# A Critical temperature for bubble nucleation

1. May 11, 2017

### spaghetti3451

Consider that the criterion for bubble nucleation (in a field theory) is the following:

$$\exp(-S_{3}/T) \gtrsim \frac{3}{4\pi} \left(\frac{H}{T}\right)^{4} \left(\frac{2\pi T}{S_{3}}\right)^{3/2},$$

where $S_3$ is the three-dimensional action of the theory and $H$ is the Hubble scale.

1. What is meant by the critical temperature of bubble nucleation?

2. Why does taking the derivative of this criterion give us the critical temperature for bubble nucleation?

N.B. : The critical temperature $T_c$ for bubble nucleation is $T_{c} = (2/11)S_{3}$.

2. May 17, 2017

### PF_Help_Bot

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