Galaxy-CMB Cross-Correlation as a Probe of Alternative Models of Gravity

TL;DR

This work tests alternative gravity by studying the cross-correlation between galaxies and the CMB to probe how gravitational potentials relate to matter overdensities in TeVeS, a covariant MOND-like theory. It derives the generalized Poisson equation in TeVeS, showing vector-field perturbations modify the potentials and their evolution, leading to a distinctive Integrated Sachs-Wolfe signal. By computing the galaxy-CMB cross-power and forecasting LSST-like survey capabilities, the authors demonstrate a high-redshift ($z \gtrsim 1$–$2$) sign flip in the cross-correlation relative to ΛCDM, enabling a powerful observational discrimination with >10σ significance. The results suggest the ISW-galaxy cross-correlation is a robust, general probe for testing modified gravity theories against standard GR plus dark matter, with clear, testable predictions for future data.

Abstract

Bekenstein's alternative to general relativity, TeVeS, reduces to Modified Newtonian Dynamics (MOND) in the galactic limit. On cosmological scales, the (potential well <-> overdensity) relationship is quite different than in standard general relativity. Here we investigate the possibility of cross-correlating galaxies with the cosmic microwave background (CMB) to probe this relationship. At redshifts of order 2, the sign of the CMB-galaxy correlation differs in TeVeS from that in general relativity. We show that this effect is detectable and hence can serve as a powerful discriminator of these two models of gravity.

Figures (6)

• Figure 1: The "poisson ratio" ${-k^2 (\Phi+\Psi)/(\Omega_b \delta_b + \Omega_\nu \delta_\nu)}$ for the two TeVeS models considered in section \ref{['sec:poisson']}. In these units, the Poisson ratio is constant and equal to 3 in standard $\Lambda$CDM cosmology (solid line). This is true in TeVeS only for the largest scales, where the standard term in the Poisson equation dominates. On smaller scales the vector field perturbations dominate and the Poisson ratio exhibits a much more complicated behavior (see § \ref{['sec:poisson']} for more details).
• Figure 2: Left Panel.$k^2D_{\rm ISW}/H_0^2$ as a function of wavenumber $k$ and redshift in standard $\Lambda$CDM. Here we show results from linear theory so the relevant growth functions do not depend on wavenumber. Dashed curves show the line along which the integral is performed for two values of $l$. Right panel.$k^2D_{\rm ISW}/H_0^2$ as a function of wavenumber $k$ and redshift in TeVeS. Note that at high reshift, the TeVeS weighting function goes negative.
• Figure 3: Left Panel.$|k^2 \Phi|$ in the TeVeS baryon model (see text). After integrating numerically the TeVeS perturbation equations we plot the output for $|k^2 \Phi|$ and the different contributions to $|k^2 \Phi|$ from the other perturbation variables, according to the Poisson equation. In the plot, "standard contrib." is the standard $\delta$ term on the R.H.S. of the Poisson equation, "$\alpha$ contrib." represents the $\left(\frac{\dot{a}}{a} + \dot{\bar{\phi}} \right) \left(1 - e^{4 \bar{\phi}} \right)\alpha$ term and "E contrib." is the ${K_B E/2}$ term (all these terms have been multiplied by $k^2$). "All terms" is the sum of all the R.H.S. terms. On the x-axis $k$ is in units of h$/$Mpc but plotted lines correspond to units in which $H_0 = 1$. Same for all the following plots. Right panel. Same curves, but in the TeVeS neutrino model.
• Figure 4: Left Panel.$|k^2 \Psi|$ in the TeVeS baryon model. After integrating numerically the TeVeS perturbation equations we plot the output for $|k^2 \Psi|$ and the different contributions to $|k^2 \Phi|$ from the other perturbation variables, according to the equation (\ref{['eq:poissonpsi']}). Right panel. Same curves, but in the TeVeS neutrino model.
• Figure 5: Left panel: Matter power spectra for a TeVeS baryon only model with fixed $\Omega_b = 0.3$ and different values of $K_B$. Right panel: Galaxy-CMB cross correlation function at $\theta=6^{\circ}$ (divided by the galaxy bias) from different surveys GaztanagaGiannantonio. The red (solid) curve shows the TeVeS neutrino model prediction, while the green (dashed) curve is the $\Lambda$CDM prediction.