Dynamical evolution of gravitational leptogenesis

Abstract

Radiatively-induced gravitational leptogenesis is a potential mechanism to ex- plain the observed matter-antimatter asymmetry of the universe. Gravitational tidal effects at the quantum loop level modify the dynamics of the leptons in curved spacetime and may be encoded in a low-energy effective action Seff . It has been shown in previous work how in a high-scale BSM theory the CP odd curvature-induced interactions in Seff modify the dispersion relations of leptons and antileptons differently in an expanding universe, giving rise to an effective chemical potential and a non-vanishing equilibrium lepton-antilepton asymmetry. In this paper, the CP even curvature interactions are shown to break lepton number current conservation and modify the evolution of the lepton number density as the universe expands. These effects are implemented in a generalised Boltzmann equation and used to trace the dynamical evolution of the lepton number density in different cosmological scenarios. The theory predicts a potentially significant gravitationally-induced lepton-antilepton asymmetry at very early times in the evolution of the universe.

Flavour effects in gravitational leptogenesis

“…It is evident that due to the large values of the decay parameters the asymmetry N G0 B−L gets washed out strongly and at z B1 one finds negligible value of N Gf B−L as shown in the right panel of figure 4. The plot has been generated for a normal light neutrino mass ordering with a benchmark value of M 1 = 10 7 GeV, M 2 = 10 16 GeV, E ∆L=2 ∼ O(1) (for a realistic flavour case we shall properly deal with E ∆L=2 ) and considering the weak gravity condition T ≤ √ M 1 M Pl [48]. 4 This conclusion is true also for the strongly boosted seesaw systems (γ 1) as well as inverted mass ordering.…”

“…where W ∆L=2 encodes the effect of ∆L = 2 process involving non-resonant N 1 -exchange and is given by [48,49]…”

“…• We have not discussed non-standard cosmological scenarios, e.g., a fast-expanding universe with an equation of state 1/3 < ω < 1 in which gravitational leptogenesis can be implemented even without hierarchical enhancement [48].…”

“…The lepton asymmetry from GW is a consequence of a chiral imbalance in the SM model which sources the asymmetry in the form of left-handed neutrinos, thus not easy to be realised in seesaw models [32]. On the other hand, the operator ∂ µ Rj µ /M 2 can be generated in seesaw models at two-loop level [45][46][47][48] (cf. figure 1) causing a chemical potential and hence a net lepton asymmetry in equilibrium proportional to the time derivative of R. The physical reason for the production of lepton asymmetry in this scenario could be attributed to the fact that C and CP violating operators when couple to the curvature at the quantum level, lead to asymmetric propagation (create a difference in lepton and anti-lepton self-energy) of matter and anti-matter-a phenomenon which is forbidden in flat space by translation and CPT invariance [45].…”

“…Although for p = 1, the equilibrium asymmetry and hence the frozen out asymmetry (N G0 B−L ) get enhanced hierarchically [47], in a generic seesaw model it is not trivial to realise a pure RH neutrino induced gravitational leptogenesis (or following ref. [48], Radiatively-induced gravitational leptogenesis (RIGL)). The reasons being, firstly, the gravitationally produced asymmetry competes with the asymmetry produced by RH neutrino decays, i.e., one has to distinguish the parameter space of each of the cases.…”