Cosmological constant from gauge fields on extra dimensions

We present a new model of dark energy which could explain the observed accelerated expansion of our Universe. We show that a five-dimensional Einstein–Yang–Mills theory defined in a flat Friedmann–Robertson–Walker universe compactified on a circle possesses degenerate vacua in four dimensions. The present Universe could be trapped in one of these degenerate vacua. With the natural requirement that the size of the extra dimension could be of the GUT scale or smaller, the energy density difference between the degenerate vacua and the true ground state can provide us with just the right amount of dark energy to account for the observed expansion rate of our Universe.     

Empty Singularities in Higher-Dimensional Gravity

We study the exact solution of Einstein’s field equations consisting of a (n+2)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density ρ and thickness d, surrounded by two different vacua. We explicitly write down the pressure and the external gravitational fields in terms of ρ and d, the pressure is positive and bounded, presenting a maximum at an asymmetrical position. And if is small enough, the dominant energy condition is satisfied all over the spacetime. We find that this solution presents many interesting features. In particular, it has an empty singular boundary in one of the vacua.     

Emergently thermalized islands in the landscape

In this Letter, we point out that in the eternal inflation driven by the metastable vacua of the landscape, it might be possible that some large and local quantum fluctuations with the null energy condition violation can stride over the barriers between different vacua and straightly create some islands with radiation and matter in new vacua. Then these thermalized islands will evolve with the standard cosmology. We show that such islands may be consistent with our observable universe, while has some distinctly observable signals, which may be tested in coming observations.     

Vacuum sampling in the landscape during inflation

We consider the phenomenological consequences of sampling multiple vacua during inflation motivated by an enormous landscape. A generic consequence of this sampling is the formation of domain walls, characterized by the scale mu of the barriers that partition the accessed vacua. We find that the success of big bang nucleosynthesis (BBN) implies mu > or = 10 TeV, as long as the sampled vacua have a nondegeneracy larger than O(MeV4). Otherwise, the walls will dominate and eventually form black holes that must reheat the universe sufficiently for BBN to take place; in this case, we obtain mu > or = 10(-5)MP. These black holes are not allowed to survive and contribute to cosmic dark matter density.     

Light quarks mass effect on the color ferromagnet model of the QCD vacuum

We study the effect of quark masses on the energy density of two ferro-magnetic vacua in QCD, corresponding to different vacuum symmetries. In the massless limit the two states have the same energy, while as the quark masses are turned on the state with more symmetry elements becomes the “true” vacuum. The dominant contribution to the energy density splitting is proportional tom ² lnm ²     

Yang-Mills cosmologies and collapsing gravitational sphalerons

Cosmological solutions with a homogeneous Yang-Mills field which oscillates and passes between topologically distinct vacua are discussed. These solutions are used to model the collapsing Bartnik-McKinnon gravitational sphaleron and the associated anomalous production of fermions. The Dirac equation is analyzed in these backgrounds. It is shown explicity that a fermion energy level crosses from the negative to positive energy spectrum as the gauge field evolves between the topologically distinct vacua. The cosmological solutions are also generalized to include an axion field.     

Slow-roll inflation in non-geometric flux compactification

By implementing a genetic algorithm we search for stable vacua in Type IIB non-geometric flux compactification on an isotropic torus with orientifold 3-planes. We find that the number of stable dS and AdS vacua are of the same order. Moreover we find that in all dS vacua the multi-field slow-roll inflationary conditions are fulfilled. Specifically we observe that inflation is driven by the axio-dilaton and the Kähler moduli. We also comment on the existence of one stable dS vacuum in the presence of exotic orientifolds.     

Effects of vacuum fluctuation suppression on atomic decay rates

The use of atomic decay rates as a probe of sub-vacuum phenomena will be studied. Because electromagnetic vacuum fluctuations are essential for radiative decay of excited atomic states, decay rates can serve as a measure of the suppression of vacuum fluctuations in non-classical states, such as squeezed vacua. In such states, the renormalized expectation value of the square of the electric field or the energy density can be periodically negative, representing suppression of vacuum fluctuations. We explore the extent to which atomic decays can be used to measure the mean squared electric field or energy density. We consider a scheme in which atoms in an excited state transit a closed cavity whose lowest mode contains photons in a non-classical state. A crucial feature of our analysis is that we do not employ the rotating wave approximation. The change in the decay probability of the atom in the cavity due to the non-classical state can, under certain circumstances, serve as a measure of the mean squared electric field or energy density in the cavity. We make some estimates of the magnitude of this effect, which indicate that an experimental test might be possible, although very challenging.     

Measures on transitions for cosmology from eternal inflation

We argue that, in the context of eternal inflation in the landscape, making predictions for cosmological--and possibly particle physics--observables requires a measure on the possible cosmological histories as opposed to one on the vacua themselves. If significant slow-roll inflation occurs, the observables are generally determined by the history after the last transition between metastable vacua. Hence, we start from several existing measures for counting vacua and develop measures for counting the transitions between vacua.     

Quantum electrodynamics with anisotropic scaling: Heisenberg-Euler action and Schwinger pair production in the bilayer graphene

We discuss quantum electrodynamics emerging in the vacua with anisotropic scaling. Systems with anisotropic scaling were suggested by Hořava in relation to the quantum theory of gravity. In such vacua, the space and time are not equivalent, and moreover they obey different scaling laws, called the anisotropic scaling. Such anisotropic scaling takes place for fermions in bilayer graphene, where if one neglects the trigonal warping effects the massless Dirac fermions have quadratic dispersion. This results in the anisotropic quantum electrodynamics, in which electric and magnetic fields obey different scaling laws. Here we discuss the Heisenberg-Euler action and Schwinger pair production in such anisotropic QED.     

The cosmological constant

The energy density of the vacuum, Λ, is at least 60 orders of magnitude smaller than several known contributions to it. Approaches to this problem are tightly constrained by data ranging from elementary observations to precision experiments. Absent overwhelming evidence to the contrary, dark energy can only be interpreted as vacuum energy, so the venerable assumption that Λ = 0 conflicts with observation. The possibility remains that Λ is fundamentally variable, though constant over large spacetime regions. This can explain the observed value, but only in a theory satisfying a number of restrictive kinematic and dynamical conditions. String theory offers a concrete realization through its landscape of metastable vacua.     

On the low energy spectra of the non-supersymmetric heterotic string theories

The ten dimensional string theories as well as eleven dimensional supergravity are conjectured to arise as limits of a more basic theory, traditionally dubbed M-theory. This notion is confined to the ten dimensional supersymmetric theories. String theory, however, also contains ten dimensional non-supersymmetric theories that have not been incorporated into this picture. In this note we explore the possibility of generating the low energy spectra of various non-supersymmetric heterotic string vacua from the Horava–Witten model. We argue that this can be achieved by imposing on the Horava–Witten model an invariance with respect to some extra operators which identify the orbifold fixed planes in a non-trivial way, and we demonstrate it for the E₈ and SO(16)×SO(16) heterotic string vacua in ten dimensions.     

Out of equilibrium dynamics of supersymmetry at high energy density

We investigate the out of equilibrium dynamics of global chiral supersymmetry at finite energy density. We concentrate on two specific models. The first is the massive Wess–Zumino model which we study in a self-consistent one-loop approximation. We find that for energy densities above a certain threshold, the fields are driven dynamically to a point in field space at which the fermionic component of the superfield is massless. The state, however, is found to be unstable, indicating a breakdown of the one-loop approximation. To investigate further, we consider an O(N) massive chiral model which is solved exactly in the large N limit. For sufficiently high energy densities, we find that for late times the fields reach a nonperturbative minimum of the effective potential degenerate with the perturbative minimum. This minimum is a true attractor for O(N) invariant states at high energy densities, and this provides a mechanism for determining which of the otherwise degenerate vacua is chosen by the dynamics. The final state for large energy density is a cloud of massless particles (both bosons and fermions) around this new nonperturbative supersymmetric minimum. By introducing boson masses which softly break the supersymmetry, we demonstrate a see-saw mechanism for generating small fermion masses. We discuss some of the cosmological implications of our results.     

Coexistence of different vacua in the effective quantum field theory and multiple point principle

According to the Multiple Point Principle, our Universe is on the coexistence curve of two or more phases of the quantum vacuum. The coexistence of different quantum vacua can be regulated by the exchange of the global fermionic charges between the vacua, such as baryonic, leptonic, or family charge. If the coexistence is regulated by the baryonic charge, all the coexisting vacua exhibit the baryonic asymmetry. Due to the exchange of the baryonic charge between the vacuum and matter, which occurs above the electroweak transition, the baryonic asymmetry of the vacuum induces the baryonic asymmetry of matter in our Standard Model phase of the quantum vacuum. The present baryonic asymmetry of the Universe indicates that the characteristic energy scale, which regulates the equilibrium coexistence of different phases of quantum vacua, is about 10⁶ GeV.     

A geometric solution to the coincidence problem, and the size of the landscape as the origin of hierarchy

Weinberg's seminal prediction of the cosmological constant relied on a provisional method for regulating eternal inflation which has since been put aside. We show that a modern regulator, the causal patch, improves agreement with observation, removes many limiting assumptions, and yields additional powerful results. Without assuming necessary conditions for observers such as galaxies or entropy production, the causal patch measure predicts the coincidence of vacuum energy and present matter density. Their common scale, and thus the enormous size of the visible Universe, originates in the number of metastable vacua in the landscape.     

Real-time instantons and suppression of collision-induced tunneling

We consider tunneling processes in QFT induced by collisions of elementary particles. We propose a semiclassical method for estimating the probability of these processes in the limit of very high collision energy. As an illustration, we evaluate the maximum probability of induced tunneling between different vacua in a (1 + 1)-dimensional scalar model with boundary interaction.     

Bounds on Higgs and top quark masses from vacuum stability(degeneracy) with gravitational contributions

Based on the two-loop RGE of standard model gauge, top-Yukawa as well as scalar quartic couplings with full one-loop gravitational contributions in harmonic gauge, we study the constraints on the Higgs and top quark mass from the requirement that the other degenerate vacua at the Planck-dominated region exists. Our numerical calculations show that nature will not develop the other degenerate vacua at the Planck-dominated region with current Higgs and top quark masses. On the other hand, requiring the existence of the other degenerate vacua at the Planck-dominated region will constrain the Higgs and top mass to lie at approximately 130 and 174 Ge V, respectively.     

Why there is something rather than nothing: cosmological constant from summing over everything in lorentzian quantum gravity

The density matrix of the Universe for the microcanonical ensemble in quantum cosmology describes an equipartition in the physical phase space of the theory (sum over everything), but in terms of the observable spacetime geometry this ensemble is peaked about the set of recently obtained cosmological instantons limited to a bounded range of the cosmological constant. This suggests the mechanism of constraining the landscape of string vacua and a possible solution to the dark energy problem in the form of the quasiequilibrium decay of the microcanonical state of the Universe.     

The spontaneous breaking of supersymmetry in curved space-time

The spontaneous breaking of supersymmetry in the presence of a cosmological constant Λ is discussed in a class of theories that includes gauged supergravity and the recently constructed model of N = 1 supergravity coupled to supermatter. The stability of de Sitter, anti-de Sitter and Minkowski vacua in these theories is investigated. Positivity of energy is demonstrated in a model independent way for supersymmetric vacua, even if the scalar potential is unbounded below, and for global minima of the potential for Λ ? 0.Free fields in anti-de Sitter space are considered and the distinction made between the coefficients of quadratic terms in the lagrangian, which vanish for Goldstone scalars, and the physical masses, which give the frequencies and total energies of modes. The number of degrees of freedom depends on gauge invariance, not on the vanishing of mass.The one-loop corrections to the cosmological constant are given for Λ ? 0 and they vanish if the physical masses obey certain sum rules. It is, however, the bilinear coefficients in the N = 1 supergravity-supermatter lagrangian, rather than the physical masses, that satisfy a quadratic sum rule. This sum rule depends on Λ so that a given mass splitting can be obtained for arbitrarily large supersymmetry breaking scales if Λ is sufficiently large and negative.     

Computational complexity of the landscape: Part I

We study the computational complexity of the physical problem of finding vacua of string theory which agree with data, such as the cosmological constant, and show that such problems are typically NP hard. In particular, we prove that in the Bousso-Polchinski model, the problem is NP complete. We discuss the issues this raises and the possibility that, even if we were to find compelling evidence that some vacuum of string theory describes our universe, we might never be able to find that vacuum explicitly. In a companion paper, we apply this point of view to the question of how early cosmology might select a vacuum.