Indirect limit on the amplitude of primordial gravitational wave background from CMB-galaxy cross correlation

While large scale cosmic microwave background (CMB) anisotropies involve a combination of the scalar and tensor fluctuations, the scalar amplitude can be independently determined through the CMB-galaxy cross correlation. Using recently measured cross correlation amplitudes, arising from the cross correlation between galaxies and the integrated Sachs-Wolfe (ISW) effect in CMB anisotropies, we obtain a constraint $r<0.5$ at 68% confidence level on the tensor-to-scalar fluctuation amplitude ratio. The data also allow us to exclude gravity waves at a level of a few percent, relative to the density field, in a low-Lambda dominated universe (Ω_Λ~0.5). In future, joining cross correlation ISW measurements, which captures cosmological parameter information, with independent determinations of the matter density and CMB anisotropy power spectrum, may constrain the tensor-to-scalar ratio to a level above 0.05. This value is the ultimate limit on tensor-to-scalar ratio from temperature anisotropy maps when all other cosmological parameters except for the tensor amplitude are known and the combination with CMB-galaxy correlation allows this limit to be reached easily be accounting for degeneracies in certain cosmological parameters.