Constraining Non-linear Dirac Equations with Neutrino Oscillations

Considering the phenomenological studies of non-linear quantum models, we use an axiomatic approach to modify the Dirac Lagrangian. We apply constraints such as Hermiticity, locality, universality, etc to obtain various generic modified energy dispersion relations. After-which, we use the parameters from the neutrino oscillations to obtain bounds on these new modified dispersion relations.

A first step towards the inflationary trans-Planckian problem treatment in loop quantum cosmology

For most initial conditions, cosmologically relevant physical modes were trans-Planckian at the bounce time, often by many magnitude orders. We improve the usual loop quantum cosmology calculation of the primordial power spectra — in the inflationary framework — by accounting for those trans-Planckian effects through modified dispersion relations. This can induce drastic changes in the spectrum, making it either compatible or incompatible with observational data, depending on the details of the choices operated.