Constraints on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> and normal-branch Dvali-Gabadadze-Porrati modified gravity model parameters with cluster abundances and galaxy clustering
Rayne Liu, Georgios Valogiannis, Nicholas Battaglia, Rachel Bean
Abstract
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 Hu-Sawicki $f(R)$ model and the nDGP braneworld Vainshtein model. A Fisher analysis is conducted using ${\ensuremath{\sigma}}_{8}$ constraints derived from thermal Sunyaev-Zel'dovich (tSZ) selected galaxy clusters as well as linear and quasilinear 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 model of $f(R)$ with a general relativity (GR) fiducial case (${f}_{R0}=0$), we find a $2\text{\ensuremath{-}}\ensuremath{\sigma}$ upper limit of ${f}_{R0}\ensuremath{\le}5.68\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$. For the well-studied log-based fiducial parameter value in $f(R)$, ${\mathrm{log}}_{10}({f}_{R0})=\ensuremath{-}5$, paired with the parameter value $n=1$, we find combined $1\text{\ensuremath{-}}\ensuremath{\sigma}$ constraints of $\ensuremath{\sigma}({\mathrm{log}}_{10}({f}_{R0}))=0.12$ and $\ensuremath{\sigma}(n)=0.36$. For the nDGP model with fiducial ${n}_{\mathrm{nDGP}}=1$ we find $\ensuremath{\sigma}({n}_{\mathrm{nDGP}})=0.087$. 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.