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 δm_{23}^{2}∼2.5×10^{3}eV^{2} in agreement with recent Earthbased measurements of atmospheric neutrino oscillations, the correction due to nondegeneracy 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 nondegenerate neutrinos the corrections due to nondegeneracy could become important for all the cosmological probes discussed here.
 Publication:

Physical Review D
 Pub Date:
 June 2006
 DOI:
 10.1103/PhysRevD.73.123501
 arXiv:
 arXiv:astroph/0602133
 Bibcode:
 2006PhRvD..73l3501S
 Keywords:

 14.60.Pq;
 98.70.Vc;
 Neutrino mass and mixing;
 Background radiations;
 Astrophysics;
 High Energy Physics  Phenomenology
 EPrint:
 5 pages, 4 figures, v2: replaced with version accepted to the PRD: added fisher matrix analysis, conclusions somewhat chaged