Refitting Cosmological Data with Neutrino Mass and Degeneracy

Abstract A simple and natural extension of the standard Lambda cold dark matter (ΛCDM) model is to allow relic neutrinos to have finite chemical potentials. We confront this ΛCDM ξ model, a ΛCDM with neutrino mass M ν and degeneracy ξ 3 as additional parameters, with various cosmological data sets. We find that the H 0 and S 8 tensions become significant only in the presence of the cosmic microwave background (CMB) polarization data. Specifically, the global and local measurements agree to within 0.8 σ and 1.6 σ for the H 0 and S 8 tensions, respectively, when the CMB polarization data are not included. Therefore, the H 0 and S 8 tensions exist between CMB temperature and polarization data, both being global measurements. Fitting the ΛCDM ξ model to the CMB temperature data, we find 3 σ evidence for nonzero neutrino mass ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.5</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>7</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.13</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.17</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">eV</mml:mi> </mml:math> ) and degeneracy ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ξ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1.1</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.19</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.41</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> ), and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> neutrino degeneracy parameter is compatible with Big Bang nucleosynthesis data. The scalar index n s exceeds 1 slightly, which is compatible with some hybrid inflation models. Furthermore, the recent DESI baryon acoustic oscillation data prefer the ΛCDM ξ model to the Planck ΛCDM model. Similar results are obtained when including additional supernova data, while the inclusion of the Atacama Cosmology Telescope τ prior shifts the preferred M ν and ξ 3 values closer to zero and brings n s back to the values favored when the polarization data are included.