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 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 ( \Omega _ { \Lambda } \sim 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 by accounting for degeneracies in certain cosmological parameters .