Multiprobe cosmology from the abundance of SPT clusters and DES galaxy clustering and weak lensing

Cosmic shear, galaxy clustering, and the abundance of massive halos each probe the large-scale structure of the Universe in complementary ways. We present cosmological constraints from the joint analysis of the three probes, building on the latest analyses of the lensing-informed abundance of clusters identified by the South Pole Telescope (SPT) and of the auto- and cross-correlation of galaxy position and weak lensing measurements (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>3</a:mn><a:mo>×</a:mo><a:mn>2</a:mn><a:mi>pt</a:mi></a:math>) in the Dark Energy Survey (DES). We consider the cosmological correlation between the different tracers and we account for the systematic uncertainties that are shared between the large-scale lensing correlation functions and the small-scale lensing-based cluster mass calibration. Marginalized over the remaining <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi mathvariant="normal">Λ</c:mi></c:math> cold dark matter (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi mathvariant="normal">Λ</f:mi><f:mi>CDM</f:mi></f:math>) parameters (including the sum of neutrino masses) and 52 astrophysical modeling parameters, we measure <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi mathvariant="normal">Ω</i:mi><i:mi mathvariant="normal">m</i:mi></i:msub><i:mo>=</i:mo><i:mn>0.300</i:mn><i:mo>±</i:mo><i:mn>0.017</i:mn></i:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>σ</m:mi><m:mn>8</m:mn></m:msub><m:mo>=</m:mo><m:mn>0.797</m:mn><m:mo>±</m:mo><m:mn>0.026</m:mn></m:math>. Compared to constraints from primary cosmic microwave background (CMB) anisotropies, our constraints are only 15% wider with a probability to exceed of 0.22 (<o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mn>1.2</o:mn><o:mi>σ</o:mi></o:math>) for the two-parameter difference. We further obtain <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>S</q:mi><q:mn>8</q:mn></q:msub><q:mo>≡</q:mo><q:msub><q:mi>σ</q:mi><q:mn>8</q:mn></q:msub><q:mo stretchy="false">(</q:mo><q:msub><q:mi mathvariant="normal">Ω</q:mi><q:mi mathvariant="normal">m</q:mi></q:msub><q:mo>/</q:mo><q:mn>0.3</q:mn><q:msup><q:mo stretchy="false">)</q:mo><q:mn>0.5</q:mn></q:msup><q:mo>=</q:mo><q:mn>0.796</q:mn><q:mo>±</q:mo><q:mn>0.013</q:mn></q:math> which is lower than the measurement at the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mn>1.6</w:mn><w:mi>σ</w:mi></w:math> level. The combined SPT cluster, DES <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mn>3</y:mn><y:mo>×</y:mo><y:mn>2</y:mn><y:mi>pt</y:mi></y:math>, and datasets mildly prefer a nonzero positive neutrino mass, with a 95% upper limit <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mo>∑</ab:mo><ab:msub><ab:mi>m</ab:mi><ab:mi>ν</ab:mi></ab:msub><ab:mo><</ab:mo><ab:mn>0.25</ab:mn><ab:mtext> </ab:mtext><ab:mtext> </ab:mtext><ab:mi>eV</ab:mi></ab:math> on the sum of neutrino masses. Assuming a <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>w</cb:mi><cb:mi>CDM</cb:mi></cb:math> model, we constrain the dark energy equation of state parameter <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>w</eb:mi><eb:mo>=</eb:mo><eb:mo>−</eb:mo><eb:mn>1.1</eb:mn><eb:msubsup><eb:mn>5</eb:mn><eb:mrow><eb:mo>−</eb:mo><eb:mn>0.17</eb:mn></eb:mrow><eb:mrow><eb:mo>+</eb:mo><eb:mn>0.23</eb:mn></eb:mrow></eb:msubsup></eb:math> and when combining with primary CMB anisotropies, we recover <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mi>w</gb:mi><gb:mo>=</gb:mo><gb:mo>−</gb:mo><gb:mn>1.2</gb:mn><gb:msubsup><gb:mn>0</gb:mn><gb:mrow><gb:mo>−</gb:mo><gb:mn>0.09</gb:mn></gb:mrow><gb:mrow><gb:mo>+</gb:mo><gb:mn>0.15</gb:mn></gb:mrow></gb:msubsup></gb:math>, a <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mn>1.7</ib:mn><ib:mi>σ</ib:mi></ib:math> difference with a cosmological constant. The precision of our results highlights the benefits of multiwavelength multiprobe cosmology and our analysis paves the way for upcoming joint analyses of next-generation datasets.