KiDS-450: Testing extensions to the standard cosmological model
  We test extensions to the standard cosmological model with weak gravitational
lensing tomography using 450 deg$^2$ of imaging data from the Kilo Degree
Survey (KiDS). In these extended cosmologies, which include massive neutrinos,
nonzero curvature, evolving dark energy, modified gravity, and running of the
scalar spectral index, we also examine the discordance between KiDS and cosmic
microwave background measurements from Planck. The discordance between the two
datasets is largely unaffected by a more conservative treatment of the lensing
systematics and the removal of angular scales most sensitive to nonlinear
physics. The only extended cosmology that simultaneously alleviates the
discordance with Planck and is at least moderately favored by the data includes
evolving dark energy with a time-dependent equation of state (in the form of
the $w_0-w_a$ parameterization). In this model, the respective $S_8 = \sigma_8
\sqrt{\Omega_{\rm m}/0.3}$ constraints agree at the $1\sigma$ level, and there
is `substantial concordance' between the KiDS and Planck datasets when
accounting for the full parameter space. Moreover, the Planck constraint on the
Hubble constant is wider than in LCDM and in agreement with the Riess et al.
(2016) direct measurement of $H_0$. The dark energy model is moderately favored
as compared to LCDM when combining the KiDS and Planck measurements, and
remains moderately favored after including an informative prior on the Hubble
constant. In both of these scenarios, marginalized constraints in the $w_0-w_a$
plane are discrepant with a cosmological constant at the $3\sigma$ level.
Moreover, KiDS constrains the sum of neutrino masses to 4.0 eV (95% CL), finds
no preference for time or scale dependent modifications to the metric
potentials, and is consistent with flatness and no running of the spectral
index. The analysis code is public at https://github.com/sjoudaki/kids450
