Constraining f(R) gravity using future galaxy cluster abundance and weak-lensing mass calibration datasets

We present forecasts for constraints on the Hu and Sawicki <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>f</a:mi><a:mo stretchy="false">(</a:mo><a:mi>R</a:mi><a:mo stretchy="false">)</a:mo></a:math> modified gravity model using realistic mock data representative of future cluster and weak lensing surveys. We create mock thermal Sunyaev-Zel’dovich effect selected cluster samples for SPT-3G and CMB-S4 and the corresponding weak gravitational lensing data from next-generation weak-lensing (ngWL) surveys like Euclid and Rubin. We employ a state-of-the-art Bayesian likelihood approach that includes all observational effects and systematic uncertainties to obtain constraints on the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>f</e:mi><e:mo stretchy="false">(</e:mo><e:mi>R</e:mi><e:mo stretchy="false">)</e:mo></e:math> gravity parameter <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>log</i:mi><i:mn>10</i:mn></i:msub><i:mo stretchy="false">|</i:mo><i:msub><i:mi>f</i:mi><i:mrow><i:mi>R</i:mi><i:mn>0</i:mn></i:mrow></i:msub><i:mo stretchy="false">|</i:mo></i:math>. In this analysis we vary the cosmological parameters <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mo stretchy="false">[</m:mo><m:msub><m:mi mathvariant="normal">Ω</m:mi><m:mi mathvariant="normal">m</m:mi></m:msub><m:mo>,</m:mo><m:msub><m:mi mathvariant="normal">Ω</m:mi><m:mi>ν</m:mi></m:msub><m:msup><m:mi>h</m:mi><m:mn>2</m:mn></m:msup><m:mo>,</m:mo><m:mi>h</m:mi><m:mo>,</m:mo><m:msub><m:mi>A</m:mi><m:mi>s</m:mi></m:msub><m:mo>,</m:mo><m:msub><m:mi>n</m:mi><m:mi>s</m:mi></m:msub><m:mo>,</m:mo><m:msub><m:mi>log</m:mi><m:mn>10</m:mn></m:msub><m:mo stretchy="false">|</m:mo><m:msub><m:mi>f</m:mi><m:mrow><m:mi>R</m:mi><m:mn>0</m:mn></m:mrow></m:msub><m:mo stretchy="false">|</m:mo><m:mo stretchy="false">]</m:mo></m:math>, which allows us to account for possible degeneracies between cosmological parameters and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>f</v:mi><v:mo stretchy="false">(</v:mo><v:mi>R</v:mi><v:mo stretchy="false">)</v:mo></v:math> modified gravity. The analysis accounts for <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi>f</z:mi><z:mo stretchy="false">(</z:mo><z:mi>R</z:mi><z:mo stretchy="false">)</z:mo></z:math> gravity via its effect on the halo mass function which is enhanced on cluster mass scales compared to the expectations within general relativity (GR). Assuming a fiducial GR model, the upcoming cluster dataset <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mrow><db:mi>SPT</db:mi><db:mtext>−</db:mtext><db:mn>3</db:mn><db:mi mathvariant="normal">G</db:mi><db:mo>×</db:mo><db:mi>ngWL</db:mi></db:mrow></db:math> is expected to obtain an upper limit of <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>log</gb:mi><gb:mn>10</gb:mn></gb:msub><gb:mo stretchy="false">|</gb:mo><gb:msub><gb:mi>f</gb:mi><gb:mrow><gb:mi>R</gb:mi><gb:mn>0</gb:mn></gb:mrow></gb:msub><gb:mo stretchy="false">|</gb:mo><gb:mo><</gb:mo><gb:mo>−</gb:mo><gb:mn>5.95</gb:mn></gb:math> at 95% credibility, which significantly improves upon the current best bounds. The <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mrow><kb:mi>CMB</kb:mi><kb:mtext>−</kb:mtext><kb:mi mathvariant="normal">S</kb:mi><kb:mn>4</kb:mn><kb:mo>×</kb:mo><kb:mi>ngWL</kb:mi></kb:mrow></kb:math> dataset is expected to improve this even further to <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:msub><nb:mi>log</nb:mi><nb:mn>10</nb:mn></nb:msub><nb:mo stretchy="false">|</nb:mo><nb:msub><nb:mi>f</nb:mi><nb:mrow><nb:mi>R</nb:mi><nb:mn>0</nb:mn></nb:mrow></nb:msub><nb:mo stretchy="false">|</nb:mo><nb:mo><</nb:mo><nb:mo>−</nb:mo><nb:mn>6.23</nb:mn></nb:math>. Furthermore, <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:mi>f</rb:mi><rb:mo stretchy="false">(</rb:mo><rb:mi>R</rb:mi><rb:mo stretchy="false">)</rb:mo></rb:math> gravity models with <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:msub><vb:mi>log</vb:mi><vb:mn>10</vb:mn></vb:msub><vb:mo stretchy="false">|</vb:mo><vb:msub><vb:mi>f</vb:mi><vb:mrow><vb:mi>R</vb:mi><vb:mn>0</vb:mn></vb:mrow></vb:msub><vb:mo stretchy="false">|</vb:mo><vb:mo>≥</vb:mo><vb:mo>−</vb:mo><vb:mn>6</vb:mn></vb:math>, which have larger numbers of clusters, would be distinguishable from GR with both datasets. We also report degeneracies between <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:msub><zb:mi>log</zb:mi><zb:mn>10</zb:mn></zb:msub><zb:mo stretchy="false">|</zb:mo><zb:msub><zb:mi>f</zb:mi><zb:mrow><zb:mi>R</zb:mi><zb:mn>0</zb:mn></zb:mrow></zb:msub><zb:mo stretchy="false">|</zb:mo></zb:math> and <dc:math xmlns:dc="http://www.w3.org/1998/Math/MathML" display="inline"><dc:msub><dc:mi mathvariant="normal">Ω</dc:mi><dc:mi mathvariant="normal">m</dc:mi></dc:msub></dc:math> as well as <hc:math xmlns:hc="http://www.w3.org/1998/Math/MathML" display="inline"><hc:msub><hc:mi>σ</hc:mi><hc:mn>8</hc:mn></hc:msub></hc:math> for <jc:math xmlns:jc="http://www.w3.org/1998/Math/MathML" display="inline"><jc:msub><jc:mi>log</jc:mi><jc:mn>10</jc:mn></jc:msub><jc:mo stretchy="false">|</jc:mo><jc:msub><jc:mi>f</jc:mi><jc:mrow><jc:mi>R</jc:mi><jc:mn>0</jc:mn></jc:mrow></jc:msub><jc:mo stretchy="false">|</jc:mo><jc:mo>></jc:mo><jc:mo>−</jc:mo><jc:mn>6</jc:mn></jc:math> and <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"><nc:msub><nc:mi>log</nc:mi><nc:mn>10</nc:mn></nc:msub><nc:mo stretchy="false">|</nc:mo><nc:msub><nc:mi>f</nc:mi><nc:mrow><nc:mi>R</nc:mi><nc:mn>0</nc:mn></nc:mrow></nc:msub><nc:mo stretchy="false">|</nc:mo><nc:mo>></nc:mo><nc:mo>−</nc:mo><nc:mn>5</nc:mn></nc:math> respectively. Our forecasts indicate that future cluster abundance studies of <rc:math xmlns:rc="http://www.w3.org/1998/Math/MathML" display="inline"><rc:mi>f</rc:mi><rc:mo stretchy="false">(</rc:mo><rc:mi>R</rc:mi><rc:mo stretchy="false">)</rc:mo></rc:math> gravity will enable substantially improved constraints that are competitive with other cosmological probes. Published by the American Physical Society 2024