Introduction to the Theory of the Early Universe: Hot Big Bang Theory - Second Edition by Valery A Rubakov & Dmitry S Gorbunov

Author:Valery A Rubakov & Dmitry S Gorbunov [Rubakov, Valery A & Gorbunov, Dmitry S]
Language: eng
Format: epub
Tags: gnv64
Publisher: World Scientific Publishing Europe Ltd.
Published: 2017-08-15T00:00:00+00:00

10.1.Order of Phase Transition

Phase transitions occur because of mismatch between the properties of the ground states of the theory at zero and nonzero temperatures. As we show below, in theories with Englert–Brout–Higgs scalar field(s) this is caused by non-trivial temperaturedependent terms in the effective potential. At finite temperature, the equilibrium state of the medium corresponds to the minimum of the Grand thermodynamic potential (Landau potential). As we discussed in Chapter 5, chemical potentials are negligibly small in the early Universe at interesting temperatures T ≳ 1 GeV, and the Grand potential reduces to the (Helmholtz) free energy F. Hence, we consider below the free energy of primordial plasma. To find the expectation value of the scalar field ⟨ϕ⟩T at temperature T, one considers a system in which the average value of the field is fixed and equal to ϕ everywhere in space, but otherwise there is thermal equilibrium. The free energy of such a system depends, of course, on the chosen value ϕ, as well as on temperature. Because of spatial homogeneity, the free energy is proportional to the spatial volume Ω,

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