Unstable Vacuum State Research Articles

Properties of the false vacuum as a quantum unstable state

We analyze properties of unstable vacuum states from the point of view of the quantum theory. In the literature one can find some suggestions that some of false (unstable) vacuum states may survive up to times when their survival probability has a non-exponential form. At asymptotically late times the survival probability as a function of time $t$ has an inverse power--like form. We show that at this time region the energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t \to \infty$. This means that the energy density in the unstable vacuum state should have analogous properties and hence the cosmological constant $\Lambda = \Lambda (t)$ too. The conclusion is that $\Lambda$ in the Universe with the unstable vacuum should have a form of the sum of the "bare" cosmological constant and of the term of a type $1/t^{2}$: $\Lambda(t) \equiv \Lambda_{bare} + d/ t^{2}$ (where $\Lambda_{bare}$ is the cosmological constant for the Universe with the true vacuum).

False vacuum as an unstable state

Calculations performed within the Standard Model suggest that the electroweak vacuum is unstable if M H M H is the mass of the Higgs particle). LHC discovery of the Higgs boson indicates that M H ≃ 125 GeV. So the vacuum in our Universe may be unstable. We analyze properties of unstable vacuum states from the point of view of the quantum theory. At asymptotically late times the survival probability as a function of time t has an inverse power–like form. We show that at this time region the energy of the false vacuum states tends to the energy of the true vacuum state as 1/ t 2 for t → ∞. This means that the energy density in the unstable vacuum state should have analogous properties and hence the cosmological constant Λ = Λ( t ) too. So Λ in the Universe with the unstable vacuum should have a form of the sum of the “bare” cosmological constant and of the term of a type , (where Λ bare is the cosmological constant for the Universe with the true vacuum).

Properties of the false vacuum as an unstable state

The false (unstable) vacuum is discussed from the point of view of the quantum theory of unstable states. Properties of the energy of the system in the unstable vacuum state are studied. Within the model considered, it is shown that at very late times, the energy of the system in the false vacuum state tends to the energy of the system in the true vacuum state as 1/t2.

Table‐top cosmology with Bose‐Einstein condensates

Cosmic inflation is the theory that the universe underwent a violent, rapid expansion at the beginning of time, giving rise to much of the observed structure in the universe 1. This theory is supported by indirect observational evidence from many different sources (e.g. see 2). However, direct experimental investigation of inflation is of course impossible. For this reason there has been considerable interest in analog models for astrophysics (e.g. see 3), in which analogous behavior is studied in systems that are experimentally convenient. Due to their cleanness and great flexibility, dilute ultra-cold atomic gases (particularly Bose-Einstein condensates) form an attractive system for realizing such analog models. Indeed, a number of such table-top-astrophysics experiments have been conducted with Bose-Einstein condensates. For example, supernova-like collapse and explosion dynamics 4, controlled by modifying inter-atomic interactions using Feshbach resonances, and later interpreted as cosmological particle creation 5; Faster-than-sound flow of a condensate has been used to produce a sonic black hole analog 6; The in situ measurements of density fluctuations in a quenched quasi-two-dimensional condensate have demonstrated Sakharov like oscillations, analogous to the process thought to give rise to the anisotropy in the cosmic microwave background radiation 7. In Quantum simulations of the early universe Opanchuk and collaborators 8 propose using a two component condensate to simulate the inflationary phase of the early universe (see Fig. 1). In appropriate limits the relative phase between the two fields describing the condensate components is known to obey the sine-Gordon equation 9. The sine-Gordon model (SGM) is one of many scalar models for inflation that have been investigated in cosmology. It is thought to provide an acceptable model of the beginning of inflation where, starting from an unstable vacuum state, quantum fluctuations seed the cosmological inhomogeneities that lead to structure formation. However, the SGM likely fails to describe the end of inflation as its scalar potential does not generate efficient parametric resonances needed to ensure reheating of the universe 10, 11. The SGM also has applications in cosmology beyond inflation, and is a model for the “axion” matter field considered as a promising candidate for dark matter12. An important innovation in the scheme proposed by Opanchuk et al. is the introduction of a microwave (linear) coupling between the components that provides a practical way to initialize the system into an unstable vacuum state and controllably explore the subsequent evolution. Approximate numerical simulations, performed using the truncated Wigner approach, verify dynamical clustering can occur within experimentally realistic parameter regimes. The main challenge to realizing the proposed scenario will be finding an atom, and a pair of internal states, with suitable interaction parameters. It is likely that such an atom will be available given the increasing diversity of atomic species that have been Bose-condensed, and the great control over interactions afforded by Feshbach resonances. Aided by the rich toolbox of techniques available to ultra-cold atomic physics an array of opportunities present themselves for developing this line of research, such as: Engineering gravitational-like effects through including long range interactions, e.g. through electromagnetically induced gravity 13; Enhancing quantum fluctuations through stronger interactions or by confining the system in an optical lattice; Engineering richer models by including more spin states and other species of atoms.

Towards a Theory of Entropy Production in the Little and Big Bang

We propose a broadly applicable formalism for the description of coarse grained entropy production in quantum mechanical processes. Our formalism is based on the Husimi transform of the quantum state, which encodes the notion that information about any quantum state is limited by the experimental resolution. We show in two analytically tractable cases (the decay of an unstable vacuum state and reheating after cosmic inflation) that the growth rate of the Wehrl entropy associated with the Husimi function approaches the classical Kolmogorov-Sinai entropy. We also discuss various possible applications of our formalism, including the production of entropy in the early stages of a relativistic heavy ion collision.

Vacuum stability, wormholes, cosmic rays and the cosmological bounds on mt and mH

In the standard model, if the top quark mass m t is larger than some critical value depending on the Higgs mass m H, then we live in an unstable vacuum state corresponding to a local minimum of the effective potential. An experimental discovery of the top quark with m t above this critical value would invalidate the standard version of the wormhole theory, according to which the vacuum energy should be zero at the absolute minimum of the effective potential. However, unless the top quark is much heavier than this, the lifetime is much heavier than this, the lifetime of the unstable vacuum state is greater than the age of our part of the universe. In this paper we develop a stochastic approach to tunneling and apply it to examine the possibility that cosmic ray collisions may trigger vacuum decay and derive improved cosmological bounds on m H and m t.