The Exact Critical Bubble Free Energy and the Effectiveness of Effective Potential Approximations

Abstract

To calculate the temperature at which a first-order cosmological phase transition occurs, one must calculate $F_c(T)$, the free energy of a critical bubble configuration. $F_c(T)$ is often approximated by the classical energy plus an integral over the bubble of the effective potential; one must choose a method for calculating the effective potential when $V^{\prime \prime }<0$. We test different effective potential approximations at one loop. The agreement is best if one pulls a factor of ${\mu }^4/T^4$ into the decay rate prefactor [where ${\mu }^2=V^{\prime \prime }({\varphi }_f)$], and takes the real part of the effective potential in the region $V^{\prime \prime }<0$. We perform a similar analysis on the 1-dimensional kink.

11 pages plus 3 figures in jyTeX; CALT-68-1881

References in corpus (6)

• Towards the Theory of Cosmological Phase Transitions
• Comments on the Electroweak Phase Transition
• Vacuum Decay in Theories with Symmetry Breaking by Radiative Corrections
• On the Evaluation of Thermal Corrections to False Vacuum Decay Rates
• Corrections to the Electroweak Effective Action at Finite Temperature
• How Effective is the Effective Potential?

Cited by in corpus (10)

• Theoretical uncertainties for cosmological first-order phase transitions
• Detection of Early-Universe Gravitational Wave Signatures and Fundamental Physics
• Vacuum energy in a spherically symmetric background field
• Dynamics of Weak First Order Phase Transitions
• Thermal Phase Mixing During First Order Phase Transitions
• Bounce in Valley: Study of the extended structures from thick-wall to thin-wall vacuum bubbles
• Evaluation of the One-loop Effective Action at Zero and Finite Temperature
• Casimir energies in spherically symmetric background potentials revisited
• Effective action for bubble nucleation rates
• Thermal Activation Rates in the Chirally Asymmetric Gross-Neveu Model