Gravitational Backreaction Effects on the Holographic Phase Transition

TL;DR

This work extends radion stabilization in RS models by incorporating backreactions of a bulk scalar on the 5D metric, reconciling the Goldberger–Wise potential with the fully backreacted radion mass via a detuned-brane framework. It derives an interpolating, physically consistent radion potential, analyzes the holographic finite-temperature phase transition, and computes the gravitational-wave imprint, finding that backreactions widen the viable parameter space and can yield a LISA-detectable signal for moderate to large $N$. The analysis clarifies how backreaction modifies radion mass scaling relative to GW and superpotential approaches and discusses implications for the AdS/CFT interpretation and phase transition cosmology. Overall, the study shows that controlled backreactions permit a viable, testable holographic RS scenario with potentially observable gravitational waves while relaxing prior $N$-dependent constraints.

Abstract

We study radion stabilization in the compact Randall-Sundrum model by introducing a bulk scalar field, as in the Goldberger and Wise mechanism, but (partially) taking into account the backreactions from the scalar field on the metric. Our generalization reconciles the radion potential found by Goldberger and Wise with the radion mass obtained with the so-called superpotential method where backreaction is fully considered. Moreover we study the holographic phase transition and its gravitational wave signals in this model. The improved control over backreactions opens up a large region in parameter space and leads, compared to former analysis, to weaker constraints on the rank N of the dual gauge theory. We conclude that, in the regime where the 1/N expansion is justified, the gravitational wave signal is detectable by LISA.

Figures (4)

• Figure 1: The functions $\Lambda_{1,2}$ leading to the two different solutions of the equations of motion. The parameters used are $k_-l = 0.5, \, v_1=0.1 M^{3/2}, \, v_2 = 0.05 M^{3/2}\,\text{and} \, l= M^{-1}$ which corresponds to $m^2 l^2 = 2.25$. The values are chosen for illustrative purposes and do not lead to a realistic hierarchy.
• Figure 2: The left plot shows the comparison of $S_3/T$ and $S_4$ as a function of the release point $\mu_0$ between the approximation in (\ref{['eq:pot_nconf']}) and the full numerical results. The two curves for $S_4$ lie on top of each other and significant deviations only occur for a release point very close to the minimum of the potential. The right plot shows the temperature $T$ as a function of the release point $\mu_0$. The used values are $v_1=4\, M^{3/2}$, $v_2=v_1/3$, $N=3$, $\xi_-=1.5$ and $k_-l\simeq-0.019$.
• Figure 3: Several example spectra of gravitational waves. The straight (dashed) lines are for a reheating temperature $T_{reh}/\sqrt{\Lambda}=10^{16}$ ($T_{reh}/\sqrt{\Lambda}=10^{14}$). From bottom to top the plots use $\beta/\sqrt{\Lambda} = \left\{ 1000,300,100,30,10\right\}$. The sensitivities of the LISA and BBO experiments are taken from Buonanno:2004tp.
• Figure 4: The regions denote the possible positions for the peak of the gravity wave spectrum depending on the parameter $N$. The signal will be detected by LISA, BBO or BBO correlated when it stands above their respective lines.