Planck-PR4 anisotropy spectra show better consistency with general relativity

We present the results from a series of analyses on two parametric tests of gravity that modify the growth of linear, subhorizon matter perturbations in the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Λ</a:mi><a:mi>CDM</a:mi></a:math> model. The first test, known as the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mrow><d:mo stretchy="false">(</d:mo><d:mi>μ</d:mi><d:mo>,</d:mo><d:mi mathvariant="normal">Σ</d:mi><d:mo stretchy="false">)</d:mo></d:mrow></d:math> framework, modifies the Poisson and lensing equations from general relativity (GR). The second test introduces the growth index <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>γ</i:mi></i:math>, which directly affects the time evolution of matter density perturbations. Our study is motivated by results from the analysis of the Planck-PR3 2018 spectra, which indicate a preference for <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:msub><k:mrow><k:mi mathvariant="normal">Σ</k:mi></k:mrow><k:mrow><k:mn>0</k:mn></k:mrow></k:msub><k:mo>≠</k:mo><k:mn>0</k:mn></k:mrow></k:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>γ</n:mi><n:mn>0</n:mn></n:msub><n:mo>&gt;</n:mo><n:mn>0.55</n:mn></n:math>, both of which deviate from the <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi mathvariant="normal">Λ</p:mi><p:mi>CDM</p:mi></p:math> predictions at a significance level of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mo>∼</s:mo><s:mn>2.5</s:mn><s:mi>σ</s:mi></s:math>. To clarify the nature of these anomalous results and understand how the lensing anomaly fits into the picture, we analyze the most recent Planck-PR4 spectra extracted from the updated maps. Overall, the Planck-PR4 data show better consistency with GR. The updated likelihood provides constraints on <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi mathvariant="normal">Σ</u:mi><u:mn>0</u:mn></u:msub></u:math> and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msub><x:mi>γ</x:mi><x:mn>0</x:mn></x:msub></x:math> that are consistent with GR within <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mn>1.5</z:mn><z:mi>σ</z:mi></z:math> and <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mn>2</bb:mn><bb:mi>σ</bb:mi></bb:math>, respectively. The updated likelihoods and show even closer agreement, with all parameter values consistent with a <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi mathvariant="normal">Λ</db:mi><db:mi>CDM</db:mi></db:math> cosmology within <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mn>1</gb:mn><gb:mi>σ</gb:mi></gb:math>. This enhanced consistency is closely correlated with the lensing anomaly. Across the different likelihoods, the tendency of <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi mathvariant="normal">Σ</ib:mi><ib:mn>0</ib:mn></ib:msub></ib:math> and <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:msub><lb:mi>γ</lb:mi><lb:mn>0</lb:mn></lb:msub></lb:math> to drift toward nonstandard values matches the observed preference for <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:msub><nb:mi>A</nb:mi><nb:mi>L</nb:mi></nb:msub><nb:mo>&gt;</nb:mo><nb:mn>1</nb:mn></nb:math>, both of which are significantly reduced or disappear within the Planck-PR4 data.