Looking for $Λ$ with the Rees-Sciama Effect

TL;DR

This paper proposes a cosmological test for a nonzero $Λ$ based on the Rees-Sciama effect, where late-time evolution of the gravitational potential in a Universe with a cosmological constant induces CMB anisotropy correlated with the local density. The authors derive the RS contribution to spherical harmonic coefficients as a convolution of the present-day density with a radial window that depends on the growth rate and expansion, showing that at high multipoles the window simplifies and the RS term tracks low-redshift structure. They estimate the cross-correlation signal-to-noise for an ideal density tracer, finding $S/N$ values of roughly 5.5–7.9 as $Ω_Λ$ varies from 0.6 to 0.9, and demonstrate robustness to bias variations. They discuss observational prospects, notably a COBE-ROSAT cross-correlation, which could yield a detectable signal (suppression factor ~0.8 for $Ω_Λ ≈ 0.8$), making this RS–density cross-correlation a viable complementary probe of $Λ$ that is relatively insensitive to high-redshift physics.

Abstract

In models with a cosmological constant, a significant component of the large scale cosmic microwave background (CMB) anisotropy is produced at rather low redshifts, z < 1. In these models, the gravitational potential perturbations begin to evolve at late times. Photons passing through these time varying potentials aquire frequency shifts, an effect first noted by Rees and Sciama. Since the gravitational potential is associated with matter at observable redshifts, the local matter density (or some tracer thereof) is correlated with the CMB anisotropy on the sky. We outline the optimal method of measuring this correlation, and discuss the prospects for using an X-ray/COBE comparison to detect a cosmological constant.

Figures (4)

• Figure 1: The large scale anisotropy power spectrum, $C_l = \langle |a_{lm}|^2 \rangle$, for a model with $\Omega_\Lambda = 0.8$ and $h = 0.7$. Also shown is the anisotropy that is produced prior to a given red shift, for $z = 0.5, 1,$ and $2$. A significant portion of the anisotropy is produced rather recently.
• Figure 2: The ideal filter function, $\dot{g}(z)$, as a function of red shift. Even for very large $\Lambda$, significant contributions result from low redshift, though contributions begin at higher redshifts.
• Figure 3: We plot the signal to noise squared as a function of $l$, where the area under the curve represents the contribution for a given logarithmic interval.
• Figure 4: We plot the reduction of the signal to noise ratio if the density survey is cut off beyond a given redshift.