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While large scale cosmic microwave background (CMB) anisotropies involve acombination of the scalar and tensor fluctuations, the scalar amplitude can beindependently determined through the CMB-galaxy cross-correlation. Usingrecently measured cross-correlation amplitudes, arising from thecross-correlation between galaxies and the Integrated Sachs Wolfe effect in CMBanisotropies, we obtain a constraint r < 0.5 at 68% confidence level on thetensor-to-scalar fluctuation amplitude ratio. The data also allow us to excludegravity waves at a level of a few percent, relative to the density field, in alow - Lambda dominated universe(Omega_Lambda~0.5). In future, joiningcross-correlation ISW measurements, which captures cosmological parameterinformation, with independent determinations of the matter density and CMBanisotropy power spectrum, may constrain the tensor-to-scalar ratio to a levelabove 0.05. This value is the ultimate limit on tensor-to-scalar ratio fromtemperature anisotropy maps when all other cosmological parameters except forthe tensor amplitude are known and the combination with CMB-galaxy correlationallows this limit to be reached easily by accounting for degeneracies incertain cosmological parameters.Comment: 5 Pages, 1 Figure, revised discussion on cosmic variance limits on  the tensor-to-scalar ratio from CMB, matches PRD accepted versio

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