Neutrinos in Astrophysics and Cosmology - INFN Sezione di Ferrara

Extending the Mass Bound to Other Low-Mass Low Mass Particles
Assume a generic hot dark matter particle that was in thermal equilibrium equilibrium
at
some cosmological epoch
• Internal particle degrees of freedom (e.g. spin states) gX • Mass mX • Effective number of thermal degrees of freedom at freeze-out freeze out g *
Contribution to cosmic
mass density
Free-streaming Free streaming length
m g 10.
75 ⎧ 1 for fermions
Ω h
2 m
= XgX
10.
75 ⎧ 1 for fermions
Ω Xh
2
= X X
X
×
⎨
183
eV
g
*
X
⎩
4
/
3
for
bosons
λ
FS
4
⎛ ⎞
⎡ ⎛ 2
20 Mpc ⎛ T
⎞⎤
⎢ ⎜ Ω
≈ ⎜ X ⎞
⎡ ⎛ 2
20 Mpc T
⎟ +
X T
⎞⎤
⎢1
log
⎜ Ω
≈ ⎜ X ⎟ + 3.
9
X T
1 log 3.
9 ν
⎟
⎥
Ω
2
Ω
2
⎝ Tν
⎠ ⎢ ⎜ Ω 2 ⎟
Xh
⎝ ν ⎠ ⎢ ⎜ Ω 2 ⎥
⎣ ⎝ m T
⎟
Xh
T
⎥
⎣ ⎝ m T
X
⎠
⎦
Perform maximum likelihood analysis for different choices of gX to derive cosmological limit on mX and g and g *
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany IDAPP 2d Meeting, 12-13 May 2006, Ferrara, Italy