Abstract

Phase transitions associated with nearly conformal dynamics are known to lead to significant supercooling. A notorious example is the phase transition in Randall-Sundrum models or their CFT duals. In fact, it was found that the phase transition in this case is first-order and the tunneling probability for the radion/dilaton is so small that the system typically remains trapped in the false vacuum and the phase transition never completes. The universe then keeps expanding and cooling. Eventually the temperature drops below the QCD scale. We show that the QCD condensates which subsequently form give an additional contribution to the radion/dilaton potential, an effect which had been ignored so far. This significantly reduces the barrier in the potential and allows the phase transition to complete in a substantially larger region of parameter space. Due to the supercooling, electroweak symmetry is then broken simultaneously. This class of models therefore naturally leads to an electroweak phase transition taking place at or below QCD temperatures, with interesting cosmological implications and signatures.

Highlights

  • Addition, it provides a framework to address the flavour puzzle in the standard model [16,17,18]

  • We show that the QCD condensates which subsequently form give an additional contribution to the radion/dilaton potential, an effect which had been ignored so far

  • As we will show in this paper, such corrections can in particular arise from the QCD condensates which form when the temperature drops to the QCD scale

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Summary

The radion potential in Randall-Sundrum models

We begin with a review of the important properties of the Randall-Sundrum model from which the nearly-conformality of the scalar potential originates. The size yIR of the extra dimension can be stabilized by means of the Goldberger-Wise mechanism [19] To this end, a bulk scalar is introduced, S⊃. As we discuss in more detail, in the early universe the radion needs to transition from the origin to the minimum of the potential. As we discuss in more detail in the appendix, in this case there is always a region around the origin in the radion potential for which the backreaction of the Goldberger-Wise scalar on the geometry can not be neglected. For small as needed to explain the hierarchy between the electroweak (EW) and Planck scales, the position of the barrier is close to the origin of the potential. We will see that they substantially improve the tunneling probability and open up parameter space for a viable cosmology

Dependence of the QCD scale on the radion in Randall-Sundrum models
Contribution of the QCD condensates to the radion potential
The phase transition in Randall-Sundrum models
Effect of the QCD condensates on the phase transition
Cosmological implications and experimental tests
Conclusions
Findings
A Perturbativity constraints for Goldberger-Wise
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