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.     

Entanglement inside the cosmological apparent horizon

Possible connections between quantum entanglement and cosmological eras are considered. In particular, assuming that two epochs are each other entangling, by measuring the entanglement degree, it is possible to recover dynamical properties of the universe. In particular, the effects of dark energy could be due to the entanglement between states, since a negative pressure arises at late times. In this process, we choose as ruler to quantify the “entanglement weight”, the so-called negativity of entanglement. It follows that a natural anti-gravitational effect occurs when the cosmological eras are entangled. Thus, dark energy could be seen as a straightforward consequence of entanglement. Specifically, our results can be compared with observational data. In doing so, it is possible to show that a pressureless term is recovered at a certain epoch dominating over dark energy and ruling the structure formation.     

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.     

Le Châtelier–Braun principle in cosmological physics

Assuming that dark energy may be treated as a fluid with a well-defined temperature, close to equilibrium, we argue that if nowadays there is a transfer of energy between dark energy and dark matter, it must be such that the latter gains energy from the former and not the other way around.     

Remarks on the Formulation of the Cosmological Constant/Dark Energy Problems

Associated with the cosmic acceleration are the old and new cosmological constant problems, recently put into the more general context of the dark energy problem. In broad terms, the old problem is related to an unexpected order of magnitude of this component while the new problem is related to this magnitude being of the same order of the matter energy density during the present epoch of cosmic evolution. Current plans to measure the equation of state or density parameters certainly constitute an important approach; however, as we discuss, this approach is faced with serious feasibility challenges and is limited in the type of conclusive answers it could provide. Therefore, is it really too early to seek actively for new tests and approaches to these problems? In view of the difficulty of this endeavor, we argue in this work that a good place to start is by questioning some of the assumptions underlying the formulation of these problems and finding new ways to put this questioning to the test. First, we calculate how much fine tuning the cosmic coincidence problem represents. Next, we discuss the potential of some cosmological probes such as weak gravitational lensing to identify novel tests to probe dark energy questions and assumptions and provide an example of consistency tests. Then, motivated by some theorems in General Relativity, we discuss if the full identification of the cosmological constant with vacuum energy is unquestionable. We discuss some implications of the simplest solution for the principles of General Relativity. Also, we point out the relevance of experiments at the interface of astrophysics and quantum field theory, such as the Casimir effect in gravitational and cosmological contexts. We conclude that challenging some of the assumptions underlying the cosmological constant problems and putting them to the test may prove useful and necessary to make progress on these questions.     

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.     

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.     

Breaking parameter degeneracy in interacting dark energy models from observations

We study the interacting dark energy model with time varying dark energy equation of state. We examine the stability in the perturbation formalism and the degeneracy among the coupling between dark sectors, the time-dependent dark energy equation of state and dark matter abundance in the cosmic microwave background radiation. Further we discuss the possible ways to break such degeneracy by doing global fitting using the latest observational data and we get a tight constraint on the interaction between dark sectors.     

Dynamical dark energy models – dynamical system approach

We study the Friedmann-Robertson-Walker model with dynamical dark energy modelled in terms of the equation of state p _X = w _X (a(z)) ρ _X in which the coefficient w _X is parameterized by the scale factor a or redshift z. We use methods of qualitative analysis of differential equations to investigate the space of all admissible solutions for all initial conditions on the two-dimensional phase plane. We show advantages of representing this dynamics as a motion of a particle in the one-dimensional potential V(a). One of the features of this reduction is the possibility of investigating how typical big rip singularities are in the future evolution of the model. The properties of potential function V can serve as a tool for qualitative classification of all evolution paths. Some important features like resolution of the acceleration problem can be simply visualized as domains on the phase plane. Then one is able to see how large is the class of solutions (labelled by the inset of the initial conditions) leading to the desired property.     

Spherically symmetric anisotropic and inhomogeneous cosmological models

Spherically symmetric cosmological models filled with dust (pressure-free fluid) content are analyzed. It has been pointed out that these models are anisotropic (of non-vanishing shear) and inhomogeneous (∂p/ρr ≠ 0), the characteristics related directly to the presence of the free gravitational field. It is demonstrated that when the free gravitational field vanishes these models degenerate to the corresponding Friedmann-Robertson-Walker (FRW) models. It is further shown that the energy density of the free gravitational field can be introduced into observational cosmology as a new parameter since it enters into the expansion and deceleration equations, as well as conservation law for total energy, implying that the present Hubble velocity can be reached in a shorter time from the big bang. Finally, the effect of shear on the redshift is also discussed. This paper is dedicated to my teacher Professor V V Narlikar on the occasion of his 81st birthday.     

Spherically symmetric static inhomogeneous cosmological models

Spherically symmetric static cosmological models filled with black-body radiation are considered. The models are isotropic about a central observer but inhomogeneous. It is suggested that the energy density of the free gravitational field, which is coupled to the isotropic radiation energy density, might play an important role in generating sufficient field (vacuum) energy (when converted into thermal energy) and initiate processes like inflation. On the central world line the energy density of the free gravitational field vanishes whereas the proper pressure and density of the isotropic black-body radiation are constants. Further, it is shown that the cosmological constant is no more arbitrary but given in terms of the central pressure and density. Also, at its maximum value the energy density of the free gravitational field is proved to be equal to one third of the combined value of radiation pressure and density.     

Cosmological constraints from radial baryon acoustic oscillation measurements and observational Hubble data

We use the Radial Baryon Acoustic Oscillation (RBAO) measurements, distant type Ia supernovae (SNe Ia), the observational H(z)$H(z)$ data (OHD) and the Cosmic Microwave Background (CMB) shift parameter data to constrain cosmological parameters of ΛCDM$\mathrm{\Lambda }\text{CDM}$ and XCDM cosmologies and further examine the role of OHD and SNe Ia data in cosmological constraints. We marginalize the likelihood function over h   by integrating the probability density P∝e−χ²/2$P\propto e^{-{\chi }^2/2}$ to obtain the best fitting results and the confidence regions in the Ωm–ΩΛ${\Omega }_m\text{–}{\Omega }_{\Lambda }$ plane. With the combination analysis for both of the ΛCDM$\mathrm{\Lambda }\text{CDM}$ and XCDM models, we find that the confidence regions of 68.3%, 95.4% and 99.7% levels using OHD+RBAO+CMB$\text{OHD}+\text{RBAO}+\text{CMB}$ data are in good agreement with that of SNe Ia+RBAO+CMB$\text{Ia}+\text{RBAO}+\text{CMB}$ data which is consistent with the result of Lin et al.'s (2009) [24] work. With more data of OHD, we can probably constrain the cosmological parameters using OHD data instead of SNe Ia data in the future.     

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.     

Kaluza-Klein Type Robertson Walker Cosmological Model with Dynamical Cosmological Term Λ

In this paper we have analyzed the Kaluza-Klein type Robertson Walker (RW) cosmological models by considering three different forms of variable Λ: , and Λ∼ρ. It is found that, the connecting free parameters of the models with cosmic matter and vacuum energy density parameters are equivalent, in the context of higher dimensional space time. The expression for the look back time, luminosity distance and angular diameter distance are also derived. This work has thus generalized to higher dimensions the well-known results in four dimensional space time. It is found that there may be significant difference in principle at least, from the analogous situation in four dimensional space time.     

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.     

Comparison of distance information given by SN Ia,BAO and CMB

The observations of Type Ia supernovae (SN Ia), Baryon Acoustic Oscillations (BAO) and Cosmic Microwave Background radiation (CMB) provide powerful tools for the measurement of cosmological parameters. One of the most useful information encodes in the distance measured by those probes. In this Letter, we test the coherence of the observational information provided by SN Ia, BAO and CMB experiments. We make two kinds of comparison: the first is the constraints on cosmological parameters of the equation of state parameter (EoS) of dark energy (DE) and matter budget parameter Ωm${\Omega }_m$ from the latest data by global fitting, and we find the large discrepancy from those different probes. The second comparison is performed among the derived distance information from these observations at certain appointed redshift, the results show that the distance provided by WMAP5 are larger than those from SN Ia and BAO on the whole.