Does a phase transition in the early universe produce the conditions needed for inflation?

Abstract

In the standard ``new inflationary scenario,'' it is assumed that when the Higgs field \ensuremath{\varphi} is cooled below its phase-transition temperature ${T}_{c}$ it is found in a metastable state which has negligible kinetic and spatial-derivative energy but has large, positive potential energy ${V}_{0}$. Hence, in this picture, the stress-energy tensor of \ensuremath{\varphi} is of the form ${T}_{\mathrm{ab}}$=-${V}_{0}$${g}_{\mathrm{ab}}$ and remains of this form until the state becomes unstable and ``rolls down the hill'' to its true minimum at \ensuremath{\varphi}=${\ensuremath{\varphi}}_{c}$. With this stress-energy tensor Einstein's equation for a Robertson-Walker model predicts expansion of the universe on an exponential time scale, i.e., inflation. We argue here that, at least in many possible models this standard picture of the behavior of \ensuremath{\varphi} as it is cooled to ${T}_{c}$ and below is wrong. Rather than be ``supercooled'' to a state with \ensuremath{\varphi}\ensuremath{\approxeq}0 locally, the field should rapidly form domains with \ensuremath{\varphi} near \ifmmode\pm\else\textpm\fi{}${\ensuremath{\varphi}}_{c}$. The dynamics of the phase transition is governed by the growth and coalescence of these domains, not by a ``roll down the hill'' of the spatially averaged value of \ensuremath{\varphi}. Furthermore, the stress-energy tensor of \ensuremath{\varphi} does not take the form needed to produce inflation. Our arguments are based mainly on physical reasoning, but they are supported by the known behavior of certain condensed-matter systems. We believe that our description of dynamical behavior near the phase transition is applicable to a wide class of field-theory models considered in inflation---in particular, to models where \ensuremath{\varphi} is not coupled to other fields and Coleman-Weinberg gauge-coupled models with ${g}^{2}$\ensuremath{\sim}1---although precise criteria for the applicability of our arguments have not been obtained.