A Test of the Standard Cosmological Model with Geometry and Growth
  We perform a general test of the $\Lambda{\rm CDM}$ and $w {\rm CDM}$
cosmological models by comparing constraints on the geometry of the expansion
history to those on the growth of structure. Specifically, we split the total
matter energy density, $\Omega_M$, and (for $w {\rm CDM}$) dark energy equation
of state, $w$, into two parameters each: one that captures the geometry, and
another that captures the growth. We constrain our split models using current
cosmological data, including type Ia supernovae, baryon acoustic oscillations,
redshift space distortions, gravitational lensing, and cosmic microwave
background (CMB) anisotropies. We focus on two tasks: (i) constraining
deviations from the standard model, captured by the parameters $\Delta\Omega_M
\equiv \Omega_M^{\rm grow}-\Omega_M^{\rm geom}$ and $\Delta w \equiv w^{\rm
grow}-w^{\rm geom}$, and (ii) investigating whether the $S_8$ tension between
the CMB and weak lensing can be translated into a tension between geometry and
growth, i.e. $\Delta\Omega_M \neq 0$, $\Delta w \neq 0$. In both the split
$\Lambda{\rm CDM}$ and $w {\rm CDM}$ cases, our results from combining all data
are consistent with $\Delta\Omega_M = 0$ and $\Delta w = 0$. If we omit BAO/RSD
data and constrain the split $w {\rm CDM}$ cosmology, we find the data prefers
$\Delta w<0$ at $3.6\sigma$ significance and $\Delta\Omega_M>0$ at $4.2\sigma$
evidence. We also find that for both CMB and weak lensing, $\Delta\Omega_M$ and
$S_8$ are correlated, with CMB showing a slightly stronger correlation. The
general broadening of the contours in our extended model does alleviate the
$S_8$ tension, but the allowed nonzero values of $\Delta\Omega_M$ do not
encompass the $S_8$ values that would point toward a mismatch between geometry
and growth as the origin of the tension.
