Detecting neutrino mass difference with cosmology

Abstract

Cosmological parameter estimation exercises usually make the approximation that the three standard neutrinos have degenerate mass, which is at odds with recent terrestrial measurements of the difference in the square of neutrino masses. In this paper we examine whether the use of this approximation is justified for the cosmic microwave background (CMB) spectrum, matter power spectrum and the CMB lensing potential power spectrum. We find that, assuming m^2_{23} ~ 2.5x10^{-3}$eV^2 in agreement with recent Earth based measurements of atmospheric neutrino oscillations, the correction due to non-degeneracy is of the order of precision of present numerical codes and undetectable for the foreseeable future for the CMB and matter power spectra. An ambitious experiment that could reconstruct the lensing potential power spectrum to the cosmic variance limit up to l~1000 will have to take the effect into account in order to avoid biases. The degeneracies with other parameters, however, will make the detection of the neutrino mass difference impossible. We also show that relaxing the bound on the neutrino mass difference will also increase the error-bar on the sum of neutrino masses by a factor of up to a few. For exotic models with significantly non-degenerate neutrinos the corrections due to non-degeneracy could become important for all the cosmological probes discussed here.

5 pages, 4 figures, v2: replaced with version accepted to the PRD: added fisher matrix analysis, conclusions somewhat chaged

References in corpus (29)

• Efficient Computation of CMB anisotropies in closed FRW models
• Cosmological parameters from SDSS and WMAP
• Measurement of the rate of nu_e + d --> p + p + e^- interactions produced by 8B solar neutrinos at the Sudbury Neutrino Observatory
• Cosmological parameter analysis including SDSS Ly-alpha forest and galaxy bias: constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy
• Status of global fits to neutrino oscillations
• Constraints on Neutrino Oscillations Using 1258 Days of Super-Kamiokande Solar Neutrino Data
• Mass Reconstruction with CMB Polarization
• Evidence for an oscillatory signature in atmospheric neutrino oscillation
• The Microwave Anisotropy Probe (MAP) Mission
• Weak Lensing of the CMB: A Harmonic Approach
• Reconstruction of lensing from the cosmic microwave background polarization
• Determining Neutrino Mass from the CMB Alone
• Neutrino masses and the number of neutrino species from WMAP and 2dFGRS
• Mapping the Dark Matter through the CMB Damping Tail
• Analyzing weak lensing of the cosmic microwave background using the likelihood function
• Lensed CMB power spectra from all-sky correlation functions
• Neutrino masses and the dark energy equation of state - relaxing the cosmological neutrino mass bound
• Probing neutrino masses with CMB lensing extraction
• Observables sensitive to absolute neutrino masses: Constraints and correlations from world neutrino data
• Probing neutrino masses with future galaxy redshift surveys
• Current cosmological bounds on neutrino masses and relativistic relics
• Cold + Hot Dark Matter and the Cosmic Microwave Background
• Measuring Dark Matter Power Spectrum from Cosmic Microwave Background
• Cosmology with High-redshift Galaxy Survey: Neutrino Mass and Inflation
• A preference for a non-zero neutrino mass from cosmological data
• Neutrino Mass Spectrum and Future Beta Decay Experiments
• Neutrino mass limits from SDSS, 2dFGRS and WMAP
• If sterile neutrinos exist, how can one determine the total solar neutrino fluxes?
• Cosmological neutrino bounds for non-cosmologists

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• Upper Bound of 0.28 eV on the Neutrino Masses from the Largest Photometric Redshift Survey
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• An improved cosmological bound on the thermal axion mass
• Testing 3+1 and 3+2 neutrino mass models with cosmology and short baseline experiments
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• A novel approach to quantifying the sensitivity of current and future cosmological datasets to the neutrino mass ordering through Bayesian hierarchical modeling
• Constraining Fundamental Physics with Future CMB Experiments
• Cosmological parameters constraints from galaxy cluster mass function measurements in combination with other cosmological data
• Constraints on the neutrino parameters by future cosmological 21cm line and precise CMB polarization observations
• Constraining fundamental physics with the cosmic microwave background
• Observational constraints on cosmic neutrinos and dark energy revisited
• Constraints on massive sterile plus active neutrino species in non minimal cosmologies
• Determination of neutrino mass hierarchy by 21 cm line and CMB B-mode polarization observations
• White Paper: Measuring the Neutrino Mass Hierarchy
• Weak lensing: Dark Matter, Dark Energy and Dark Gravity
• Revised WMAP constraints on neutrino masses and other extensions of the minimal $\Lambda$CDM model
• Cosmological implications of the KATRIN experiment
• Relaxing cosmological constraints on current neutrino masses