Vacuum defects without a vacuum

Topological defects can arise in symmetry breaking models where the scalar field potential V (φ) has no minima and is a monotonically decreasing function of |φ|. The properties of such vacuumless defects are quite different from those of the “usual” strings and monopoles. In some models such defects can serve as seeds for structure formation, or produce an appreciable density of miniblack holes. PACS number(s): 98.80.Cq Typeset using REVTEX Electronic address: [email protected] Electronic address: [email protected] 1 Symmetry-breaking phase transitions in the early universe can result in the formation of topological defects: domain walls, strings, monopoles, and their hybrids [1,2]. A prototypical symmetry breaking model is of the form L = 1 2 ∂μφa∂ φa − V (f) , (1) where φa is a set of scalar fields, a = 1, ..., N , f = (φaφa) , and the potential V (f) has a minimum at a non-zero value of f . Domain walls, for example, are obtained for a singlet scalar field, N = 1. Domain wall solutions, φ = φ(x), interpolate between −η at x → −∞ and +η at x → +∞, where f = η is the minimum of V (f). In this paper, we are going to consider defects in models where V (f) has a local maximum at f = 0 but no minima; instead, it monotonically decreases to zero at f → ∞. Potentials with this asymptotic behavior can arise, for example, due to non-perturbative effects in supersymmetric gauge theories [3]. In a cosmological context, they have been discussed in the so-called quintessence models [4]. Defects arising in such models could be called “quintessential”, but we shall resist this temptation and use a more descriptive term “vacuumless”. We shall see that the properties and evolution of vacuumless defects can be quite different from the usual ones. We begin with the simplest case of a domain wall described by a real scalar field φ with a potential V (f) = λM cosh(f/M) . (2)