Large Scale Structure as a Probe of Gravitational Slip

TL;DR

The paper introduces a time-dependent gravitational slip parameter $\varpi$ within a parametrized post-Friedmannian (PPF) framework to test departures from General Relativity on cosmological scales. By enforcing $\psi=(1+\varpi)\phi$ and linking $\varpi$ to dark energy through $\varpi(\tau,\vec{x})=\varpi_0\rho_{\rm DE}/\rho_m$, the authors implement the modified perturbation evolution in a CMBfast-based code and explore implications for the CMB, growth of structure, weak lensing, and ISW–galaxy cross-correlations. They find that current data mildly favor a non-zero $\varpi_0$ in some probes (notably weak lensing) but show tension with ISW measurements, and that a joint, multi-parameter analysis is needed to draw robust conclusions. The work emphasizes the potential of a single, standardized parameter to probe gravity on large scales and calls for improved data to resolve the viability of gravitational slip in cosmology.

Abstract

A new time-dependent, scale-independent parameter, \varpi, is employed in a phenomenological model of the deviation from General Relativity in which the Newtonian and longitudinal gravitational potentials slip apart on cosmological scales as dark energy, assumed to be arising from a new theory of gravitation, appears to dominate the universe. A comparison is presented between \varpi and other parameterized post-Friedmannian models in the literature. The effect of \varpi on the cosmic microwave background anisotropy spectrum, the growth of large scale structure, the galaxy weak-lensing correlation function, and cross-correlations of cosmic microwave background anisotropy with galaxy clustering are illustrated. Cosmological models with conventional maximum likelihood parameters are shown to find agreement with a narrow range of gravitational slip.

Figures (16)

• Figure 1: CMB anisotropy power spectra for different $\varpi_0$ cosmologies are shown with the binned WMAP 3-year data. All differences are localized to the low multipole moments: the spectra are normalized so that the higher multipole moments for all models are identical to the case of $\varpi_0=0$, corresponding to the WMAP3 ML model.
• Figure 2: The predicted CMB temperature anisotropy quadrupole power is shown as a function of $\varpi_0$ (solid curve). All other parameters are set to the WMAP3 ML cosmology. The central value and 1$\sigma$ upper bound of the WMAP 3 year data, $6 C_2/2\pi=211\pm860$wmapdata, are shown by the dashed and dot-dashed curves.
• Figure 3: The likelihood of $\varpi_0$ due to the CMB, calculated using the November 2006 version of the WMAP likelihood code wmapdata, is shown. All other cosmological parameters are set to the WMAP3 ML (solid curve) or the WMAP3+SNGold ML (dashed curve) model. The results include the TT and TE spectra. The results are consistent with $\varpi_0=0$ ($\Lambda$CDM), but favor positive values of $\varpi_0$. The locations of the primary (left) and secondary (right) likelihood peaks correspond to the range of $\varpi_0$ for which the predicted quadrupole lies within the 2$\sigma$ range of WMAP.
• Figure 4: The equivalence of alternative techniques for evolving cosmological perturbations under PPF gravitation is illustrated by the effect on CMB anisotropy spectra. Lines show the spectra produced following our procedure (equations \ref{['alphadot']}-\ref{['hdot']}) with the parameterization (\ref{['varpievolution']}) replaced by that proposed in BZ, $\varpi(a)=-\beta a^s/(1+\beta a^s)$ with $s=3$. Symbols indicate the spectra produced following BZ's procedure (equations \ref{['zetaeqn']}-\ref{['alphadotbz']}). The agreement between the techniques is exact.
• Figure 5: The effect of the parameterization of gravitational slip on CMB anisotropy spectra is shown. Lines show the spectra produced using our parameterization, equation (\ref{['varpievolution']}); symbols indicate spectra produced using the BZ's parameterization, $\phi/\psi=1+\beta a^s$ with $s=3$. To compare, the parameter $\beta$ is set to $\beta=-\varpi_0\Omega_\Lambda/\Omega_m$. The agreement is excellent in the limit of small $\beta$.