Marco Matteini

We consider a single real scalar field in flat spacetime with a polynomial potential up to ϕ ⁴, that has a local minimum, the false vacuum, and a deeper global minimum, the true vacuum. When the vacua are almost degenerate we are in the thin wall regime, while as their difference in potential energy increases, we approach the thick wall regime. We give explicit simple formulae for the decay rate of the false vacuum in 3 and 4 spacetime dimensions. Our results include a careful treatment both of the bounce action, which enters at the exponent of the decay rate, and of the functional determinant at one loop, which determines the prefactor. The bounce action is computed analytically as an expansion in the thin wall parameter in generic D dimensions. We find that truncating such an expansion at second order we obtain a remarkably accurate bounce action also deep into thick wall regimes. We calculate the functional determinant numerically in 3 and 4 dimensions and fit the results with simple polynomials of the same thin wall parameter. This allows us to write the complete one-loop decay rate as a compact expression, which works accurately from thin to thick wall regimes.

I present a recap of a fully analytical calculation of the Euclidean action for a self-interacting scalar field with a quartic potential, in the thin-wall approximation. I then apply this result to the coupled fluid-scalar field model, a phenomenologically relevant model for cosmological first order phase transitions, and compare results with numerical simulations from the literature.

I present a recap of a fully analytical calculation of the Euclidean action for a self-interacting scalar field with a quartic potential, in the thin-wall approximation. I then apply this result to the coupled fluid-scalar field model, a phenomenologically relevant model for cosmological first order phase transitions, and compare results with numerical simulations from the literature.

We present a fully analytical calculation of the false vacuum decay rate for a self-interacting scalar field in the thin-wall approximation. We obtain the bounce solution, together with the Euclidean action, counter-terms and renormalization group running, and we extract the functional determinant via the Gel’fand-Yaglom theorem. Our procedure is valid for a generic spacetime dimension 𝐷, and we provide an explicit finite renormalized decay rate in 𝐷 = 3, 4.

We derive a closed-form false vacuum decay rate at one loop in the thin wall limit, where the true and false vacua are nearly degenerate. We obtain the bounce configuration in D dimensions, together with the Euclidean action with a higher order correction, counter-terms and renormalization group running. We extract the functional determinant via the Gel’fand-Yaglom theorem for low and generic orbital multipoles. The negative and zero eigenvalues appear for low multipoles and the translational zeroes are removed. We compute the fluctuations for generic multipoles, multiply and regulate the orbital modes. We find an explicit finite renormalized decay rate in D = 3, 4 and give a closed-form expression for the finite functional determinant in any dimension.