Spacetime Curvature Coupling of Spinors in Early Universe: Neutrino Asymmetry and a Possible Source of Baryogenesis

Abstract

It is well known that when a fermion propagates in curved space-time, its spin couples to the curvature of background space-time. We propose that this interaction for neutrinos propagating in early curved universe could give rise to a new set of dispersion relations and then neutrino asymmetry at equilibrium. We demonstrate this with the Bianchi models which describe the homogeneous but anisotropic and axially symmetric universe. If the lepton number violating processes freeze out at 10 −37 second when temperature T ∼ 10 15 GeV, neutrino asymmetry of the order of 10 −10 can be generated. A net baryon asymmetry of the same magnitude can thus be generated from this lepton asymmetry either by a GUT B − L symmetry or by the electro-week sphaleron processes which have B + L symmetry.KEY WORDS : neutrino asymmetry, early universe, anisotropic space-time, CPT violation PACS NO. : 04.62.+v, 11.30.Er, 11.30.Fs The asymmetry of neutrino in universe is a known fact. This asymmetry is thought to arise due to lepton number asymmetry, e.g., via the Affleck-Dine mechanism [1]. There are several important consequences of a large neutrino asymmetry in early universe which may have effects on production of light elements during BBN, contribution of relic neutrinos to the present energy density of universe, change of neutrino decoupling temperature, cosmic microwave background etc. [2]. Also the massive neutrinos with large asymmetry can explain the existence of cosmic radiation with energy greater than GZK cutoff [3]. Keeping all these importance in mind, our present goal is to prescribe a new mechanism which can give an insight to the origin of neutrino asymmetry fixed up in the early era.When any fermion propagates in curved space-time its spin couples to the background curvature connection and gives rise to an interaction. The various aspects of this feature have been studied in past (e.g., [4][5][6][7][8][9][10][11][12]). It has also been shown that this interaction may be responsible for an additional neutrino asymmetry even in the present era of universe [13][14][15]. However, it is very difficult to visualize as the strength of the above mentioned interaction is negligible in our earth which is practically flat. In a similar fashion, the space-time around a black hole can generate neutrino asymmetry locally [13,15], but as we do not have overall information about number of black holes and their * ujjal@iucaa.ernet.in † bmukhopa@cfa.harvard.edu ‡ nkd@iucaa.ernet.in 1 corresponding spin orientation, it is very difficult to predict whether it produces a significant asymmetry over the relic value or not. A similar mechanism to produce asymmetry was noted earlier [16]. Later, the Lorentz and the CPT violating scenarios were addressed in the context of Riemann-Cartan space-times [17] and in the neutrino sector [18], although in curved space-time a precise definition of the CPT symmetry is challenging to establish.The important fact to note is that the interaction term, arising due to spin-curvature coupling, does not preserve...

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