The Cosmological constant problem

Observational evidence seems to indicate that the expansion of the universe is currently accelerating. Such an acceleration strongly suggests that the content of the universe is dominated by a non-clustered form of matter, the so-called dark energy. The cosmological constant, introduced by Einstein to reconcile General Relativity with a closed and static Universe, is the most likely candidate for dark energy although other options such as a weakly interacting field, also known as quintessence, have been proposed. The fact that the dark energy density is some one hundred and twenty orders of magnitude lower than the energy scales present in the early universe constitutes the cosmological constant problem. We review various aspects of the cosmological constant problem and some interesting scenarios using supersymmetry or extra-dimensions attempting to solve one of the most puzzling issues in physics.     

Cosmological constant and lensing

The effect of the cosmological constant on the curvature of light due to an isolated spherical mass is recalculated without using the lens equation and compared to a lensing cluster. Unité Mixte de Recherche (UMR 6207) du CNRS et des Universités Aix–Marseille 1 et 2 et Sud Toulon–Var, Laboratoire affilié à la FRUMAM (FR 2291).     

Cosmological constant and Minkowski space

Using the framework of classical gravitational field theory, it is shown that the equations of Einstein’s General Relativity with a cosmological constant, if requested to be compatible with the Minkowski space, change form and become the equations of Relativistic Theory of Gravitation. These equations, in contrast to General Relativity, lead us to fundamentally different physical conclusions about the Universe’s evolution and Collapse.     

Cosmological constant and black hole evaporation

An evaporating black hole model based on the Vaidya-de Sitter solution is proposed. The incoming component of the stress tensor is evaluated and its influence on the evaporation process is examined.     

Cosmological constant from quarks and torsion

We present a simple and natural way to derive the observed small, positive cosmological constant from the gravitational interaction of condensing fermions. In the Riemann‐Cartan spacetime, torsion gives rise to the axial–axial vector four‐fermion interaction term in the Dirac Lagrangian for spinor fields. We show that this nonlinear term acts like a cosmological constant if these fields have a nonzero vacuum expectation value. For quark fields in QCD, such a torsion‐induced cosmological constant is positive and its energy scale is only about 8 times larger than the observed value. Adding leptons to this picture could lower this scale to the observed value.     

Cosmological constant from degenerate vacua

Under the hypothesis that the cosmological constant vanishes in the true ground state with lowest possible energy density, we argue that the observed small but finite vacuumlike energy density can be explained if we consider a theory with two or more degenerate perturbative vacua, which are unstable due to quantum tunneling, and if we still live in one of such states. An example is given making use of the topological vacua in non-Abelian gauge theories.     

Cosmological constant and quantum gravitational corrections to the running fine structure constant

The quantum gravitational contribution to the renormalization group behavior of the electric charge in Einstein-Maxwell theory with a cosmological constant is considered. Quantum gravity is shown to lead to a contribution to the running charge not present when the cosmological constant vanishes. This reopens the possibility, suggested by Robinson and Wilczek, of altering the scaling behavior of gauge theories at high energies although our result differs. We show the possibility of an ultraviolet fixed point that is linked directly to the cosmological constant.     

Cosmological constant in SUGRA models and the multiple-point principle

Physics of Atomic Nuclei - An attempt is made to explain the tiny order of magnitude of the cosmological constant in a model involvingt he following ingredients: supersymmetry breaking in N = 1...     

The null energy condition in wormholes with cosmological constant

Dynamic and static wormhole solutions of Einsteins equations with the cosmological constant are presented. The dynamic solutions can be interpreted as Friedmann–Robertson–Walker models with traversable wormholes. The null energy condition is checked for both dynamic and static wormholes and it is shown explicitly that the cosmological constant modifies the violation of this condition.     

Cosmological models with constant deceleration parameter

Berman presented elsewhere a law of variation for Hubble's parameter that yields constant deceleration parameter models of the universe. By analyzing Einstein, Pryce-Hoyle and Brans-Dicke cosmologies, we derive here the necessary relations in each model, considering a perfect fluid.     

Cosmological constant in the Bianchi type-I-modified Brans-Dicke cosmology

In 1961, Brans and Dicke [1] provided an interesting alternative to general relativity based on Mach’s principle. To understand the reasons leading to their field equations, we first consider homogeneous and isotropic cosmological models in the Brans-Dicke theory. Accordingly we start with the Robertson-Walker line element and the energy tensor of a perfect fluid. The scalar field φ is now a function of the cosmic time only. Then we consider spatially homogeneous and anisotropic Bianchi type-I-cosmological solutions of modified Brans-Dicke theory containing barotropic fluid. These have been obtained by imposing a condition on the cosmological parameter Λ(φ). Again we try to focus the meaning of this cosmological term and to relate it to the time coordinate which gives us a collapse singularity or the initial singularity. On the other hand, our solution is a generalization of the solution found by Singh and Singh [2]. As far as we are aware, such solution has not been given earlier.     

Cosmological constant: a lesson from Bose-Einstein condensates

The cosmological constant is one of the most pressing problems in modern physics. We address this issue from an emergent gravity standpoint, by using an analogue gravity model. Indeed, the dynamics of the emergent metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. The direct computation of this term shows that in emergent gravity scenarios this constant may be naturally much smaller than the naive ground-state energy of the emergent effective field theory. This suggests that a proper computation of the cosmological constant would require a detailed understanding about how Einstein equations emerge from the full microscopic quantum theory. In this light, the cosmological constant appears as a decisive test bench for any quantum or emergent gravity scenario.     

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.