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

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Method

`cosmomc`modules and associated data files for weak lensing tomography cosmology fitting with KiDS [3,37] (see [38]).

## 3. Results

#### 3.1. Standard Cosmological Model

#### 3.2. Massive Neutrinos

#### 3.3. The Lensing Amplitude

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**$68\%$ credible intervals for cosmological parameters for several data combination in the $\mathsf{\Lambda}$CDM model.

Parameter | Planck TT | CFHTLenS-linear-cut | CFHTLenS | KiDS-linear-cut | KiDS | Planck TT + KiDS | Planck TT + KiDS-linear-cut |
---|---|---|---|---|---|---|---|

${\mathsf{\Omega}}_{\mathrm{m}}$ | $0.315\phantom{\rule{0.166667em}{0ex}}\pm 0.013$ | $0.35\phantom{\rule{0.166667em}{0ex}}\pm 0.16$ | $0.44\phantom{\rule{0.166667em}{0ex}}\pm 0.33$ | $0.222\phantom{\rule{0.166667em}{0ex}}\pm 0.088$ | $0.26\phantom{\rule{0.166667em}{0ex}}\pm 0.12$ | $0.2911\phantom{\rule{0.166667em}{0ex}}\pm 0.0083$ | $0.299\phantom{\rule{0.166667em}{0ex}}\pm 0.010$ |

${\sigma}_{8}$ | $0.830\phantom{\rule{0.166667em}{0ex}}\pm 0.015$ | $0.72\phantom{\rule{0.166667em}{0ex}}\pm 0.16$ | $0.58\phantom{\rule{0.166667em}{0ex}}\pm 0.21$ | $0.92\phantom{\rule{0.166667em}{0ex}}\pm 0.20$ | $0.63\phantom{\rule{0.166667em}{0ex}}\pm 0.21$ | $0.8221\phantom{\rule{0.166667em}{0ex}}\pm 0.0062$ | $0.8279\phantom{\rule{0.166667em}{0ex}}\pm 0.0072$ |

${S}_{8}$ | $0.849\phantom{\rule{0.166667em}{0ex}}\pm 0.024$ | $0.726\phantom{\rule{0.166667em}{0ex}}\pm 0.027$ | $0.61\phantom{\rule{0.166667em}{0ex}}\pm 0.12$ | $0.750\phantom{\rule{0.166667em}{0ex}}\pm 0.040$ | $0.55\phantom{\rule{0.166667em}{0ex}}\pm 0.15$ | $0.810\phantom{\rule{0.166667em}{0ex}}\pm 0.017$ | $0.827\phantom{\rule{0.166667em}{0ex}}\pm 0.020$ |

Planck TTTEEE | Planck TTTEEE + KiDS | Planck TTTEEE + KiDS-linear-cut | CFHTLenS + KiDS | CFHTLenS-linear-cut + KiDS-linear-cut | KiDS + BAO + JLA + R16 | KiDS-linear-cut + BAO + JLA + R16 | |

${\mathsf{\Omega}}_{\mathrm{m}}$ | $0.3162\phantom{\rule{0.166667em}{0ex}}\pm 0.0090$ | $0.3006\phantom{\rule{0.166667em}{0ex}}\pm 0.0065$ | $0.3077\phantom{\rule{0.166667em}{0ex}}\pm 0.0078$ | $0.245\phantom{\rule{0.166667em}{0ex}}\pm 0.085$ | $0.28\phantom{\rule{0.166667em}{0ex}}\pm 0.11$ | $0.319\phantom{\rule{0.166667em}{0ex}}\pm 0.027$ | $0.316\phantom{\rule{0.166667em}{0ex}}\pm 0.026$ |

${\sigma}_{8}$ | $0.831\phantom{\rule{0.166667em}{0ex}}\pm 0.013$ | $0.8282\phantom{\rule{0.166667em}{0ex}}\pm 0.0048$ | $0.8332\phantom{\rule{0.166667em}{0ex}}\pm 0.0054$ | $0.87\phantom{\rule{0.166667em}{0ex}}\pm 0.16$ | $0.73\phantom{\rule{0.166667em}{0ex}}\pm 0.21$ | $0.702\phantom{\rule{0.166667em}{0ex}}\pm 0.048$ | $0.581\phantom{\rule{0.166667em}{0ex}}\pm 0.090$ |

${S}_{8}$ | $0.853\phantom{\rule{0.166667em}{0ex}}\pm 0.018$ | $0.829\phantom{\rule{0.166667em}{0ex}}\pm 0.013$ | $0.844\phantom{\rule{0.166667em}{0ex}}\pm 0.016$ | $0.754\phantom{\rule{0.166667em}{0ex}}\pm 0.029$ | $0.651\phantom{\rule{0.166667em}{0ex}}\pm 0.095$ | $0.721\phantom{\rule{0.166667em}{0ex}}\pm 0.035$ | $0.595\phantom{\rule{0.166667em}{0ex}}\pm 0.094$ |

**Table A2.**$68\%$ credible intervals for cosmological parameters for several data combination in the $\mathsf{\Lambda}$CDM + $\mathsf{\Sigma}{m}_{\nu}$ model.

Parameter | Planck TT | CFHTLenS | CFHTLenS-linear-cut | KiDS | KiDS-linear-cut | Planck TT + KiDS | Planck TT + KiDS-linear-cut |
---|---|---|---|---|---|---|---|

${\mathsf{\Omega}}_{\mathrm{m}}$ | $0.344\phantom{\rule{0.166667em}{0ex}}\pm 0.041$ | $0.41\phantom{\rule{0.166667em}{0ex}}\pm 0.16$ | $0.44\phantom{\rule{0.166667em}{0ex}}\pm 0.55$ | $0.27\phantom{\rule{0.166667em}{0ex}}\pm 0.10$ | $0.31\phantom{\rule{0.166667em}{0ex}}\pm 0.15$ | $0.306\phantom{\rule{0.166667em}{0ex}}\pm 0.027$ | $0.313\phantom{\rule{0.166667em}{0ex}}\pm 0.027$ |

${\sigma}_{8}$ | $0.790\phantom{\rule{0.166667em}{0ex}}\pm 0.051$ | $0.64\phantom{\rule{0.166667em}{0ex}}\pm 0.12$ | $0.47\phantom{\rule{0.166667em}{0ex}}\pm 0.17$ | $0.81\phantom{\rule{0.166667em}{0ex}}\pm 0.17$ | $0.53\phantom{\rule{0.166667em}{0ex}}\pm 0.19$ | $0.799\phantom{\rule{0.166667em}{0ex}}\pm 0.037$ | $0.807\phantom{\rule{0.166667em}{0ex}}\pm 0.037$ |

${S}_{8}$ | $0.841\phantom{\rule{0.166667em}{0ex}}\pm 0.026$ | $0.705\phantom{\rule{0.166667em}{0ex}}\pm 0.026$ | $0.56\phantom{\rule{0.166667em}{0ex}}\pm 0.11$ | $0.731\phantom{\rule{0.166667em}{0ex}}\pm 0.039$ | $0.51\phantom{\rule{0.166667em}{0ex}}\pm 0.16$ | $0.805\phantom{\rule{0.166667em}{0ex}}\pm 0.018$ | $0.822\phantom{\rule{0.166667em}{0ex}}\pm 0.024$ |

Planck TTTEEE | Planck TTTEEE + KiDS | Planck TTTEEE + KiDS-linear-cut | CFHTLenS-linear-cut + KiDS-linear-cut | KiDS + BAO + JLA + R16 | KiDS-linear-cut + BAO + JLA + R16 | ||

${\mathsf{\Omega}}_{\mathrm{m}}$ | $0.329\phantom{\rule{0.166667em}{0ex}}\pm 0.023$ | $0.315\phantom{\rule{0.166667em}{0ex}}\pm 0.024$ | $0.318\phantom{\rule{0.166667em}{0ex}}\pm 0.020$ | $0.35\phantom{\rule{0.166667em}{0ex}}\pm 0.15$ | $0.325\phantom{\rule{0.166667em}{0ex}}\pm 0.028$ | $0.328\phantom{\rule{0.166667em}{0ex}}\pm 0.026$ | |

${\sigma}_{8}$ | $0.811\phantom{\rule{0.166667em}{0ex}}\pm 0.033$ | $0.807\phantom{\rule{0.166667em}{0ex}}\pm 0.036$ | $0.817\phantom{\rule{0.166667em}{0ex}}\pm 0.029$ | $0.61\phantom{\rule{0.166667em}{0ex}}\pm 0.17$ | $0.693\phantom{\rule{0.166667em}{0ex}}\pm 0.048$ | $0.50\phantom{\rule{0.166667em}{0ex}}\pm 0.11$ | |

${S}_{8}$ | $0.848\phantom{\rule{0.166667em}{0ex}}\pm 0.020$ | $0.824\phantom{\rule{0.166667em}{0ex}}\pm 0.016$ | $0.840\phantom{\rule{0.166667em}{0ex}}\pm 0.017$ | $0.611\phantom{\rule{0.166667em}{0ex}}\pm 0.090$ | $0.719\phantom{\rule{0.166667em}{0ex}}\pm 0.035$ | $0.52\phantom{\rule{0.166667em}{0ex}}\pm 0.11$ |

**Table A3.**$68\%$ credible intervals for cosmological parameters for several data combination in the $\mathsf{\Lambda}$CDM + ${A}_{lens}$ model.

Parameter | Planck TT | Planck TT + KiDS-linear-cut | Planck TTTEEE | Planck TTTEEE + KiDS | Planck TTTEEE + KiDS-linear-cut |
---|---|---|---|---|---|

${\mathsf{\Omega}}_{\mathrm{m}}$ | $0.295\phantom{\rule{0.166667em}{0ex}}\pm 0.015$ | $0.278\phantom{\rule{0.166667em}{0ex}}\pm 0.012$ | $0.329\phantom{\rule{0.166667em}{0ex}}\pm 0.023$ | $0.2919\phantom{\rule{0.166667em}{0ex}}\pm 0.0074$ | $0.2983\phantom{\rule{0.166667em}{0ex}}\pm 0.0086$ |

${\sigma}_{8}$ | $0.802\phantom{\rule{0.166667em}{0ex}}\pm 0.018$ | $0.8138\phantom{\rule{0.166667em}{0ex}}\pm 0.0094$ | $0.806\phantom{\rule{0.166667em}{0ex}}\pm 0.017$ | $0.8224\phantom{\rule{0.166667em}{0ex}}\pm 0.0056$ | $0.8271\phantom{\rule{0.166667em}{0ex}}\pm 0.0063$ |

${S}_{8}$ | $0.795\phantom{\rule{0.166667em}{0ex}}\pm 0.032$ | $0.783\phantom{\rule{0.166667em}{0ex}}\pm 0.026$ | $0.817\phantom{\rule{0.166667em}{0ex}}\pm 0.024$ | $0.811\phantom{\rule{0.166667em}{0ex}}\pm 0.015$ | $0.825\phantom{\rule{0.166667em}{0ex}}\pm 0.018$ |

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**Figure 1.**Constraints at $68\%$ and $95\%$ confidence levels on the ${\sigma}_{8}$ vs. ${\mathsf{\Omega}}_{m}$ plane for several combination of datasets in the $\mathsf{\Lambda}$CDM scenario. In both the cases, Planck is in tension at more than $2\sigma $ with the cosmic shear experiments with the original cut, while is in agreement considering their conservative cut.

**Figure 2.**Constraints at $68\%$ (solid) and $95\%$ (dashed) on ${S}_{8}$ for several combination of datasets and models considered in this work. The gray band corresponds to the KiDS bounds in each cosmological scenario.

**Figure 3.**Constraints at $68\%$ and $95\%$ confidence levels on the ${\sigma}_{8}$ vs. ${\mathsf{\Omega}}_{m}$ plane for several combination of datasets in the $\mathsf{\Lambda}$CDM + $\mathsf{\Sigma}{m}_{\nu}$ model. In both of the cases, Planck is still in tension at more than $2\sigma $ with the cosmic shear experiments with the original cut, while is in agreement considering their conservative cut.

**Figure 4.**Constraints at $68\%$ and $95\%$ confidence levels on the ${\sigma}_{8}$ vs. ${\mathsf{\Omega}}_{m}$ plane for several combination of datasets in the $\mathsf{\Lambda}$CDM + ${A}_{lens}$ model. In both of the plots, Planck shifts in agreement with the cosmic shear experiments within $2\sigma $.

Parameter | Prior |
---|---|

${\mathsf{\Omega}}_{b}{h}^{2}$ | $[0.013,0.033]$ |

${\mathsf{\Omega}}_{\mathrm{c}}{h}^{2}$ | $[0.001,0.99]$ |

${\theta}_{s}$ | $[0.5,10]$ |

$\tau $ | $[0.01,0.8]$ |

${n}_{\mathrm{S}}$ | $[0.7,1.3]$ |

$logA$ | $[1.7,5.0]$ |

$\mathsf{\Sigma}{m}_{\nu}$ | $[0,5]$ |

${A}_{lens}$ | $[0,10]$ |

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Di Valentino, E.; Bridle, S.
Exploring the Tension between Current Cosmic Microwave Background and Cosmic Shear Data. *Symmetry* **2018**, *10*, 585.
https://doi.org/10.3390/sym10110585

**AMA Style**

Di Valentino E, Bridle S.
Exploring the Tension between Current Cosmic Microwave Background and Cosmic Shear Data. *Symmetry*. 2018; 10(11):585.
https://doi.org/10.3390/sym10110585

**Chicago/Turabian Style**

Di Valentino, Eleonora, and Sarah Bridle.
2018. "Exploring the Tension between Current Cosmic Microwave Background and Cosmic Shear Data" *Symmetry* 10, no. 11: 585.
https://doi.org/10.3390/sym10110585