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 γ, 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 ρ_{DE}/ρ_{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.

Figures (7)

• Figure 1: The CMB anisotropy spectra under recipe R1 are shown for different values of $\varpi_0$. R3 produces identical spectra. The backgrounds for all models are identical: $\Omega_m = 0.35$, $h=0.65$ and dark energy with $w=-1$.
• Figure 2: The CMB anisotropy spectra under different recipes are shown for $\varpi_0=-0.1$.
• Figure 3: Likelihood distribution for $\varpi_0$ due to WMAP 3-year CMB temperature measurements for a flat, "concordance," $\Lambda$CDM model with $\Omega_{\Lambda}=0.76$, $\Omega_b=0.02$, $h=0.73$, adiabatic and scalar inflationary pertubations with a spectral index of $n_s=0.958$, and an optical depth of $\tau=0.08$. The $95 \%$ CL range is $-0.28 < \varpi_0 <0.05$ with a peak at a slightly negative value of $\varpi_0$ owing to the decrease in large-scale power.
• Figure 4: Likelihood distributions for $\varpi_0$ due to WMAP 3-year CMB temperature measurements within the framework of different dark energy models. The curve with dots is for $\Lambda$CDM, as in the previous figure. The solid and dotted curves are for a dark energy model with $w=-0.8$, with parameters chosen to reproduce the acoustic peak structure of the $\Lambda$CDM model, but with dark energy perturbation sound speed $c_s^2=1,\,0$. The sound speed does not have a strong effect on the likelihood range. Allowing for a range in equation of state $-1.2 < w < -0.8$, then we obtain a conservative bound $-0.4 <\varpi_0 <0.1$ at $95 \%$ CL.
• Figure 5: Contributions to the integrated Sachs-Wolfe effect as a function of the redshift $z$ for different values of $\varpi_0$.