Relativistic bubble dynamics: From cosmic inflation to hadronic bags

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Abstract
In this paper we develop the complete theory of the relativistic motion of a singular layer of matter under the influence of surface tension and volume tension. In order to account for vacuum tension effects we suggest a formalism of universal applicability: the single degree of freedom of a relativistic ‘‘bubble’’ is coupled in a gauge-invariant manner to a potential three-form A in the presence of gravity. The mathematical and physical consequences of this coupling can be summarized as follows. (i) The action functional of the theory, when written in geometric form, is formally quite similar to the Einstein-Maxwell action for the dynamics of a point charge on a Riemannian manifold. However, in comparison with electrodynamics, bubble dynamics is a highly constrained theory with a vastly different physical content: the gauge field F=dA propagates no degrees of freedom and when it is coupled to gravity alone, it gives rise to a cosmological constant of arbitrary magnitude. (ii) We exploit this peculiar property of the gauge field to solve exactly some of the equations of motion of bubble dynamics. The net physical result is the nucleation of bubbles in different ‘‘vacuum phases’’ of the de Sitter type characterized by two effective and distinct cosmological constants, one inside and one outside the domain wall. (iii) Because of the generality of the above mechanism, the theory is applicable to a variety of different physical situations; in the case of a spherical bubble we derive the radial equation of motion and solve it explicitly in a number of cases of physical interest ranging from cosmology to particle physics. Thus, in curved spacetime we find that our action functional provides a natural basis for the so-called inflationary cosmology; in flat spacetime we find that our action functional generates the same vacuum tension advocated in the so-called ‘‘bag model’’ of strong interactions in order to confine quarks and gluons.