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M. Gell-Mann, P. Ramond, and R. Slansky, Supergravity Workshop Stony Brook, New York, September 27-28, 1979 , Conf. Proc. C790927
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2017

Neutrino Mass Priors for Cosmology from Random Matrices

Long, Andrew J., Raveri, Marco, Hu, Wayne et al.

Understand

Cosmological measurements of structure are placing increasingly strong constraints on the sum of the neutrino masses, $\Sigma m_\nu$, through Bayesian inference.

Because these constraints depend on the choice for the prior probability $\pi(\Sigma m_\nu)$, we argue that this prior should be motivated by fundamental physical principles rather than the ad hoc choices that are common in the literature.
The first step in this direction is to specify the prior directly at the level of the neutrino mass matrix $M_\nu$, since this is the parameter appearing in the Lagrangian of the particle physics theory.
Thus by specifying a probability distribution over $M_\nu$, and by including the known squared mass splittings, we predict a theoretical probability distribution over $\Sigma m_\nu$ that we interpret as a Bayesian prior probability $\pi(\Sigma m_\nu)$.

Built on

H. Jeffreys, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 186
1946
Earlier work this paper cites.
P. Minkowski, Phys.Lett. B67
1977
Earlier work this paper cites.
M. Gell-Mann, P. Ramond, and R. Slansky, Supergravity Workshop Stony Brook, New York, September 27-28, 1979 , Conf. Proc. C790927
Original
1979
Earlier work this paper cites.
R. N. Mohapatra and G. Senjanovic, Phys.Rev.Lett. 44
1980
Earlier work this paper cites.
T. Yanagida, Prog.Theor.Phys. 64
1980
Earlier work this paper cites.
J. Schechter and J. Valle, Phys.Rev. D22
1980
Earlier work this paper cites.
R. N. Mohapatra and G. Senjanovic, Phys.Rev. D23
1981
Earlier work this paper cites.
R. E. Kass and L. Wasserman, Journal of the American Statistical Association 91
1996
Earlier work this paper cites.
L. J. Hall, H. Murayama, and N. Weiner, Phys. Rev. Lett. 84
2000
Earlier work this paper cites.
N. Haba and H. Murayama, Phys. Rev. D63
2001
Earlier work this paper cites.
A. de Gouvea and H. Murayama, Phys. Lett. B573
2003
Earlier work this paper cites.
L. Susskind, (2003), arXiv:hep-th/0302219 [hep-th]
2003
Earlier work this paper cites.
D. Sivia and J. Skilling, Data analysis: a Bayesian tutorial , Oxford science publications (Oxford University Press, 2006)
2006
Earlier work this paper cites.
L. J. Hall, M. P. Salem, and T. Watari, Phys. Rev. D76
Original
2007
Earlier work this paper cites.
L. J. Hall, M. P. Salem, and T. Watari, Phys. Rev. Lett. 100
Original
2008
Earlier work this paper cites.
L. J. Hall, M. P. Salem, and T. Watari, Phys. Rev. D79
Original
2009
Earlier work this paper cites.