Thick-wall Limits Research Articles

Consequences of a stabilizing field’s self-interactions for RS cosmology

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.

Exact one-loop false vacuum decay rate

We discuss an exact false vacuum decay rate at one loop for a real and complex scalar field in a quartic-quartic potential with two tree-level minima. The bounce solution is used to compute the functional determinant from both fluctuations. We obtain the finite product of eigenvalues and remove translational zero modes. The orbital modes are regularized with the zeta function and we end up with a complete renormalized decay rate. We derive simple expansions in the thin and thick wall limits and determine their validity.

SupersymmetricQ-balls and boson stars in(d+1)dimensions

We construct supersymmetric $Q$-balls and boson stars in $(d+1)$ dimensions. These nontopological solitons are solutions of a scalar field model with global $U(1)$ symmetry and a scalar field potential that appears in gauge-mediated supersymmetry breaking in the minimal supersymmetric extension of the standard model. We are interested in both the asymptotically flat as well as in the asymptotically anti-de Sitter (AdS) solutions. In particular, we show that for our choice of the potential gravitating, asymptotically flat boson stars exist in $(2+1)$ dimensions. We observe that the behavior of the mass and charge of the asymptotically flat solutions at the approach of the maximal frequency depends strongly on the number of spatial dimensions. In particular, we find that in the ``thick-wall limit'' $Q$-balls are always unstable in flat space-time, but that they can become stable in AdS. Moreover, for the asymptotically AdS solutions the model on the conformal boundary can be interpreted as describing $d$-dimensional condensates of scalar glueballs.

How does gravity save or killQ-balls?

We explore stability of gravitating Q-balls with potential $V_4(\phi)={m^2\over2}\phi^2-\lambda\phi^4+\frac{\phi^6}{M^2}$ via catastrophe theory, as an extension of our previous work on Q-balls with potential $V_3(\phi)={m^2\over2}\phi^2-\mu\phi^3+\lambda\phi^4$. In flat spacetime Q-balls with $V_4$ in the thick-wall limit are unstable and there is a minimum charge $Q_{{\rm min}}$, where Q-balls with $Q<Q_{{\rm min}}$ are nonexistent. If we take self-gravity into account, on the other hand, there exist stable Q-balls with arbitrarily small charge, no matter how weak gravity is. That is, gravity saves Q-balls with small charge. We also show how stability of Q-balls changes as gravity becomes strong.

Q-balls in flat potentials

We study the classical and absolute stability of Q-balls in scalar field theories with flat potentials arising in both gravity-mediated and gauge-mediated models. We show that the associated Q-matter formed in gravity-mediated potentials can be stable against decay into their own free particles as long as the coupling constant of the nonrenormalizable term is small, and that all of the possible three-dimensional Q-ball configurations are classically stable against linear fluctuations. Three-dimensional gauge-mediated Q-balls can be absolutely stable in the thin-wall limit, but are completely unstable in the thick-wall limit.

Slow nucleation rates in chain inflation with QCD axions or monodromy

The previous proposal (by two of us) of chain inflation with the QCD axion is shown to fail. The proposal involved a series of fast tunneling events, yet here it is shown that tunneling is too slow. We calculate the bubble nucleation rates for phase transitions in the thick wall limit, approximating the barrier by a triangle. A similar problem arises in realization of chain inflation in the string landscape that uses series of minima along the monodromy staircase around the conifold point. The basic problem is that the minima of the potential are too far apart to allow rapid enough tunneling in these two models. We entertain the possibility of overcoming this problem by modifying the gravity sector to a Brans-Dicke theory. However, one would need extremely small values for the Brans-Dicke parameter in the early universe. Many successful alternatives exist, including other axions (with mass scales not set by QCD) or potentials with comparable heights and widths that do not suffer from the problem of slow tunneling and provide successful candidates for chain inflation.

Finite-temperature phase transition in ϕ6 potential

The temperature dependance of the action in thin-wall and thick-wall limits is obtained analytically for the ϕ6 scalar potential. The nature of the phase transition is investigated from the quantum tunnelling regime at low temperatures to the thermal hopping regime at high temperatures. It is first-order for the case of a thin wall while for the thick wall it is second- order. PACS Nos.: 10.10.Wx, 05.70.Fh, 10.10.Ef

Some stationary properties of aQ-ball in arbitrary space dimensions

Introducing new physically motivated ansaetze, we explore both analytically and numerically the classical and absolute stabilities of a single Q-ball in an arbitrary number of spatial dimensions D, working in both the thin and thick wall limits.

Stability of Q-Balls and Catastrophe

We propose a practical method for analyzing stability of Q-balls for the whole parameter space, which includes the intermediate region between the thin-wall limit and thick-wall limit as well as Q-bubbles (Q-balls in false vacuum), using catastrophe theory. We apply our method to the two concrete models, V3 = m 2 φ 2 /2 − μφ 3 + λφ 4 and V4 = m 2 φ 2 /2 − λφ 4 + φ 6 /M 2 . We find that V3 and V4 Models fall into fold catastrophe and cusp catastrophe, respectively, and their stability structures are quite different from each other.

Bubble formation in ϕ6 potential

The scalar field theory of the ϕ6 potential is studied at zero temperature and at high temperature. The equations of motion are solved numerically to obtain O(4) spherical symmetric and O(3) cylindrical symmetric bounce solutions. These solutions control the rates for tunneling from the false vacuum to the true vacuum by bubble formation. The range of validity of the thin-wall approximation is investigated. An analytical solution for the bounce is presented, which reproduces the action in the thin-wall as well as the thick-wall limits. PACS Nos.: 11.10.Ef, 05.70.Fh, 11.10.Wx

Phase Transition in Potential

Scalar field theory with an asymmetric potential was studied at zero temperature and high-temperature for Φ6 potential. The equations of motion are solved numerically to obtain O(4) spherical symmetric and O(3) cylindrical symmetric bounce solutions. These solutions control the rates for tunneling from the false vacuum to the true vacuum by bubble formation. The range of validity of the thin-wall approximation (TWA) was investigated. An analytical solution for the bounce is presented, which reproduces the action in the thin-wall as well as the thick-wall limits.

QUANTUM TUNNELLING OR THERMAL HOPPING

The nature of the transition from the quantum tunneling regime to the thermal hopping regime has importance in the study of condensed matter physics and cosmological phase transitions. It may also be of significance in collapse from quantum state to a classical state due to measurement (or loss of coherence due to some other process). We study this transition analytically in scalar field theory with a fourth order term. We obtain analytic bounce solutions which correctly give the action in thin and thick wall limits of the potential. We find that the transition is of the second order for the case of thick wall while it seems to be of first order for the case of thin wall.

Analytical approach to the transition to thermal hopping in the thin- and thick-wall approximations

The nature of the transition from the quantum tunneling regime at low temperatures to the thermal hopping regime at high temperatures is investigated analytically in scalar field theory. An analytical bounce solution is presented, which reproduces the action in the thin-wall as well as thick-wall limits. The transition is first order for the case of a thin wall while for the thick wall case it is second order.

Analytical and numerical properties of Q-balls

Stable non-topological solitons, Q-balls, are studied using analytical and numerical methods. Three different physically interesting potentials that support Q-ball solutions are considered: two typical polynomial potentials and a logarithmic potential inspired by supersymmetry. It is shown that Q-balls in these potentials exhibit different properties in the thick-wall limit where the charge of a Q-ball is typically considerably smaller than in the thin-wall limit. Analytical criteria are derived to check whether stable Q-balls exist in the thick-wall limit for typical potentials. Q-ball charge, energy and profiles are presented for each potential studied. Evaporation rates are calculated in the perfect thin-wall limit and for realistic Q-ball profiles. It is shown that in each case the evaporation rate increases with decreasing charge.