Abstract
The recent observation of 4He implies that our universe has a large lepton asymmetry. We consider the Affleck-Dine (AD) mechanism for lepton number generation. In the AD mechanism, non-topological solitons called L-balls are produced, and the generated lepton number is confined in them. The L-balls protect the generated lepton number from being converted to baryon number through the sphaleron processes. We study the formation and evolution of the L-balls and find that the universe with large lepton asymmetry suggested by the recent 4He measurement can be realized.