Constraints on f(R) gravity from thermal-Sunyaev-Zel’dovich-effect-selected SPT galaxy clusters and weak lensing mass calibration from DES and HST

We present constraints on the <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> gravity model using a sample of 1005 galaxy clusters in the redshift range 0.25–1.78 that have been selected through the thermal Sunyaev-Zel’dovich effect from South Pole Telescope data and subjected to optical and near-infrared confirmation with the multicomponent matched filter algorithm. We employ weak gravitational lensing mass calibration from the Dark Energy Survey Year 3 data for 688 clusters at <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>z</e:mi><e:mo><</e:mo><e:mn>0.95</e:mn></e:math> and from the Hubble Space Telescope for 39 clusters with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mn>0.6</g:mn><g:mo><</g:mo><g:mi>z</g:mi><g:mo><</g:mo><g:mn>1.7</g:mn></g:math>. Our cluster sample is a powerful probe of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>f</i:mi><i:mo stretchy="false">(</i:mo><i:mi>R</i:mi><i:mo stretchy="false">)</i:mo></i:math> gravity, because this model predicts a scale-dependent enhancement in the growth of structure, which impacts the halo mass function (HMF) at cluster mass scales. To account for these modified gravity effects on the HMF, our analysis employs a semianalytical approach calibrated with numerical simulations. Combining calibrated cluster counts with primary cosmic microwave background temperature and polarization anisotropy measurements from the Planck 2018 release, we derive robust constraints on the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>R</m:mi><m:mo stretchy="false">)</m:mo></m:math> parameter <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>f</q:mi><q:mrow><q:mi>R</q:mi><q:mn>0</q:mn></q:mrow></q:msub></q:math>. Our results, <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>log</s:mi><s:mn>10</s:mn></s:msub><s:mo stretchy="false">|</s:mo><s:msub><s:mi>f</s:mi><s:mrow><s:mi>R</s:mi><s:mn>0</s:mn></s:mrow></s:msub><s:mo stretchy="false">|</s:mo><s:mo><</s:mo><s:mo>−</s:mo><s:mn>5.32</s:mn></s:math> at the 95% credible level, are the tightest current constraints on <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>f</w:mi><w:mo stretchy="false">(</w:mo><w:mi>R</w:mi><w:mo stretchy="false">)</w:mo></w:math> gravity from cosmological scales. This upper limit rules out <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>f</ab:mi><ab:mo stretchy="false">(</ab:mo><ab:mi>R</ab:mi><ab:mo stretchy="false">)</ab:mo></ab:math>-like deviations from general relativity that result in more than a <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mo>∼</eb:mo><eb:mn>20</eb:mn><eb:mo>%</eb:mo></eb:math> enhancement of the cluster population on mass scales <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mrow><gb:msub><gb:mrow><gb:mi>M</gb:mi></gb:mrow><gb:mrow><gb:mn>200</gb:mn><gb:mi mathvariant="normal">c</gb:mi></gb:mrow></gb:msub><gb:mo>></gb:mo><gb:mn>3</gb:mn><gb:mo>×</gb:mo><gb:msup><gb:mrow><gb:mn>10</gb:mn></gb:mrow><gb:mrow><gb:mn>14</gb:mn></gb:mrow></gb:msup><gb:msub><gb:mrow><gb:mi>M</gb:mi></gb:mrow><gb:mrow><gb:mo stretchy="false">⊙</gb:mo></gb:mrow></gb:msub></gb:mrow></gb:math>.