Exploring the Tension between Current Cosmic Microwave Background and Cosmic Shear Data

Abstract

This paper provides a snapshot of the formal <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>S</mi> <mn>8</mn> </msub> <mo>&#8801;</mo> <msub> <mi>&#963;</mi> <mn>8</mn> </msub> <msqrt> <mrow> <msub> <mi mathvariant="sans-serif">&#937;</mi> <mi>m</mi> </msub> <mo>/</mo> <mn>0.3</mn> </mrow> </msqrt> </mrow> </semantics> </math> </inline-formula> tension between Planck 2015 and the Kilo Degree Survey of450 deg<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mn>2</mn> </msup> </semantics> </math> </inline-formula> of imaging data (KiDS-450) or the Canada France Hawaii Lensing Survey (CFHTLenS). We find that the Cosmic Microwave Bckground (CMB) and cosmic shear datasets are in tension in the standard <inline-formula> <math display="inline"> <semantics> <mi mathvariant="sans-serif">&#923;</mi> </semantics> </math> </inline-formula> Cold Dark Matter (<inline-formula> <math display="inline"> <semantics> <mi mathvariant="sans-serif">&#923;</mi> </semantics> </math> </inline-formula>CDM) model, and that adding massive neutrinos does not relieve the tension. If we include an additional scaling parameter on the CMB lensing amplitude <inline-formula> <math display="inline"> <semantics> <msub> <mi>A</mi> <mrow> <mi>l</mi> <mi>e</mi> <mi>n</mi> <mi>s</mi> </mrow> </msub> </semantics> </math> </inline-formula>, we find that this can put in agreement the Planck 2015 with the cosmic shear data. <inline-formula> <math display="inline"> <semantics> <msub> <mi>A</mi> <mrow> <mi>l</mi> <mi>e</mi> <mi>n</mi> <mi>s</mi> </mrow> </msub> </semantics> </math> </inline-formula> is a phenomenological parameter that is found to be more than <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mi>&#963;</mi> </mrow> </semantics> </math> </inline-formula> higher than the expected value in the Planck 2015 data, suggesting an higher amount of lensing in the power spectra, not supported by the trispectrum analysis

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