Analytic discussion of spatially closed friedman universes with cosmological constant and radiation pressure

We derive explicit formulas for various quantities of interest in the universes described in the title, and discuss the interpretation of cosmological constant in quantum field theories.     

Analytic solutions of Friedman equation for spatially opened universes with cosmological constant and radiation pressure

Present paper is a continuation of a discussion given by R. Coquereaux and A. Grossmann (Ann. Phys. N.Y.143 (1982), 296) on analytic solutions of spatially closed Friedman universes with cosmological constant and radiation pressure. Our purpose is to find such solutions in the case of opened universes. Explicit formulae are given.     

Gravitational collapse with a cosmological constant

We give a simple example of a spacetime in which one region undergoes gravitational collapse while another undergoes inflation. The spacetime is a spherical ball of dust in a region with a cosmological constant. The implications of this example for the cosmic no hair conjecture are discussed.     

Quantizing gravity with a cosmological constant

We argue that the quantization of gravity with a cosmological constant, Λ, is both necessary and feasible (in the sense that the evaluation of the functional integral is no more difficult than when Λ= 0). We illustrate this point by evaluating the one-loop counterterms and anomalous scaling behavior for pure gravity with a Λ term and for matter fieldsin an external gravitational field. Previous attempts at these calculations are found to be in error. The new results have implications for Hawking's “spacetime foam”.     

Tunnelling with a negative cosmological constant

The point of this paper is to see what light new results in hyperbolic geometry may throw on gravitational entropy and whether gravitational entropy is relevant for the quantum origin of the universe. We introduce some new gravitational instantons which mediate the birth from nothing of closed universes containing wormholes and suggest that they may contribute to the density matrix of the universe. We also discuss the connection between their gravitational action and the topological and volumetric entropies introduced in hyperbolic geometry. These coincide for hyperbolic 4-manifolds, and increase with increasing topological complexity of the 4-manifold. We raise the question of whether the action also increases with the topological complexity of the initial 3-geometry, measured either by its 3-volume or its Matveev complexity. We point out, in distinction to the non-supergravity case, that universes with domains of negative cosmological constant separated by supergravity domain walls cannot be born from nothing. Finally we point out that our wormholes provide examples of the type of Perpetual Motion machines envisaged by Frolov and Novikov.     

Stability of gravity with a cosmological constant

The stability properties of Einstein theory with a cosmological constant Λ are investigated. For Λ > 0, stability is established for small fluctuations, about the de Sitter background, occurring inside the event horizon and semiclassical stability is analyzed. For Λ < 0, stability is demonstrated for all asymptotically anti-de Sitter metrics. The analysis is based on the general construction of conserved flux-integral expressions associated with the symmetries of a chosen background. The effects of an event horizon, which lead to Hawking radiation, are expressedfor general field hamiltonians. Stability for Λ < 0 is proved, using supergravity techniques, in terms of the graded anti-de Sitter algebra with spinorial charges also expressed as flux integrals.     

The Oppenheimer-Snyder space-time with a cosmological constant

We investigate the Oppenheimer-Snyder space-time with a positive cosmological constant A. The interior of the dust sphere is described by the closed Friedmann-Robertson-Walker space-time while the exterior is the Schwarzschild-de Sitter space-time. Due to the cosmological constant A, when the gravitational massM _o of the dust sphere is very large, there is no collapsing solution with the de Sitter-like asymptotic region which expands exponentially in the expanding universe frame. This fact suggests that the very large initial inhomogeneity does not necessarily lead to the failure of the cosmic no hair conjecture.     

Relaxing a large cosmological constant

The cosmological constant (CC) problem is the biggest enigma of theoretical physics ever. In recent times, it has been rephrased as the dark energy (DE) problem in order to encompass a wider spectrum of possibilities. It is, in any case, a polyhedric puzzle with many faces, including the cosmic coincidence problem, i.e. why the density of matter ρm${\rho }_m$ is presently so close to the CC density ρΛ${\rho }_{\Lambda }$. However, the oldest, toughest and most intriguing face of this polyhedron is the big CC problem, namely why the measured value of ρΛ${\rho }_{\Lambda }$ at present is so small as compared to any typical density scale existing in high energy physics, especially taking into account the many phase transitions that our Universe has undergone since the early times, including inflation. In this Letter, we propose to extend the field equations of General Relativity by including a class of invariant terms that automatically relax the value of the CC irrespective of the initial size of the vacuum energy in the early epochs. We show that, at late times, the Universe enters an eternal de Sitter stage mimicking a tiny positive cosmological constant. Thus, these models could be able to solve the big CC problem without fine-tuning and have also a bearing on the cosmic coincidence problem. Remarkably, they mimic the ΛCDM$\mathrm{\Lambda }\text{CDM}$ model to a large extent, but they still leave some characteristic imprints that should be testable in the next generation of experiments.     

Topologically massive planar universes with constant twist

We derive the general from of the topologically massive Einstein equations for stationary metrics. It is found that all these metrics have a nonvanishing twist. We then provide the complete set of solutions with constant twist and show their isometries.     

Wormhole with varying cosmological constant

It has been suggested that the cosmological constant is a variable dynamical quantity. A class of solution has been presented for the spherically symmetric space time describing wormholes by assuming the erstwhile cosmological constant Λ to be a space variable scalar, viz., Λ = Λ (r) . It is shown that the averaged null energy condition (ANEC) violating exotic matter can be made arbitrarily small.     

Self-dual space-times with cosmological constant

It is shown that self-dual solutions of Einstein's equations, with cosmological constant , correspond to certain complex manifolds. This result generalizes the work of Penrose [1], who dealt with the case =0.     

Instabilities in thermal gravity with a cosmological constant

It is shown that in quantum gravity at finite temperature, the effective potential evaluated in the tadpole approximation can have a local minimum below a certain critical temperature. However, when the leading higher order thermal loop corrections are included, one finds that no static solution exists at high temperature.     

Time-dependent cosmological constant

Within the framework of the gauge covariant theory of gravitation it is showed that a time-dependent cosmological constant arises quite naturally as a result of Weyl conformai symmetry broken by quantum effects.On leave of absence from Department de Física Matemática, Universidad de Salamanca, Spain.     

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.     

Conformal cosmology with no cosmological constant

We present a locally conformal invariant cosmology based on the Weyl tensor rather than the Einstein one. The cosmology admits of a de Sitter solution with no cosmological constant.