Conjoined constraints on modified gravity from the expansion history and
  cosmic growth
  In this paper we present conjoined constraints on several cosmological models
from the expansion history $H(z)$ and cosmic growth $f\sigma_8(z)$. The models
we study include the CPL $w_0w_a$ parametrization, the Holographic Dark Energy
(HDE) model, the Time varying vacuum ($\Lambda_t$CDM) model, the Dvali,
Gabadadze and Porrati (DGP) and Finsler-Randers (FRDE) models, a power law
$f(T)$ model and finally the Hu-Sawicki $f(R)$ model. In all cases we perform a
simultaneous fit to the SnIa, CMB, BAO, $H(z)$ and growth data, while also
following the conjoined visualization of $H(z)$ and $f\sigma_8(z)$ as in Linder
(2017). Furthermore, we introduce the Figure of Merit (FoM) in the
$H(z)-f\sigma_8(z)$ parameter space as a way to constrain models that jointly
fit both probes well. We use both the latest $H(z)$ and $f\sigma_8(z)$ data,
but also LSST-like mocks with $1\%$ measurements and we find that the conjoined
method of constraining the expansion history and cosmic growth simultaneously
is able not only to place stringent constraints on these parameters but also to
provide an easy visual way to discriminate cosmological models. Finally, we
confirm the existence of a tension between the growth rate and Planck CMB data
and we find that the FoM in the conjoined parameter space of
$H(z)-f\sigma_8(z)$ can be used to discriminate between the $\Lambda$CDM model
and certain classes of modified gravity models, namely the DGP and $f(T)$.
