Cosmological Consequences of Nearly Conformal Dynamics at the TeV scale

TL;DR

The paper investigates cosmological consequences of nearly conformal dynamics at the TeV scale, arguing for a strongly first-order phase transition that undergoes significant supercooling and ends via bubble collisions. It models the transition with a nearly conformal potential $V(\mu)=\mu^4 P[(\mu/\mu_0)^\epsilon]$ and shows that the nucleation temperature $T_n$ is set by the release point $\mu_r$, often yielding $T_n \ll T_c$. Reheating from bubble collisions yields a reheat temperature $T_{\rm reh}$ that can be around the electroweak scale or lower, profoundly affecting baryogenesis and dark matter production, including nonthermal production during reheating. The work also identifies a distinctive stochastic gravity-wave signal in the millihertz range as a smoking-gun signature and discusses experimental probes at the LHC and future GW detectors, along with implications for dark matter and baryogenesis across parameter regimes.

Abstract

Nearly conformal dynamics at the TeV scale as motivated by the hierarchy problem can be characterized by a stage of significant supercooling at the electroweak epoch. This has important cosmological consequences. In particular, a common assumption about the history of the universe is that the reheating temperature is high, at least high enough to assume that TeV-mass particles were once in thermal equilibrium. However, as we discuss in this paper, this assumption is not well justified in some models of strong dynamics at the TeV scale. We then need to reexamine how to achieve baryogenesis in these theories as well as reconsider how the dark matter abundance is inherited. We argue that baryonic and dark matter abundances can be explained naturally in these setups where reheating takes place by bubble collisions at the end of the strongly first-order phase transition characterizing conformal symmetry breaking, even if the reheating temperature is below the electroweak scale $\sim 100$ GeV. We also discuss inflation as well as gravity wave smoking gun signatures of this class of models.

Figures (7)

• Figure 1: Comparison of a typical polynomial potential given here by $\lambda(\mu^2 -\mu_0^2)^2 +\frac{1}{\Lambda^2} (\mu^2 -\mu_0^2)^3$ with a nearly conformal potential of the type of eq. (\ref{['equation:nearlyconformal']}). Both have a minimum at $\mu_{\rm min}\sim 1.2$ TeV. For the usual polynomial potential $\mu_{\rm max}/ \mu_{\rm min} \sim {\cal O}(1)$, unless coefficients are fine-tuned while for the potential (\ref{['equation:nearlyconformal']}) with $|\epsilon| < 1$, one can easily get a shallow potential with widely separated extrema. In this particular example $|\epsilon|=0.2$. The $\bullet$ indicates the position of the maxima.
• Figure 2: The tunneling action $S_3/T$ as a function of $T/T_c$ for a typical nearly conformal potential (solid line) (we used the Goldberger-Wise potential for illustration) and for a usual polynomial Higgs potential (dashed line). The horizontal blue line indicates the tunneling value $S_3/T\sim 4 \log (M_{\rm Pl}/T_{\rm EW})\sim 140$. For a standard potential, the nucleation temperature $T_n$ is always close to the critical one, $T_c$, unless some fine-tuning is invoked. For a nearly conformal potential, supercooling is a general feature and $T_n$ can easily be several orders of magnitude below $T_c$.
• Figure 3: The running of the effective quartic coupling $\kappa$. Tunneling typically occurs when the quartic coupling is close to maximal, for a value of the release point close to $\mu_r \gtrsim \sqrt{\mu_+ \mu_-}$, which can be orders of magnitude smaller than the value $\mu_-$ at the minimum of the potential.
• Figure 4: Number of efolds of inflation as a function of the radion mass. Left: Randall-Sundrum model for different values of $(Ml)^3$ and $\mu_- = 4$ TeV; Right: A generic model with potential (\ref{['equation:nearlyconformal']}) where the constraint fixing the hierarchy, eq. (\ref{['eq:hierarchy']}), is relaxed. At the point where the curves stop, the system cannot tunnel and is stuck in the symmetric phase.
• Figure 5: Contours for the number of efolds (more precisely $\log \mu_-/\mu_r$). The shaded region is where calculability can be trusted, as defined by the constraints in (\ref{['eq:efolds_constraint']}). Below the bottom line, the system never tunnels to the broken phase. From top to bottom, the plots show $N=2$, $3$ and $5$; from left to right the series of three plots respectively use $\xi_-/\xi_+=1.05$, $1.2$ and $1.65$. For larger $N$ the phase transition becomes stronger and beyond $N>6$ the system is generally stuck in the symmetric phase, at least in the domain of calculability and only considering thermal tunneling.