Wide-area tomography of CMB lensing and the growth of cosmological density fluctuations

We describe a tomographic dissection of the Planck CMB lensing data, cross-correlating this map with galaxies in different ranges of photometric redshift. We use the nearly all-sky 2MPZ and WISExSCOS catalogues for z<0.35, extending to z<0.6 using SDSS. We describe checks for consistency between the different datasets, and perform a test for possible leakage of thermal Sunyaev--Zel'dovich signal into our cross-correlation measurements. The amplitude of the cross-correlation allows us to estimate the evolution of density fluctuations as a function of redshift, thus providing a test of theories of modified gravity. Assuming the common parametrisation for the logarithmic growth rate, f_g=Omega_m(z)^gamma, we infer gamma=0.77 +/- 0.18 when Omega_m is fixed using external data. Thus CMB lensing tomography is currently consistent with Einstein gravity, where gamma=0.55 is expected. We discuss how such constraints may be expected to improve with future data.