Resolving the Negative Effective Neutrino Mass Parameter with Cosmic Birefringence

The recent measurement of baryonic acoustic oscillations by the Dark Energy Spectroscopic Instrument reveals a mild tension with observations of the cosmic microwave background (CMB) within the standard <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>) cosmological model. This discrepancy leads to a preference for a total neutrino mass that is lower than the minimum value inferred from neutrino oscillation experiments. Alternatively, this tension can be eased within <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi mathvariant="normal">Λ</g:mi><g:mi>CDM</g:mi></g:math> by assuming a higher optical depth (<j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>τ</j:mi><j:mo>≃</j:mo><j:mn>0.09</j:mn></j:math>), but such a value conflicts with large-scale CMB polarization data. We point out that cosmic birefringence, as suggested by recent Planck reanalyses, resolves this discrepancy if the birefringence angle varies significantly during reionization. Specifically, we consider the fact that the measured cosmic birefringence angle <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mrow><l:msub><l:mrow><l:mi>β</l:mi></l:mrow><l:mrow><l:mn>0</l:mn></l:mrow></l:msub><l:mo>=</l:mo><l:mn>0.34</l:mn><l:mo>±</l:mo><l:mn>0.09</l:mn><l:mo stretchy="false">(</l:mo><l:mn>1</l:mn><l:mi>σ</l:mi><l:mo stretchy="false">)</l:mo><l:mtext> </l:mtext><l:mtext> </l:mtext><l:mi>deg</l:mi></l:mrow></l:math> has the phase ambiguity, i.e., the measured rotation angle is described by <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:mi>β</p:mi><p:mo>=</p:mo><p:msub><p:mrow><p:mi>β</p:mi></p:mrow><p:mrow><p:mn>0</p:mn></p:mrow></p:msub><p:mo>+</p:mo><p:mn>180</p:mn><p:mi>n</p:mi><p:mtext> </p:mtext><p:mtext> </p:mtext><p:mi>deg</p:mi></p:mrow></p:math> (<r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>n</r:mi><r:mo>∈</r:mo><r:mi mathvariant="double-struck">Z</r:mi></r:math>). We show that cosmic birefringence induced by axionlike particles with nonzero <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>n</u:mi></u:math> suppresses the reionization bump, allowing a higher <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>τ</w:mi></w:math> consistent with data. We provide a viable parameter space where the birefringence effect simultaneously accounts for the low-<y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mo>ℓ</y:mo></y:math> polarization spectra, the Planck <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>E</ab:mi><ab:mi>B</ab:mi></ab:math> correlations, and the elevated value of <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>τ</cb:mi></cb:math>, suggesting a key role for cosmic birefringence in current cosmological tensions.