"Big Bang" as a first-order phase transition in the early Universe

Abstract

It is argued that the "Big Bang" initiating the creation of our Universe may be a consequence of a first-order phase transition induced by interaction of a fundamental non-linear scalar field with gravitational field. The Lagrangian describing the scalar field f characterized by "imaginary mass" and nonlinearity of ${\phi}^4$ type, existing in the space-time with non-zero scalar curvature $R$, is proposed to be augmented with an additional linear term $\propto R{\phi}$, along with the standard term $\propto R|{\phi}|^2$ quadratic in ${\phi}$. The term linear in ${\phi}$, playing the role of an "external field", leads to a cubic equation in ${\phi}$ for the extrema of the potential energy of the scalar field and ensures the possibility of a first-order phase transition driven by the parameter proportional to $R$. It is assumed that the early Universe is filled with non-linear scalar field in the ground state and cold matter, neutral with respect to all charges, satisfying the equation of state $p={\nu}{\epsilon}$. It is shown that given the condition ${\nu}>1/3$ the scalar curvature $R={\kappa}(3{\nu}-1){\epsilon}-4{\Lambda}$ (where ${\Lambda}$ is the cosmological constant) decreases with diminishing of the energy density of matter during the Universe's expansion and reaches certain critical value $R_c<0$ when the first-order phase transition occurs. Using parameters characterizing the Higgs field, the rapid "roll-down" of the system into the potential minimum is shown to take place in a time span of about $10^{-31}$ s. During this time the latent heat of the transition is released increasing the temperature of the Universe to the Planck value $T_P=10^{32}$ K, which may be seen as the "Big Bang" producing $4 \cdot 10^{30}$ GW of power.