Growth of bubbles in cosmological phase transitions

We study how bubbles grow after the initial nucleation event in generic first-order cosmological phase transitions characterized by the values of the latent heat $L$, interface tension $\sigma$, and correlation length $\xi$, and driven by a scalar order parameter $\phi$. Equations coupling $\phi (t,\mathbf{x})$ and the fluid variables $\mathbf{v}(t,\mathbf{x})$, $T(t,\mathbf{x})$ and depending on a dissipative constant $\Gamma$ are derived and solved numerically in the (1+1)-dimensional case starting from a slightly deformed critical bubble configuration $\phi (0,\mathbf{x})$. The parameters $L$, $\sigma$, $\xi$ corresponding to QCD and electroweak phase transitions are chosen and the whole history of the bubble with the formation of combustion and shock fronts is computed as a function of $\Gamma$. Both deflagrations and detonations can appear depending on the values of the parameters. Reheating due to collisions of bubbles is also computed.