Stress-energy connection and cosmological constant problem

We study gravitational properties of vacuum energy by erecting a geometry on the stress-energy tensor of vacuum, matter and radiation. Postulating that the gravitational effects of matter and radiation can be formulated by an appropriate modification of the spacetime connection, we obtain varied geometrodynamical equations which properly comprise the usual gravitational field equations with, however, Planck-suppressed, non-local, higher-dimensional additional terms. The prime novelty brought about by the formalism is that, the vacuum energy does act not as the cosmological constant but as the source of the gravitational constant. The formalism thus deafens the cosmological constant problem by channeling vacuum energy to gravitational constant. Nevertheless, quantum gravitational effects, if any, restore the problem via the graviton and graviton-matter loops, and the mechanism proposed here falls short of taming such contributions to cosmological constant.     

Possible effects of a cosmological constant on black hole evolution

We explore possible effects of vacuum energy on the evolution of black holes. If the universe contains a cosmological constant, and if black holes can absorb energy from the vacuum, then black hole evaporation could be greatly suppressed. For the magnitude of the cosmological constant suggested by current observations, black holes larger than 4×10²⁴ g would accrete energy rather than evaporate. In this scenario, all stellar and supermassive black holes would grow with time until they reach a maximum mass scale of 6×10⁵⁵ g, comparable to the mass contained within the present day cosmological horizon.     

Twisting type N vacuums with cosmological constant

We provide the first examples of vacuum metrics with cosmological constant which have a twisting quadruple principal null direction.     

Axiomatic approach to the cosmological constant

A theory of the cosmological constant Λ is currently out of reach. Still, one can start from a set of axioms that describe the most desirable properties a cosmological constant should have. This can be seen in certain analogy to the Khinchin axioms in information theory, which fix the most desirable properties an information measure should have and that ultimately lead to the Shannon entropy as the fundamental information measure on which statistical mechanics is based. Here we formulate a set of axioms for the cosmological constant in close analogy to the Khinchin axioms, formally replacing the dependence of the information measure on probabilities of events by a dependence of the cosmological constant on the fundamental constants of nature. Evaluating this set of axioms one finally arrives at a formula for the cosmological constant given by , where G is the gravitational constant, m_e the electron mass, and α_el the low-energy limit of the fine structure constant. This formula is in perfect agreement with current WMAP data. Our approach gives physical meaning to the Eddington-Dirac large-number hypothesis and suggests that the observed value of the cosmological constant is not at all unnatural.     

Dimensionality and the cosmological constant

In the Kaluza-Klein model with a cosmological constant Λ and a flux, the external spacetime of the created universe from aS ^s × S ^n−s seed instanton can be identified in quantum cosmology. One can also show that in the internal space theeffective cosmological constant is most probably zero.     

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.     

Effective cosmological constant within the expanding axion universe

We show that the value of an effective cosmological constant, _Λeff${\Lambda }_{\mathit{eff}}$, is influenced by the dimensionality of the space. Results were obtained in the framework of the axion model describing expansion of the inhomogeneous universe. _Λeff${\Lambda }_{\mathit{eff}}$ determines the tension of the space (i.e. elasticity), and is relaxed when extra dimensions are accessible. We demonstrate that the effective value of the cosmological constant may be tuned to be consistent with experimental observation. Inhomogeneities considered are representative of temperature fluctuations observed within the cosmic microwave background radiation.     

Screening of cosmological constant in non-local gravity

We discuss a possible mechanism to screen a cosmological constant in non-local gravity. We find that in a simple model of non-local gravity with the Lagrangian of the form, R+f(^□−1R)−2Λ$R+f({\square }^{-1}R)-2\Lambda$ where f(X)$f(X)$ is a quadratic function of X, there is a flat spacetime solution despite the presence of the cosmological constant Λ. Unfortunately, however, we also find that this solution contains a ghost in general. Then we discuss the condition to avoid a ghost and find that one can avoid it only for a finite range of ‘time’. Nevertheless our result suggests the possibility of solving the cosmological constant problem in the context of non-local gravity.     

Gravitational instabilities of isothermal spheres in the presence of a cosmological constant

Gravitational instabilities of isothermal spheres are studied in the presence of a positive or negative cosmological constant, in the Newtonian limit. In gravity, the statistical ensembles are not equivalent. We perform the analysis both in the microcanonical and the canonical ensembles, for which the corresponding instabilities are known as ‘gravothermal catastrophe’ and ‘isothermal collapse’, respectively. In the microcanonical ensemble, no equilibria can be found for radii larger than a critical value, which is increasing with increasing cosmological constant. In contrast, in the canonical ensemble, no equilibria can be found for radii smaller than a critical value, which is decreasing with increasing cosmological constant. For a positive cosmological constant, characteristic reentrant behavior is observed.     

On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass μ≠0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy–momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form g_μ,νρ with ρ>0, thus providing a concrete quantum field theoretic model of the cosmological constant. This ρ represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p0.     

The cosmological constant as an eigenvalue of the Hamiltonian constraint in a varying speed of light theory

In the framework of a Varying Speed of Light theory, we study the eigenvalues associated with the Wheeler‐DeWitt equation representing the vacuum expectation values associated with the cosmological constant. We find that the Wheeler‐DeWitt equation for the Friedmann‐Lemaître‐Robertson‐Walker metric is completely equivalent to a Sturm‐Liouville problem provided that the related eigenvalue and the cosmological constant be identified. The explicit calculation is performed with the help of a variational procedure with trial wave functionals related to the Bessel function of the second kind . After having verified that in ordinary General Relativity no eigenvalue appears, we find that in a Varying Speed of Light theory this is not the case. Nevertheless, instead of a single eigenvalue, we discover the existence of a family of eigenvalues associated to a negative power of the scale. A brief comment on what happens at the inflationary scale is also included.     

A naturally light dilaton and a small cosmological constant

We explore off-diagonal deformations of ‘prime’ metrics in Einstein gravity (for instance, for wormhole configurations) into ‘target’ exact solutions in $f(R,T)$ -modified and massive/bi-metric gravity theories. The new classes of solutions may, or may not, possess Killing symmetries and can be characterized by effective induced masses, anisotropic polarized interactions, and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small eccentricity rotoid configurations, we can generate wormhole-like objects matching an external black ellipsoid—de Sitter geometries. We conclude that there are nonholonomic transforms and/or non-trivial limits to exact solutions in general relativity when modified/massive gravity effects are modeled by off-diagonal and/or nonholonomic parametric interactions.     

Republication of: The cosmological constant and the theory of elementary particles (By Ya. B. Zeldovich)

The seminal paper by Ya. B. Zeldovich (Soviet Physics Uspekhi 11, 381–393, 1968) is reprinted here, together with an editorial comment on its lasting scientific relevance, and a biography of the author.

Quintessential inflation from a variable cosmological constant in a 5D vacuum

We explore an effective 4D cosmological model for the universe where the variable cosmological constant governs its evolution and the pressure remains negative along all the expansion. This model is introduced from a 5D vacuum state where the (space-like) extra coordinate is considered as noncompact. The expansion is produced by the inflaton field, which is considered as nonminimally coupled to gravity. We conclude from experimental data that the coupling of the inflaton with gravity should be weak, but variable in different epochs of the evolution of the universe.     

Brane gravitational interactions from 6D supergravity

We investigate the massive graviton contributions to 4D gravity in a 6D brane world scenario, whose bulk field content can include that of 6D chiral gauged supergravity. We consider a general class of solutions having 3-branes, 4D Poincaré symmetry and axisymmetry in the internal space. We show that these contributions, which we compute analytically, can be independent of the brane vacuum energy as a consequence of geometrical and topological properties of the above-mentioned codimension two brane world. These results support the idea that in such models the gravitational interactions may be decoupled from the brane vacuum energy.     

Fine tuning problem of the cosmological constant in a generalized Randall-Sundrum model

To solve the cosmological constant fine tuning problem, we investigate an \begin{document}$(n+1)$\end{document}-dimensional generalized Randall-Sundrum brane world scenario with two \begin{document}$(n-1)$\end{document}-branes instead of two 3-branes. Adopting an anisotropic metric ansatz, we obtain the positive effective cosmological constant \begin{document}$\Omega_{\rm eff}$\end{document} of order \begin{document}$10^{-124}$\end{document} and only require a solution \begin{document}$\simeq50-80$\end{document}. Meanwhile, both the visible and hidden branes are stable because their tensions are positive. Therefore, the fine tuning problem can be solved quite well. Furthermore, the Hubble parameter \begin{document}$H_{1}(z)$\end{document} as a function of redshift \begin{document}$z$\end{document} is in good agreement with the cosmic chronometers dataset. The evolution of the universe naturally shifts from deceleration to acceleration. This suggests that the evolution of the universe is intrinsically an extra-dimensional phenomenon. It can be regarded as a dynamic model of dark energy that is driven by the evolution of the extra dimensions on the brane.