Planck-PR4 anisotropy spectra show better consistency with general relativity
Enrico Specogna, William Giarè, Eleonora Di Valentino
Abstract
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>></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>></nb:mo> <nb:mn>1</nb:mn> </nb:math> , both of which are significantly reduced or disappear within the Planck-PR4 data.