A new look at the accelerating universe

We show that the cosmological model having zero cosmological constant, but containing the vacuum energy of a simple quantized free scalar field of low mass (VCDM model), agrees with the cosmic microwave background radiation (CMBR) and supernova (SNe-Ia) data at least as well as the classical cosmological model with a small nonzero cosmological constant. We also show that in the VCDM model the ratio of vacuum pressure to vacuum energy density is less than -1. We display the VCDM results for a set of parameters that give a very good fit to the CMBR power spectrum, and show that the same parameters also give a good fit to the SNe-Ia data.     

Charged perfect fluids in the presence of a cosmological constant

We consider the static and spherically symmetric field equations of general relativity for charged perfect fluid spheres in the presence of a cosmological constant. Following work by Florides (J Phys A Math Gen 16:1419–1433, 1983) we find new exact solutions of the field equations, and discuss their mass radius ratios. These solutions, for instance, require the charged Nariai metric to be the vacuum part of the spacetime. We also find charged generalizations of the Einstein static universe and speculate that the smallness problem of the cosmological constant might become less problematic if charge is taken into account.     

Cosmological constant—the weight of the vacuum

Recent cosmological observations suggest the existence of a positive cosmological constant Λ with the magnitude Λ(G/c³)≈10⁻¹²³. This review discusses several aspects of the cosmological constant both from the cosmological (Sections 1–6) and field theoretical (Sections 7–11) perspectives. After a brief introduction to the key issues related to cosmological constant and a historical overview, a summary of the kinematics and dynamics of the standard Friedmann model of the universe is provided. The observational evidence for cosmological constant, especially from the supernova results, and the constraints from the age of the universe, structure formation, Cosmic Microwave Background Radiation (CMBR) anisotropies and a few others are described in detail, followed by a discussion of the theoretical models (quintessence, tachyonic scalar field, …) from different perspectives. The latter part of the review (Sections 7–11) concentrates on more conceptual and fundamental aspects of the cosmological constant like some alternative interpretations of the cosmological constant, relaxation mechanisms to reduce the cosmological constant to the currently observed value, the geometrical structure of the de Sitter spacetime, thermodynamics of the de Sitter universe and the role of string theory in the cosmological constant problem.     

Surface tension and the cosmological constant

One of the few predictions from quantum gravity models is Sorkin's observation that the cosmological constant has quantum fluctuations originating in the fundamental discreteness of spacetime at the Planck scale. Here we present a compelling analogy between the cosmological constant of the Universe and the surface tension of fluid membranes. The discreteness of spacetime on the Planck scale translates into the discrete molecular structure of a fluid membrane. We propose an analog quantum gravity experiment which realizes Sorkin's idea in the laboratory. We also notice that the analogy sheds light on the cosmological constant problem, suggesting a mechanism for dynamically generating a vanishingly small cosmological constant. We emphasize the generality of Sorkin's idea and suggest that similar effects occur generically in quantum gravity models.     

The relevance of the cosmological constant for lensing

This review surveys some recent developments concerning the effect of the cosmological constant on the bending of light by a spherical mass in Kottler (Schwarzschild–de Sitter) spacetime. Some proposals of how such an effect may be put into a setting of gravitational lensing in cosmology are also discussed. The picture that emerges from this review is that it seems fair to assert that the contribution of Λ to the bending of light has by now been well established, while putting the Λ light-bending terms into a cosmological context is still subject to some interpretation and requires further work and clarification.     

Conformally coupled scalar field solutions and the cosmological constant

Solutions are presented for a scalar field coupled conformally to Einstein gravity with a nonvanishing cosmological constant, in the case that the spacetime metric is spatially homogeneous and isotropic. Since the cosmological constant destroys the conformal invariance of the action, these solutions cannot be obtained by solving the flat space wave equation for the scalar field. It turns out that the metric is determined entirely by the cosmological constant, while the scalar field acquires an apparent mass squared which is proportional to the cosmological constant. It is conjectured that the cosmological constant in the universe at present may thus be disguised as the mass of some scalar field.     

Cosmological Constant and Stability of the Cosmological Models

The importance of cosmological constant for the cosmological models is given. The variations of the cosmological model for parameters λ and k were discussed respectively. Near λ = 0, the cosmological model is unstable with the change of λ, and near λ = β = 0, the cosmological model is unstable with the change of k. So when we consider the stable cosmological model, we must consider the nonzero cosmological constant.     

The solution of the cosmological constant problem from the inhomogeneous equation of state — a hint from modified gravity?

The cosmological constant problem is studied in a two component cosmological model. The universe contains a cosmological constant of an arbitrary size and sign and an additional component with an inhomogeneous equation of state. It is shown that, in a proper parameter regime, the expansion of the universe with a large absolute value of the cosmological constant may asymptotically tend to de Sitter space corresponding to a small effective positive cosmological constant. It is argued that such a behavior can be regarded as a solution of the cosmological constant problem in this model. The mechanism behind the relaxation of the cosmological constant is discussed. A connection with modified gravity theories is discussed and an example of a possible realization of the cosmological constant relaxation in f(R) modified gravity is described.     

Essay: Deconstructing the Cosmological Constant

Deconstruction provides a novel way of dealing with the notoriously difficult ultraviolet problems of four-dimensional gravity. This approach also naturally leads to a new perspective on the holographic principle, tying it to the fundamental requirements of unitarity and diffeomorphism invariance, as well as to a new viewpoint on the cosmological constant problem. The numerical smallness of the cosmological constant is implied by a unique combination of holography and supersymmetry, opening a new window into the fundamental physics of the vacuum.     

Black holes and the weak cosmic censorship

A theory of black holes is developed under the assumption of the weak cosmic censorship. It includes Hawking's theory of black holes in the future asymptotically predictable spacetimes as a special case but it also applies to the cosmological situations including models with nonzero cosmological constant of both signs.     

爱因斯坦宇宙常数和宇宙中暗能量

综述了宇宙在加速膨胀的观察证据,从爱因斯坦场方程和动力学方程出发详细分析爱因斯坦引入宇宙常数在宇宙加速膨胀中的作用,探讨宇宙常数和宇宙中暗能量的关系．     

Cosmic strings in a space–time with positive cosmological constant

We study Abelian strings in a fixed de Sitter background. We find that the gauge and Higgs fields extend smoothly across the cosmological horizon and that the string solutions have oscillating scalar fields outside the cosmological horizon for all currently accepted values of the cosmological constant. If the gauge to Higgs boson mass ratio is small enough, the gauge field function has a power-like behaviour, while it is oscillating outside the cosmological horizon if Higgs and gauge boson mass are comparable. Moreover, we observe that Abelian strings exist only up to a maximal value of the cosmological constant and that two branches of solutions exist that meet at this maximal value. We also construct radially excited solutions that only exist for non-vanishing values of the cosmological constant and are thus a novel feature as compared to flat space–time. Considering the effect of the de Sitter string on the space–time, we observe that the deficit angle increases with increasing cosmological constant. Lensed objects would thus be separated by a larger angle as compared to asymptotically flat space–time.     

General relativity,the massless scalar field,and the cosmological constant

For gravity coupled to a neutral, massless scalar field, Wyman suggested a method of solution in power series valid provided the scalar field depends only on time. In this work we generalize his approach to nonzero cosmological constant.     

Large Numbers and the Time Variation of Physical Constants

We consider a cosmological model consistent withobservation which not only explains the well-knownlarge-number coincidences, but also deduces the valuesof the mass, radius, and age of the universe, the Hubble constant and the cosmological constant,a relation between the pion mass and the Hubble constantknown so far only as a mysterious empirical coincidence,and other features. This model predicts an ever-expanding universe, as indeed latestastrophysical data indicate.     

The spherically symmetric Einstein-scalar field system with positive and vanishing cosmological constant: a comparison

We review recent results concerning the spherically symmetric Einstein-scalar field system with positive cosmological constant. We do so by comparing with the classical results of Christodoulou concerning the asymptotically flat case (vanishing cosmological constant) and by discussing some of the issues which have emerged since the publication of our main results. Concerning the positive cosmological constant case, we also sketch an alternative proof of global in (Bondi) time existence, based on energy estimates, which is presumably more flexible and, consequently, amenable to generalizations; other potential improvements and generalizations of our main results are also discussed.     

A dynamical approach to the cosmological constant

This Letter presents an exact analytic solution of a simple cosmological model in presence of both nonrelativistic matter and scalar field where Einstein's cosmological constant Λ appears as an integration constant. Unlike Einstein's cosmological constant ascribed to vacuum energy, the dark energy density and the energy density of the ordinary matter decrease at the same rate during the expansion of the universe. Therefore the model is free of the coincidence problem. Comparing the predictions using this model with the current cosmological observations shows that the results are consistent.