A Multi-Parameter Investigation of Gravitational Slip

TL;DR

The paper tests deviations from general relativity on cosmological scales by introducing a gravitational slip parameter varpi0 in a LambdaCDM background, with varpi(z) = varpi0 (1+z)^{-3} and psi = [1+varpi(z)] phi. It develops a full perturbation analysis, implements varpi0 in CosmoMC, and confronts CMB, weak lensing, SN, and galaxy-CMB cross-correlation data, finding varpi0 = 0.09^{+0.74}_{-0.59} (2σ), i.e., consistency with GR within current uncertainties. The study highlights degeneracies with sigma8 and demonstrates that large-scale structure data are crucial to constrain gravitational slip. Forecasts for Planck and Euclid suggest roughly fourfold improvement, potentially revealing or ruling out PPF-type departures from GR with higher precision.

Abstract

A detailed analysis of gravitational slip, a new post-general relativity cosmological parameter characterizing the degree of departure of the laws of gravitation from general relativity on cosmological scales, is presented. This phenomenological approach assumes that cosmic acceleration is due to new gravitational effects; the amount of spacetime curvature produced per unit mass is changed in such a way that a universe containing only matter and radiation begins to accelerate as if under the influence of a cosmological constant. Changes in the law of gravitation are further manifest in the behavior of the inhomogeneous gravitational field, as reflected in the cosmic microwave background, weak lensing, and evolution of large-scale structure. The new parameter, $\varpi_0$, is naively expected to be of order unity. However, a multiparameter analysis, allowing for variation of all the standard cosmological parameters, finds that $\varpi_0 = 0.09^{+0.74}_{-0.59} (2σ)$ where $\varpi_0=0$ corresponds to a $Λ$CDM universe under general relativity. Future probes of the cosmic microwave background (Planck) and large-scale structure (Euclid) may improve the limits by a factor of four.

Figures (9)

• Figure 1: The potentials $\phi$ and $\psi$ are shown versus the scale factor, for different values of $\varpi_0$. The blue, dark curves are $\phi$, whereas the green, light curves are $\psi$. Note that they behave oppositely; when $\phi$ becomes shallower, $\psi$ becomes deeper, and vice versa.
• Figure 2: The matter density contrast is shown versus the scale factor, for different values of $\varpi_0$. The time evolution is obtained by integrating Eqs. (\ref{['phidoteqn']}) and (\ref{['deltadoteqn']}), with initial conditions $\phi=-10^{-5}$, $\dot{\phi}=0.0$ for $k=0.01 \text{Mpc}^{-1}$. Positive (negative) values of $\varpi_0$ enhance (slow) the growth of density perturbations.
• Figure 3: The degree of deviation from the Poisson equation versus scale factor is shown for different values of $\varpi_0$. Because $\varpi$ is scale-independent, so too is the ratio $-k^2 \phi/(4 \pi G a^2 \delta\rho)$. For positive (negative) $\varpi_0$, a given $\phi$ corresponds to a larger (smaller) density contrast than in GR.
• Figure 4: The CMB quadrupole moment is shown versus $\varpi_0$. As explained in the text, the quadratic dependence can be understood in terms of the influence of $\varpi_0$ on the ISW effect.(Reproduced from DCCM with our new normalization Eq. (\ref{['varpieqn']}).)
• Figure 5: The conformal time derivative of the gravitational potential $\phi$ is shown versus scale factor, for different values of $\varpi_0$. Initial conditions are the same as in Fig. \ref{['deltafig']}. The potential well is decaying when $\frac{d\phi}{d\tau}/|\phi_i H_0|>0$, and is deepening when negative.