Solitogenesis: Primordial Origin of Non-topological Solitons

We discuss the formation of nontopological solitons in a second-order phase transition in the early Universe. Ratios of dimensionless coupling constants in the Lagrangian determine their abundance and mass. For a large range of parameters, non-topological solitons can be cosmologically significant, contributing a significant fraction of the present mass density of the Universe. Submitted to Physical Review Letters * Work supported by the Department of Energy, contract DE-AC03-76SFOO515. Non-topological soliton solutions of classical field theories were introduced a number of years ago by Rosen,l and by Friedberg, Lee, and Sirlin.2 In the recent literature, variations on this theme include Q-balls,3 cosmic neutrino balls,4 quark nuggets,5 and soliton stars6 Unlike magnetic monopoles and cosmic strings, which arise in theories with non-trivial vacuum topology, non-topological solitons (hereafter, NT%) are rendered stable by the existence of a conserved Noether charge carried by fields confined to a finite region of space. The minimum charge of the stable soliton depends upon ratios of coupling constants,2 and in principle can be very small (of order one). Although the properties of non-topological solitons have been studied by a number of authors,lB6 scenarios for actually producing such objects in the Universe have not been discussed. In this letter, we consider the possibility of forming NTSs during a phase transition in the early Universe. In the context of renormalizable theories ,7 the simplest NTS solution arises from the interaction between a real scalar field u and a complex scalar 4 with Lagrangian L: = ld,$12 + (l/2)(d1a)2 U, where q41,a> = +p2 -u;)2+h/912(o--m)2++uo)3uo+gld/4+A; (1) the constant A is adjusted to give U = 0 at the absolute minimum of the potential. An important feature of this potential is the explicit breaking of the discrete symmetry Q c+ -u driven by the +cr coupling term. It is this term that requires us to include the cubic term for the real scalar field and the 141” term in the Lagrangian (even if they are absent at tree level). Although these terms are traditionally neglected in analyses of NTSS,~~~ as we discuss below, inclusion of