A correlation of the cosmic microwave sky with large scale structure

Abstract

We cross correlate the large-scale cosmic microwave background (CMB) sky measured by WMAP with two probes of large-scale structure at z ~ 1. The hard X-ray background, measured by the HEAO-1 satellite, is positively correlated with the WMAP data at the 2.5-3.0 sigma level. The number counts of radio galaxies in the NVSS survey are also correlated at a slightly weaker level (2.-2.5 sigma). These correlations appear to arise from both hemispheres on the sky and are resilient to changes in the levels of masking of the Galaxy and point sources, suggesting that foregrounds are not responsible for the signal. The implication is that some of the observed CMB fluctuations arise at low redshifts. The level of the correlations is consistent with that expected for the cosmological constant (Omega_Lambda = 0.72) concordance model resulting from the integrated Sachs-Wolfe effect. Thus, we may be observing dark energy's effect on the growth of structure.

Figures (3)

• Figure 1: The X-ray intensity measured by HEAO-A1 is correlated with the microwave sky measured by WMAP at a higher level than would be expected by chance correlations. Here we plot the cross correlation between the X-ray intensity fluctuations and the CMB temperature fluctuations along with the theoretical predictions for the ISW effect in a cosmological constant ($\Omega_\Lambda = 0.72$), the best fit WMAP model for scale invariant fluctuations. To give an idea of the level of accidental correlations, the green curves show the result of correlating the X-ray map with 100 independent Monte Carlo realized CMB maps with the same power spectrum as the WMAP data. The variance increases at smaller angular separations, where there are fewer pairs of pixels contributing to the correlation and one can see that the signals in neighboring bins are highly correlated for a given realization. Due to the shape of the expected correlation, the signal to noise is greatest at smaller angular separations. For $\theta = 0^{\circ}$, $1.3^{\circ}$, and $2.6^{\circ}$, the Monte Carlo trials exceed the amplitude of the actual X-ray/CMB correlation only $0.3$%, $0.8\%$, and $0.3\%$ of the time respectively. These correspond to $2.4$ to $2.8~\sigma$. At larger angular separations, the observed correlations appear to fall faster than predicted by theory. The blue line shows the theoretical predictions if the quadrupole and octupole modes are suppressed as suggested by the measured WMAP temperature spectrum. While it seems to fit the data better, the larger angular separations have very low signal to noise.
• Figure 2: The observed X-ray/CMB cross correlation for $\theta = 0^{\circ}$ (in green) exceeds the value found for most Monte Carlo simulations. Here we plot the distribution of the correlation from 400 simulations, where the observed X-ray map was cross correlated with random CMB maps with the same power spectrum as the observed WMAP CMB sky. The underlying distribution of the Monte Carlos is not precisely Gaussian, but should be nearly Gaussian by the central limit theorem.
• Figure 3: The NVSS radio galaxies also appear correlated with the microwave sky, but at lower confidence level than the X-rays. Here we plot the correlation between the radio galaxy number counts and the WMAP temperature maps. The other curves are as in Figure \ref{['xt.fig']}. The Monte Carlo trials exceed the amplitude of the actual radio/CMB correlation in the lowest three bins $1.2\%$, $1.9\%$, and $3.4\%$ of the time respectively, corresponding to a $1.8$ to $2.3~\sigma$ signal detection. Again, there is good agreement with the theoretical predictions, with the signal falling off faster than predicted at larger angles (at fairly low statistical significance.) The consistency of the NVSS and X-ray CCF's suggests that the signal is not the result of unknown systematics in either the X-ray or the NVSS map.