A Perturbative RS I Cosmological Phase Transition

TL;DR

The paper addresses how Randall-Sundrum I–type geometries with soft-wall backreaction can realize a robust, first-order cosmological phase transition while remaining perturbative in the 5D gravity dual. By formulating a 5D Einstein–scalar system with flat 4D slices and brane potentials, and analyzing both zero- and finite-temperature potentials, the authors show that soft-wall constructions support a light dilaton, enhanced bubble nucleation, and a TeV–Planck hierarchy governed by a dual CFT with $N$ around $20$, enabling transitions to complete without losing perturbativity. They compute the nucleation dynamics and predict gravitational-wave signals from the transition, finding that the spectrum strengthens with $N$ and can fall within the reach of LISA or pulsar timing arrays for plausible parameter choices. Overall, the work provides a concrete, testable framework for early-universe near-conformal dynamics with potentially observable gravitational-wave signatures.

Abstract

We identify a class of Randall-Sundrum type models with a successful first order cosmological phase transition during which a 5D dual of approximate conformal symmetry is spontaneously broken. Our focus is on soft-wall models that naturally realize a light radion/dilaton and suppressed dynamical contribution to the cosmological constant. We discuss phenomenology of the phase transition after developing a theoretical and numerical analysis of these models both at zero and finite temperature. We demonstrate a model with a TeV-Planck hierarchy and with a successful cosmological phase transition where the UV value of the curvature corresponds, via AdS/CFT, to an $N$ of $20$, where 5D gravity is expected to be firmly in the perturbative regime.

Figures (12)

• Figure 1: This cartoon shows the evolution of the field $\phi$. It begins in a region where $\phi$ is nearly constant, and the geometry is nearly AdS. At a critical value of the coordinate, $y = y_c$ which is close in proper distance to a curvature singularity, $\phi$ then begins linear evolution, as shown and the curvature quickly grows large. The gap of the theory is set by the position of this "soft-wall."
• Figure 2: These are plots of $f$ vs $\widetilde{\Lambda}_1$ for different values of $N$ (the rows correspond to $N=3$, $6$, and $12$), different values of $v_1$ (left plots are $v_1 = 1$, right are $v_1 = 10$), and on each plot, various values of $\epsilon$ correspond to the various curves. The color shading corresponds to values of $\frac{|V_\text{min}|}{f^4}$.
• Figure 3: This figure displays the conical singularity appearing in the t-y slice of the geometry. A spherical cap of small radius, r is put to regularize the singularity.
• Figure 4: In this figure, we show the minimum of the free energy function rescaled by the fourth power of the temperature. The temperature is set by the inverse compactification radius of the time coordinate. On the right hand side, for comparison, we give the minimum of the free energy divided by the result obtained while neglecting the back-reaction on the geometry, with very large deviations clear at lower values of the temperature. Results are presented in terms of the temperature divided by the 4D effective Planck scale.
• Figure 5: Each panel includes plots of the values for the $O(3)$ and $O(4)$ symmetric bubble actions as a function of the dimensionless IR brane tension $\widetilde{\Lambda}_1$. The critical value for the action as a function of $f/M_\text{Pl}$ is shown. Plots on the left side correspond to $v_1=1$, while plots on the right correspond to $v_1=10$. All plots take $\epsilon = -0.1$.