Bianchi Type-I Space-Time with Variable Cosmological Constant

A spatially homogeneous and anisotropic Bianchi type-I perfect fluid model is considered with variable cosmological constant. Einstein’s field equations are solved by using a law of variation for mean Hubble’s parameter, which is related to average scale factor and that yields a constant value of deceleration parameter. An exact and singular Bianchi-I model is presented, where the cosmological constant remains positive and decreases with the cosmic time. It is found that the solutions are consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the model is carried out.     

A Quantum Mechanical Relation Connecting Time,Temperature, and Cosmological Constant of the Universe: Gamow’S Relation Revisited as a Special Case

Considering our expanding universe as made up of gravitationally interacting particles which describe particles of luminous matter, dark matter and dark energy which is represented by a repulsive harmonic potential among the points in the flat 3-space and incorporating Mach’s principle into our theory, we derive a quantum mechanical relation connecting, temperature of the cosmic microwave background radiation, age, and cosmological constant of the universe. When the cosmological constant is zero, we get back Gamow’s relation with a much better coefficient. Otherwise, our theory predicts a value of the cosmological constant 2.0×10⁻⁵⁶ cm⁻² when the present values of cosmic microwave background temperature of 2.728 K and age of the universe 14 billion years are taken as input.     

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.     

Letter: A Cosmological Constant Interpreted as the Field Energy of a Quaternionic Field

The expression of a time-dependent cosmological constant 1/t² is interpreted as the energy density of a special type of the quaternionic field which is coupled to its own field energy. The general solution of the corresponding field equations yields the field energy which contains an integration constant t ₀. If t ₀ > 0 then the cosmological constant exhibits no initial singularity at t = 0. In the early universe the black energy associated with can be made small enough for the structure forming of galaxies getting, however, its observational value at the present time.     

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.     

Time and distance constraints on accelerating cosmological models

The absence of guidance from fundamental physics about the mechanism behind cosmic acceleration has given rise to a number of alternative cosmological scenarios. These are based either on modifications of general relativistic gravitation theory on large scales or on the existence of new fields in Nature. In this Letter we investigate the observational viability of some accelerating cosmological models in light of 32 age measurements of passively evolving galaxies as a function of redshift and recent estimates of the product of the cosmic microwave background acoustic scale and the baryonic acoustic oscillation peak scale. By using information-criteria model selection, we select the best-fit models and rank the alternative scenarios. We show that some of these models may provide a better fit to the data than does the current standard cosmological constant dominated (ΛCDM) model.     

Anthropic Approach to the Cosmological Constant Problems

There are now two cosmological constant problems: (i) why the vacuum energy is so small and (ii) why it comes to dominate at about the epoch of galaxy formation. Anthropic selection appears to be the only approach that can naturally resolve both problems. Here I review this approach, emphasizing the testable predictions that it makes for the dark energy density and for its equation of state.     

Cosmological Acceleration from Virtual Gravitons

Intrinsic properties of the space itself and quantum fluctuations of its geometry are sufficient to provide a mechanism for the acceleration of cosmological expansion (dark energy effect). Applying Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy approach to self-consistent equations of one-loop quantum gravity, we found exact solutions that yield acceleration. The permanent creation and annihilation of virtual gravitons is not in exact balance because of the expansion of the Universe. The excess energy comes from the spontaneous process of graviton creation and is trapped by the background. It provides the macroscopic quantum effect of cosmic acceleration.     

Oscillations in the dark energy equation of state: New MCMC lessons

We study the possibility of detecting oscillating patterns in the equation of state (EoS) of the dark energy using different cosmological datasets. We follow a phenomenological approach and study three different oscillating models for the EoS, one of them periodic and the other two damped (proposed here for the first time). All the models are characterized by the amplitude, the center and the frequency of oscillations. In contrast to previous works in the literature, we do not fix the frequency to a fiducial value related to the time extension of chosen datasets, but consider a discrete set of values, so to avoid arbitrariness and try to detect any possible time period in the EoS. We test the models using a recent collection of SNeIa, direct Hubble data and Gamma Ray Bursts data. Main results are: I. even if constraints on the amplitude are not too strong, we detect a trend of it versus the frequency, i.e. decreasing (and even negatives) amplitudes for higher frequencies; II. the center of oscillation (which corresponds to the present value of the EoS parameter) is very well constrained, and phantom behavior seems statistically disfavored; III. the frequency is hard to constrain, showing similar statistical validity for all the values of the discrete set chosen, but the best fit of all the considered scenarios is associated with a period which is in the redshift range depicted by our cosmological data. The “best” oscillating models are compared with ΛCDM using different dimensionally consistent and Bayesian-based information criteria; the conclusion is reached that at present, data cannot discriminate between a cosmological constant and oscillating equation of state.     

ESSAY: The Cosmological Constant Problem in Brane-Worlds and Gravitational Lorentz Violations

Brane worlds are theories with extra spatial dimensions in which ordinary matter is localized on a (3+1) dimensional submanifold. Such theories could have interesting consequences for particle physics and gravitational physics. In this essay we concentrate on the cosmological constant (CC) problem in the context of brane worlds. We show how extra-dimensional scenarios may violate Lorentz invariance in the gravity sector of the effective 4D theory, while particle physics remains unaffected. In such theories the usual no-go theorems for adjustment of the CC do not apply, and we indicate a possible explanation of the smallness of the CC. Lorentz violating effects would manifest themselves in gravitational waves travelling with a speed different from light, which can be searched for in gravitational wave experiments.     

Letter: Charged Black Hole Solutions in Einstein-Born-Infeld Gravity with a Cosmological Constant

We construct black hole solutions to Einstein-Born-Infeld gravity with a cosmological constant. Since an elliptic function appears in the solutions for the metric, we construct horizons numerically. The causal structure of these solutions differs drastically from their counterparts in Einstein-Maxwell gravity with a cosmological constant. The charged de-Sitter black holes can have up to three horizons and the charged anti-de Sitter black hole can have one or two depending on the parameters chosen.     

Physics of Dark Energy Particles

We consider the astrophysical and cosmological implications of the existence of a minimum density and mass due to the presence of the cosmological constant. If there is a minimum length in nature, then there is an absolute minimum mass corresponding to a hypothetical particle with radius of the order of the Planck length. On the other hand, quantum mechanical considerations suggest a different minimum mass. These particles associated with the dark energy can be interpreted as the “quanta” of the cosmological constant. We study the possibility that these particles can form stable stellar-type configurations through gravitational condensation, and their Jeans and Chandrasekhar masses are estimated. From the requirement of the energetic stability of the minimum density configuration on a macroscopic scale one obtains a mass of the order of 10⁵⁵ g, of the same order of magnitude as the mass of the universe. This mass can also be interpreted as the Jeans mass of the dark energy fluid. Furthermore we present a representation of the cosmological constant and of the total mass of the universe in terms of ‘classical’ fundamental constants.     

Purely kinetic coupled gravity

Cosmic acceleration can be achieved not only with a sufficiently flat scalar field potential but through kinetic terms coupled to gravity. These derivative couplings impose a shift symmetry on the scalar field, aiding naturalness. We write the most general purely kinetic action not exceeding mass dimension 6 and obeying second order field equations. The result reduces to a simple form involving a coupling of the Einstein tensor with the kinetic term and can be interpreted as adding a new term to Galileon gravity in curved spacetime. We examine the cosmological implications of the effective dark energy and classify the dynamical attractor solutions, finding a quasistable loitering phase mimicking late time acceleration by a cosmological constant.     

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.     

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.     

Cosmological consequences of exponential gravity in Palatini formalism

We investigate cosmological consequences of a class of exponential f(R)$f(R)$ gravity in the Palatini formalism. By using the current largest type Ia Supernova sample along with determinations of the cosmic expansion at intermediary and high-z   we impose tight constraints on the model parameters. Differently from other f(R)$f(R)$ models, we find solutions of transient acceleration, in which the large-scale modification of gravity will drive the Universe to a new decelerated era in the future. We also show that a viable cosmological history with the usual matter-dominated era followed by an accelerating phase is predicted for some intervals of model parameters.