Abstract
It has been argued that the Randall-Sundrum (RS) phase transition rate is suppressed when the holographic theory corresponds to a large N Yang-Mills and when the stabilizing field has a small mass. Here we argue that self-interactions can alleviate the latter suppression. We consider a cubic term in the bulk potential for the Goldberger-Wise (GW) scalar that is responsible for stabilizing the RS geometry. Adding a cubic term suffices to separate the two roles of the GW stabilization: generating a large hierarchy and triggering confinement. We study the resulting radion potential and the dynamics of the early universe phase transition. For a negative coefficient of the cubic term, the effect of the cubic becomes important in the infra-red, and the resulting radion potential is deeper, thereby increasing the radion mass while maintaining a large hierarchy. Staying within the radion effective field theory, we calculate the rate of bubble nucleation from the hot phase to the confined RS phase, both in thin and thick wall limits. The cubic term enhances the rate and allows relaxing the condition on the maximum number of colors Nmax of the dual theory for which the phase transition can be completed. Importantly, this reduces the amount of supercooling that the false vacuum undergoes, increases the peak frequency of the gravitational waves (GW) produced from bubble collisions, and reduces the strength of the GW signal. The reduced GW signal is however still within the reach of proposed space-based GW detectors.
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Acknowledgments
We would like to thank P. Creminelli, P. Du and A. Pomarol for comments and discussions at various stages. We would also like to thank N. DePorzio, J. Lodman and W. L. Xu for collaborations at an early stage. The work of RKM and LR is supported by the National Science Foundation under Grant Nos. PHY-1620806, PHY-1748958 and PHY-1915071, the Chau Foundation HS Chau postdoc award, the Kavli Foundation grant “Kavli Dream Team”, and the Moore Foundation Award 8342. Part of this work was completed at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-2210452.
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Mishra, R.K., Randall, L. Consequences of a stabilizing field’s self-interactions for RS cosmology. J. High Energ. Phys. 2023, 36 (2023). https://doi.org/10.1007/JHEP12(2023)036
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DOI: https://doi.org/10.1007/JHEP12(2023)036