This paper presents the first application of 3D cosmic shear to a wide-field weak lensing survey .
3D cosmic shear is a technique that analyses weak lensing in three dimensions using a spherical harmonic approach , and does not bin data in the redshift direction .
This is applied to CFHTLenS , a 154 square degree imaging survey with a median redshift of 0.7 and an effective number density of 11 galaxies per square arcminute usable for weak lensing .
To account for survey masks we apply a 3D pseudo- C _ { \ell } approach on weak lensing data , and to avoid uncertainties in the highly non-linear regime , we separately analyse radial wavenumbers k \leq 1.5 h Mpc ^ { -1 } and k \leq 5.0 h Mpc ^ { -1 } , and angular wavenumbers \ell \approx 400 - 5000 .
We show how one can recover 2D and tomographic power spectra from the full 3D cosmic shear power spectra and present a measurement of the 2D cosmic shear power spectrum , and measurements of a set of 2 -bin and 6 -bin cosmic shear tomographic power spectra ; in doing so we find that using the 3D power in the calculation of such 2D and tomographic power spectra from data naturally accounts for a minimum scale in the matter power spectrum .
We use 3D cosmic shear to constrain cosmologies with parameters \Omega _ { M } , \Omega _ { B } , \sigma _ { 8 } , h , n _ { s } , w _ { 0 } , w _ { a } .
For a non-evolving dark energy equation of state , and assuming a flat cosmology , lensing combined with WMAP7 results in h = 0.78 \pm 0.12 , \Omega _ { M } = 0.252 \pm 0.079 , \sigma _ { 8 } = 0.88 \pm 0.23 and w = -1.16 \pm 0.38 using only scales k \leq 1.5 h Mpc ^ { -1 } .
We also present results of lensing combined with first year Planck results , where we find no tension with the results from this analysis , but we also find no significant improvement over the Planck results alone .
We find evidence of a suppression of power compared to LCDM on small scales 1.5 < k \leq 5.0 h Mpc ^ { -1 } in the lensing data , which is consistent with predictions of the effect of baryonic feedback on the matter power spectrum .