Dynamical CP Violation in the Early Universe

Following earlier ideas of Dolgov, we show that the asymmetrical dynamical evolution of fields in the early Universe provides a new source for CP violation. This can lead to baryogenesis without any additional CP-violating interactions. The magnitude of this CP violation is time-dependent. In particular, it vanishes (or is very small) in the late Universe after the fields have relaxed (or are in their final approach) to their vacuum values. We provide an explicit example in which our mechanism is realized. [email protected] [email protected] [email protected] 1 Introducing Dynamical CP Violation The observed CP violation in our Universe has so far only been measured in the K-meson and B-meson sectors (see e.g. Ref. [1] for recent reviews on the status of CP violation), and is generally believed to be due to CP-violating phases in the quark mass matrix (the Kobayashi-Maskawa (KM) mechanism [2]). CP violation is one of the key criteria required in order to generate the observed baryon-antibaryon asymmetry of the Universe starting with symmetric initial conditions. However, because of the smallness of the quark masses, CP violation from the KM mechanism is highly suppressed for processes relevant to baryogenesis [3], and all successful mechanisms of baryogenesis studied to date postulate new CP-violating couplings arising in new physics beyond the Standard Model (for recent reviews of baryogenesis see e.g. Ref. [4]). On the other hand, the three required criteria for baryogenesis [5], namely the existence of baryon number violating processes, CP violation, and out-ofequilibrium dynamics, all are present in the Standard Model. Thus, one may wonder if it might not be possible to realize successful baryogenesis without introducing new sources of baryon number violation and new couplings which explicitly break CP (for attempts in this direction see Refs. [6, 7]). In this Letter we point out that within early Universe cosmology there exists a natural source for CP violation. This can be used to obtain the enhanced CP violation required to make it possible to generate a large enough baryon asymmetry in the context of Standard Model baryogenesis. The key observation, already made some time ago by Dolgov [8], is that in a model which contains several complex scalar fields, initial conditions in a given small region of the early Universe will typically generate an asymmetry in the phases of the fields. This asymmetry can be initially induced by thermal or quantum excitations of the fields about the symmetric state. A stage of inflation in the early Universe will lead to an exponential increase in the wavelength of the local fluctuation regions, thus rendering our present Hubble patch of the Universe asymmetric. If the asymmetry in the phases of the fields can be connected with a CP asymmetry, then it is possible to realize a scenario in which the Lagrangian is CP symmetric (modulo the CP-violating phases in the quark mass matrix of the Standard Model), but the phase asymmetry of the fields in the early Universe leads to (possibly large) CP violation during the period when the fields are relaxing to their ground state values (which we assume are symmetric) 4 Thus, a specific feature of our mechanism is that the magnitude of CP violation is time dependent. Large CP violation in the early Universe in sectors other than the KM mass matrix could thus be compatible With respect to the use of rolling scalar fields, our scenario has a certain analogy with the Affleck-Dine (AD) mechanism [9]. However, while the AD mechanism involves new scalar fields carrying baryonic charge and generating a net baryon number, our scalar fields do not involve new baryon-number-violating processes. Note that rolling scalar fields are also used in inflationary baryogenesis scenarios [10, 11, 12, 13, 14]. Once again, in these scenarios the Lagrangian contains new CP or baryon-number-violating interactions.