Rotti, AdityaSouradeep, Tarun2013-09-202013-09-202013-09-20http://hdl.handle.net/11007/2661A stochastic gravitational wave background (SGWB) would gravitationally lens the cosmic mi- crowave background (CMB) photons. We correct the results provided in existing literature for modi cations to the CMB polarization power spectra due to lensing by gravitational waves (GW). Weak lensing by gravitational waves (GW) distorts all the four CMB power spectra, however its e ect is most striking in the mixing of power between the E-mode and B-mode of CMB polarization. This suggests the possibility of using measurements of the CMB angular power spectra to constrain the energy density ( GW) of the SGWB. Using current data sets (QUAD, WMAP and ACT), we nd that the most stringent constraints on the present GW come from measurements of the angular power spectra of CMB temperature anisotropies. In near future more stringent bounds on GW can be expected with improved upper limits on the B-modes of CMB polarization. Any detection of B-modes of CMB polarization above the expected signal from large scale structure(LSS) lensing could be a signal for a SGWBenStochestic Gravitational WaveArticle