Testing the Concordance model of Cosmology
The concordance model of cosmology is built on several assumptions:
The Universe is homogeneous and isotropic
Gravity is described by General Relativity (GR)
Under these assumptions, the metric of the Universe is described by the Friedmann-Lemaître-Robsertson-Walker (FLRW) metric, describing an expanding universe.
Under these hypotheses, the current concordance model is the Lambda CDM model, where energy is dominated by the cosmological constant Lambda, responsible for the late-time acceleration of the expansion, and matter is dominated by a cold, smooth, non-baryonic component ("dark matter").
However, these components are still to be directly detected, and are not part of the standard model of particle physics.
Therefore, one may question the underlying hypotheses.
Is the FLRW the correct metric? Is the Universe isotropic and homogeneous? Is Dark energy a cosmological constant?
Testing the FLRW metric and the Curvature
Combining model-independent reconstruction of the expansion history h(z) = H(z) / H0 from the Joint Likelihood Lightcurve (JLA) to from the Baryon Oscillation Spectroscopic Survey (SDSS III / BOSS), with Arman Shafieloo, we measured in a model-independent way the combination of the Hubble constant H0 and the sound horizon at the drag epoch rd. We then introduced a new litmus test of the Flat-FLRW metric Theta(z) such that the Clarkson test $O_k(z) = Theta^2(z)-1)/D^2(z)$.
For a Flat FLRW universe, Theta = 1 and O_k = 0.
Our results are consistent with a Flat-FLRW Universe, but show some hint of tension in the CMASS subsample (L'Huillier & Shafieloo JCAP01(2017)015).
Model-independent test of GR
With Arman Shafieloo and Hyungjin Kim (U. Waterloo), we then combined the independent reconstructions to growth measurements from redshift-space distortion, and put model-independent constraints on the matter density Omega_m, the rms fluctuation sigma_8, and the growth factor gamma.
For GR, gamma = 0.55. Our results are consistent with LCDM+GR (L'Huillier, Shafieloo & Kim 2018, MNRAS 476, 3263).
With Arman Shafieloo and Alexei Starobinsky, we then combined the latest SNIa data (Pantheon) and growth measurements (including eBOSS DR14Q) and obtained more stringent constraints, but are still consistent with LCDM+GR (Shafieloo, L'Huillier & Starobinsky 2018, PRD).