Neutrino mass tension or suppressed growth rate of matter perturbations?

Assuming a minimal <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">Λ</a:mi> </a:math> cold dark matter ( <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi mathvariant="normal">Λ</d:mi> <d:mi>CDM</d:mi> </d:math> ) cosmology with three massive neutrinos, the joint analysis of Planck cosmic microwave background data, DESI baryon acoustic oscillations, and distance moduli measurements of type Ia supernovae from the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mi>Pantheon</g:mi> <g:mo>+</g:mo> <g:mtext>sample</g:mtext> </g:mrow> </g:math> sets an upper bound on the total neutrino mass, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:mo>∑</i:mo> <i:msub> <i:mrow> <i:mi>m</i:mi> </i:mrow> <i:mrow> <i:mi>ν</i:mi> </i:mrow> </i:msub> <i:mo>≲</i:mo> <i:mn>0.06</i:mn> <i:mi>–</i:mi> <i:mn>0.07</i:mn> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:mi>eV</i:mi> </i:mrow> </i:math> , that lies barely above the lower limit from oscillation experiments. These constraints are mainly driven by mild differences in the inferred values of the matter density parameter across different probes that can be alleviated by introducing additional background-level degrees of freedom (e.g., by dynamical dark energy models). However, in this work, we explore an alternative possibility. Since both <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi mathvariant="normal">Ω</k:mi> <k:mi mathvariant="normal">m</k:mi> </k:msub> </k:math> and massive neutrinos critically influence the growth of cosmic structures, we test whether the neutrino mass tension may originate from the way matter clusters, rather than from a breakdown of the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi mathvariant="normal">Λ</o:mi> <o:mi>CDM</o:mi> </o:math> expansion history. To this end, we introduce the growth index <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>γ</r:mi> </r:math> , which characterizes the rate at which matter perturbations grow. Deviations from the standard <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi mathvariant="normal">Λ</t:mi> <t:mi>CDM</t:mi> </t:math> value ( <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>γ</w:mi> <w:mo>≃</w:mo> <w:mn>0.55</w:mn> </w:math> ) can capture a broad class of models, including nonminimal dark sector physics and modified gravity. We show that allowing <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>γ</y:mi> </y:math> to vary significantly relaxes the neutrino mass bounds to <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mo>∑</ab:mo> <ab:msub> <ab:mi>m</ab:mi> <ab:mi>ν</ab:mi> </ab:msub> <ab:mo>≲</ab:mo> <ab:mn>0.13</ab:mn> <ab:mi>–</ab:mi> <ab:mn>0.2</ab:mn> <ab:mtext> </ab:mtext> <ab:mtext> </ab:mtext> <ab:mi>eV</ab:mi> </ab:math> , removing any tension with terrestrial constraints without altering the inferred value of <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msub> <cb:mi mathvariant="normal">Ω</cb:mi> <cb:mi mathvariant="normal">m</cb:mi> </cb:msub> </cb:math> . However, this comes at the cost of departing from standard growth predictions: to have <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mo>∑</gb:mo> <gb:msub> <gb:mi>m</gb:mi> <gb:mi>ν</gb:mi> </gb:msub> <gb:mo>≳</gb:mo> <gb:mn>0.06</gb:mn> <gb:mtext> </gb:mtext> <gb:mtext> </gb:mtext> <gb:mi>eV</gb:mi> </gb:math> , one needs <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>γ</ib:mi> <ib:mo>&gt;</ib:mo> <ib:mn>0.55</ib:mn> </ib:math> , and we find a consistent preference for <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mi>γ</kb:mi> <kb:mo>&gt;</kb:mo> <kb:mn>0.55</kb:mn> </kb:math> at the level of <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mo>∼</mb:mo> <mb:mn>2</mb:mn> <mb:mi>σ</mb:mi> </mb:math> . This preference increases to <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:mo>∼</ob:mo> <ob:mn>2.5</ob:mn> <ob:mi>–</ob:mi> <ob:mn>3</ob:mn> <ob:mi>σ</ob:mi> </ob:math> when a physically motivated prior <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:mo>∑</qb:mo> <qb:msub> <qb:mi>m</qb:mi> <qb:mi>ν</qb:mi> </qb:msub> <qb:mo>≥</qb:mo> <qb:mn>0.06</qb:mn> <qb:mtext> </qb:mtext> <qb:mtext> </qb:mtext> <qb:mi>eV</qb:mi> </qb:math> from oscillation experiments is imposed.