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 WISE×SCOS catalogues for z < 0.35, extending to z < 0.6 using SDSS. We describe checks for consistency between the different data sets, 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 parametrization for the logarithmic growth rate, f_g = Ω_m(z)^γ, we infer γ = 0.77 ± 0.18 when Ω_m is fixed using external data. Thus CMB lensing tomography is currently consistent with Einstein gravity, where γ = 0.55 is expected.We discuss how such constraints may be expected to improve with future data.