1. CMB constraints on Lorentz violation in the neutrino sector Zong-Kuan Guo (ITP, CAS) Weihai August 13, 2012

2. outline motivations deformed dispersion relation Boltzmann equation cosmological constraints remarks This talk is based on ZKG, Q-G Huang, R-G Cai, Y-Z Zhang, PRD in press [arXiv:1206.5588]

3.  motivations  neutrino oscillations  neutrinos influence the CMB (massive or massless)  neutrinos influence the LSS

4.  the deformed dispersion relation  the scalar perturbations of the FLRW metric in the synchronous gauge

5.  the action in the first-order formalism  the Lagrangian in the synchronous gauge

6.  the number density, energy density and pressure  the perturbed energy density, pressure, energy flux and shear stress

7.  the Boltzmann equation

8.  the initial conditions

10.  cosmological constraints

11.  remarks  Compared to particle physics experiments, cosmological observations yield much weaker constraints on the Lorentz-violation parameter in the neutrino sector.  We neglects neutrino oscillations, possible species dependence, anisotropies associated with violations of rotation symmetry, and CPT violation.

12. Thanks!