Constraints on $f(R)$ and normal-branch Dvali-Gabadadze-Porrati modified gravity model parameters with cluster abundances and galaxy clustering

Constraints on $f (R)$ and normal-branch Dvali-Gabadadze-Porrati modified gravity model parameters with cluster abundances and galaxy clustering

Rayne Liu, Georgios Valogiannis, Nicholas Battaglia, and Rachel Bean

Phys. Rev. D 104, 103519 – Published 18 November 2021

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 $σ_{8}$ 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 ( $f_{R 0} = 0$ ), we find a $2 − σ$ upper limit of $f_{R 0} \leq 5.68 \times 10^{- 7}$ . For the well-studied log-based fiducial parameter value in $f (R)$ , $\log_{10} (f_{R 0}) = - 5$ , paired with the parameter value $n = 1$ , we find combined $1 − σ$ constraints of $σ (\log_{10} (f_{R 0})) = 0.12$ and $σ (n) = 0.36$ . For the nDGP model with fiducial $n_{nDGP} = 1$ we find $σ (n_{nDGP}) = 0.087$ . 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.

Received 29 January 2021
Accepted 4 October 2021

DOI:https://doi.org/10.1103/PhysRevD.104.103519

Physics Subject Headings (PhySH)

Alternative gravity theories Cosmological parameters Dark energy Large scale structure of the Universe

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Rayne Liu ^1,*, Georgios Valogiannis ^2,*, Nicholas Battaglia¹, and Rachel Bean¹

¹Department of Astronomy, Cornell University, Ithaca, New York 14853, USA
²Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

^*R. L. and G. V. contributed equally to the work.

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Vol. 104, Iss. 10 — 15 November 2021

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Images

Figure 1
The fractional deviations of the monopole [top], quadrupole [middle] and hexadecapole [bottom] of the anisotropic correlation function in the $f_{R 0} = 10^{- 5}$ [red dashed] and $f_{R 0} = 10^{- 6}$ [solid blue] $f (R)$ scenarios with respect to the corresponding $Λ CDM$ prediction for the ELG sample at $z = 0.05$ .
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Figure 2
Galaxy clustering constraints on the parameters in the F5 case (fiducial values $f_{R 0} = 10^{- 5}$ , $n = 1$ ) using the DESI LRG sample [red], the ELG sample [blue] and both combined [cyan] for a minimum survey scale of $r_{\min} \sim 25.0 Mpc / h$ , the smallest scale we anticipate can be probed with the survey. Combined constraints for a more conservative minimum scale of $r_{\min} \sim 43.79 Mpc / h$ [yellow] are also presented to show the impact of scale on the constraints.
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Figure 3
Galaxy clustering constraints on ${\log_{10} (f_{R 0}), n}$ in the F5 (top) and F6 (bottom) cases (fiducial values $f_{R 0} = 10^{- 5}$ and $10^{- 6}$ , $n = 1$ ) for the LRG sample [red], ELG sample [blue] and both combined [cyan] assuming $r_{\min} \sim 25.0 Mpc / h$ .
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Figure 4
The MG predicted $σ_{8} (z)_{MG} / σ_{8} (z)_{Λ CDM}$ normalized at $z = 10$ , plotted against the error of this ratio forecasted by cluster abundances. Left, (a): shows scenarios with different $f_{R 0}$ values while fixing $n$ in $f (R)$ as 1. Center, (b): shows scenarios fixing $f_{R 0} = 10^{- 6}$ while changing $n$ . Right, (c): shows the case in nDGP, where $n_{nDGP}$ is varied.
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Figure 5
The 1D likelihood distribution for [Left, (a)] the near-GR $f (R)$ model, with fiducial value $f_{R 0} = 0$ (the value of $n$ becomes redundant) and for the nDGP model with fiducial values [Center, (b)] $n_{nDGP} = 1$ and [Right, (c)] $n_{nDGP} = 5$ , under a Gaussian assumption in the Fisher forecast. The constraints from [red] galaxy clustering ( $ELG + LRG$ ), [yellow] cluster abundances and [cyan] the two combined are shown, with the darker fill-in shades denoting the corresponding $1 − σ$ (68%) confidence levels, lighter shades the $2 − σ$ (95%) confidence levels.
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Figure 6
The constraints on the [(a)] F5 and [(b)] F6 $f (R)$ scenarios are shown from [red] galaxy clustering, [yellow] cluster abundances and [cyan] the two combined. The covariance ellipses in the ${\log_{10} (f_{R 0}), n}$ parameter space indicating the joint $1 − σ$ (68%) confidence levels, and their respective marginalized 1D Gaussian likelihoods are shown for each scenario, with the darker fill-in shades denoting the corresponding $1 − σ$ (68%) confidence levels, lighter shades the $2 − σ$ (95%) confidence levels.
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