Constraints on $f(R)$ and nDGP Modified Gravity Model Parameters with
  Cluster Abundances and Galaxy Clustering
  We present forecasted cosmological constraints from combined measurements of
galaxy cluster abundances from the Simons Observatory and galaxy clustering
from a DESI-like experiment on two well-studied modified gravity models, the
chameleon-screened $f(R)$ Hu-Sawicki model and the nDGP braneworld Vainshtein
model.
  A Fisher analysis is conducted using $\sigma_8$ constraints derived from
thermal Sunyaev-Zel'dovich (tSZ) selected galaxy clusters, as well as linear
and mildly non-linear redshift-space 2-point galaxy correlation functions. We
find that the cluster abundances drive the constraints on the nDGP model while
$f(R)$ constraints are led by galaxy clustering. The two tracers of the
cosmological gravitational field are found to be complementary, and their
combination significantly improves constraints on the $f(R)$ in particular in
comparison to each individual tracer alone.
  For a fiducial model of $f(R)$ with $\text{log}_{10}(f_{R0})=-6$ and $n=1$ we
find combined constraints of $\sigma(\text{log}_{10}(f_{R0}))=0.48$ and
$\sigma(n)=2.3$, while for the nDGP model with $n_{\text{nDGP}}=1$ we find
$\sigma(n_{\text{nDGP}})=0.087$. Around a fiducial General Relativity (GR)
model, we find a $95\%$ confidence upper limit on $f(R)$ of
$f_{R0}\leq5.68\times 10^{-7}$. Our results present the exciting potential to
utilize upcoming galaxy and CMB survey data available in the near future to
discern and/or constrain cosmic deviations from GR.
