Probing the largest cosmological scales with the correlation between the cosmic microwave background and peculiar velocities

Cross correlation between the cosmic microwave background (CMB) and large-scale structure is a powerful probe of dark energy and gravity on the largest physical scales. We introduce a novel estimator, the CMB-velocity correlation, that has most of its power on large scales and that, at low redshift, delivers up to a factor of 2 higher signal-to-noise ratio than the recently detected CMB-dark matter density correlation expected from the integrated Sachs-Wolfe effect. We propose to use a combination of peculiar velocities measured from supernovae type Ia and kinetic Sunyaev-Zeldovich cluster surveys to reveal this signal and forecast dark energy constraints that can be achieved with future surveys. We stress that low redshift peculiar velocity measurements should be exploited with complementary deeper large-scale structure surveys for precision cosmology.

Figure 1

Cross power spectra for the CMB temperature-velocity, $Tv$ (top), and the temperature-density, $T\delta$ (bottom), for different mean survey depths, $z_m$. Most of the signal in the $Tv$ correlation comes from larger scales (lower multipoles) than the $T\delta$. We amplify the velocity correlation signal by 100 to match the ISW amplitude from the density correlation.

Figure 2

Contribution to the ISW effect power spectra from different 3D wave numbers, $k$, and thin redshift $z$ shells, for various multipoles $\ell$. As in Fig. 1, the top panels display the $Tv$ kernel, amplified by a factor of 100, whereas the bottom panels show the $T\delta$ kernel. Kernels are given by $\ell (\ell +1)/2\pi$ times the integrand in Eq. (1).

Figure 3

Contribution of multipoles to the signal-to-noise ratio $\mathrm{S}/\mathrm{N}$ for $Tv$ (solid lines) and $T\delta$ (dashed lines) for full-sky surveys with different depths, for our baseline $\Lambda \mathrm{CDM}$ model. Total $(\mathrm{S}/\mathrm{N}{)}^2$ is given by the area under the curves. Velocities give a $\mathrm{S}/\mathrm{N}$ in cross correlation with the temperature that is systematically larger than that for densities, $T\delta$, the gain factor depending on survey depth and cosmology. Note that $\mathrm{S}/\mathrm{N}$ scales as $\sqrt{f_{\mathrm{sky}}}$, where $f_{\mathrm{sky}}$ is the fraction of sky covered by the survey.

Figure 4

Constraints on the DE parameters from the cross correlation of the CMB with shallow full-sky surveys. Contours show 68% (inner line) and 95% (outer line) confidence levels for 1 DOF. Solid (dashed) lines show parameter errors from the $Tv$ ($T\delta$) correlation, whereas thick (thin) lines correspond to constraints with (without) PLANCK priors. Left (right) panel shows the case for surveys with median redshift $z_m=0.15$ ($z_m=0.3$) and top (bottom) panels display two different choices of the DE equation of state: $w=-1$ ($\Lambda \mathrm{CDM}$) and $-2/3$ (quintessence).