Abstract
We study the cosmological transition of 5D warped compactifications, from the high-temperature black-brane phase to the low-temperature Randall-Sundrum I phase. The transition proceeds via percolation of bubbles of IR-brane nucleating from the black-brane horizon. The violent bubble dynamics can be a powerful source of observable stochastic gravitational waves. While bubble nucleation is non-perturbative in 5D gravity, it is amenable to semiclassical treatment in terms of a “bounce” configuration interpolating between the two phases. We demonstrate how such a bounce configuration can be smooth enough to maintain 5D effective field theory control, and how a simple ansatz for it places a rigorous lower-bound on the transition rate in the thin-wall regime, and gives plausible estimates more generally. When applied to the Hierarchy Problem, the minimal Goldberger-Wise stabilization of the warped throat leads to a slow transition with significant supercooling. We demonstrate that a simple generalization of the Goldberger-Wise potential modifies the IR-brane dynamics so that the transition completes more promptly. Supercooling determines the dilution of any (dark) matter abundances generated before the transition, potentially at odds with data, while the prompter transition resolves such tensions. We discuss the impact of the different possibilities on the strength of the gravitational wave signals. Via AdS/CFT duality the warped transition gives a theoretically tractable holographic description of the 4D Composite Higgs (de)confinement transition. Our generalization of the Goldberger-Wise mechanism is dual to, and concretely models, our earlier proposal in which the composite dynamics is governed by separate UV and IR RG fixed points. The smooth 5D bounce configuration we introduce complements the 4D dilaton/radion dominance derivation presented in our earlier work.
Highlights
These theories often need large number of degrees of freedom ∼ N 2 of the confined constituents and an approximate conformal symmetry in order to generate the large flavor hierarchies
In [16] we showed that in a scenario where the composite theory runs from the proximity of an ultraviolet (UV) renormalization group (RG) fixed point (FP) to that of an infrared (IR) FP, it is possible to have a much faster transition rate, avoiding large primordial matter dilution
In ref. [16], we proposed a scenario from the dualCFT perspective with distinct UV and IR fixed points, which can simultaneously achieve a large Planck-Weak hierarchy and have a larger controlling the phase transitions (PT), such that it can complete promptly in a theoretically controlled parameter regime
Summary
This absence of the IR boundary indicates an absence of confinement This lets us model the deconfined 4D theory using the dual AdS-S geometry in eq (2.3). That is to say that even for finite but large ΛUV, AdSS metric in eq (2.3) represents an approximate solution if we take ρh → ρh(t), determined by the redshifting (2.4) and the Friedmann equations In terms of this quasi-static T , one can calculate the free energy density of the deconfined phase [24], Fdeconfined = V0 − 2π4M53T 4,. The above fact indicates that at the temperature Tc we can have a simultaneous existence of both the confined and the deconfined phases, and the PT under consideration is first order in nature It follows from eq (2.13) that V0 = 2π4M53Tc4 for the almost vanishing cosmological constant today i.e. at φ = φ. The semi-classical bounce solution that we will compute will correspond to quantum tunneling in terms of the gravitational radius ρh, but in terms of T (to match with CFT expectations), it will correspond to a thermal transition as is clear from the presence of in eq (2.4)
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