FRW barotropic zero modes: dynamical systems observability

International Journal of Theoretical Physics, 2003

In 1999, Faraoni wrote a simple second-order linear differential equation for FRW cosmologies with barotropic fluids. His results have been extended by Rosu, who employed techniques belonging to nonrelativistic supersymmetry to obtain time-dependent effective adiabatic indices. Further extensions are presented here using the known connection between the linear second-order differential equations and Dirac-like equations in the same supersymmetric context. These extensions are equivalent to adding an imaginary part to the effective adiabatic index, which is proportional to the mass parameter of the Dirac spinor. The natural physical interpretation of the imaginary part is related to the particular dissipation and instabilities of the effective barotropic FRW hydrodynamics that are introduced by means of this supersymmetric scheme.

2012

In this paper within the scope of FRW cosmology for k = 0, ±1 we study the dynamics of the universe for a cosmological model with a scalar field nonminimally coupled to matter. By bestfitting the model parameters with the observational data for the direct interaction between the dark sectors in the model we obtain observational constraints on cosmological parameters. The result shows that with the best fitted model parameters, only in flat universe, the phantom crossing occurs twice in the past and once in the future, whereas no crossing occurs for open and closed models of the universe.

In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and useful tools from the qualitative theory of dynamical systems. They provide the theoretical basis for the qualitative study of concrete cosmological models. Chapters 1 and 2 are a review of well-known results. Chapters 3, 4, 5 and 6 are devoted to our main results. In these chapters are extended and settled in a substantially different, more strict mathematical language, several results obtained by one of us in arXiv:0812.1013 [gr-qc]; arXiv:1009.0689 [gr-qc]; arXiv:0904.1577[gr-qc]; and arXiv:0909.3571 [hep-th]. In chapter 6, we provide a different approach to the subject discussed in astro-ph/0503478. Additionally, we perform a Poincar\'e compactification process allowing to construct a global phase space containing all the cosmological info...

1997

Journal of Cosmology and Astroparticle Physics, 2011

We constrain the parameters of dynamical dark energy in the form of a classical or tachyonic scalar field with barotropic equation of state jointly with other cosmological ones using the combined datasets which include the CMB power spectra from WMAP7, the baryon acoustic oscillations in the space distribution of galaxies from SDSS DR7, the power spectrum of luminous red galaxies from SDSS DR7 and the light curves of SN Ia from 2 different compilations: Union2 (SALT2 light curve fitting) and SDSS (SALT2 and MLCS2k2 light curve fittings). It has been found that the initial value of dark energy equation of state parameter is constrained very weakly by most of the data while the rest of main cosmological parameters are well constrained: their likelihoods and posteriors are similar, have the forms close to Gaussian (or half-Gaussian) and their confidential ranges are narrow. The most reliable determinations of the best fitting value and 1σ confidence range for the initial value of dark energy equation of state parameter were obtained from the combined datasets including SN Ia data from the full SDSS compilation with MLCS2k2 fitting of light curves. In all such cases the best fitting value of this parameter is lower than the value of corresponding parameter for current epoch. Such dark energy loses its repulsive properties and in future the expansion of the Universe will change into contraction.

Physical Review D, 1994

We derive the effective equations for the out of equilibrium time evolution of the order parameter and the fluctuations of a scalar field theory in spatially flat FRW cosmologies.The calculation is performed both to one-loop and in a non-perturbative, self-consistent Hartree approximation.The method consists of evolving an initial functional thermal density matrix in time and is suitable for studying phase transitions out of equilibrium. The renormalization aspects are studied in detail and we find that the counterterms depend on the initial state. We investigate the high temperature expansion and show that it breaks down at long times. We also obtain the time evolution of the initial Boltzmann distribution functions, and argue that to one-loop order or in the Hartree approximation, the time evolved state is a ``squeezed'' state. We illustrate the departure from thermal equilibrium by numerically studying the case of a free massive scalar field in de Sitter and radiation dominated cosmologies. It is found that a suitably defined non-equilibrium entropy per mode increases linearly with comoving time in a de Sitter cosmology, whereas it is {\it not} a monotonically increasing function in the radiation dominated case.

We use dynamical system methods to explore the general behaviour of f (T) cosmol-ogy. In contrast to the standard applications of dynamical analysis, we present a way to transform the equations into a one-dimensional autonomous system, taking advantage of the crucial property that the torsion scalar in flat FRW geometry is just a function of the Hubble function, thus the field equations include only up to first derivatives of it, and therefore in a general f (T) cosmological scenario every quantity is expressed only in terms of the Hubble function. The great advantage is that for one-dimensional systems it is easy to construct the phase space portraits, and thus extract information and explore in detail the features and possible behaviours of f (T) cosmology. We utilize the phase space portraits and we show that f (T) cosmology can describe the universe evolution in agreement with observations, namely starting from a Big Bang singularity, evolving into the subsequent thermal history and the matter domination, entering into a late-time accelerated expansion, and resulting to the de Sitter phase in the far future. Nevertheless, f (T) cosmology can present a rich class of more exotic behaviours, such as the cosmological bounce and turnaround, the phantom-divide crossing, the Big Brake and the Big Crunch, and it may exhibit various singu-larities, including the non-harmful ones of type II and type IV. We study the phase space of three specific viable f (T) models offering a complete picture. Moreover, we present a new model of f (T) gravity that can lead to a universe in agreement with observations, free of perturbative instabilities, and applying the Om(z) diagnostic test we confirm that it is in agreement with the combination of SNIa, BAO and CMB data at 1σ confidence level.

2012

The aim of this paper is to answer the following two questions: (1) Given cosmological observations of the expansion history and linear perturbations in a range of redshifts and scales as precise as is required, which of the properties of dark energy could actually be reconstructed without imposing any parameterization? (2) Are these observables sufficient to rule out not just a particular dark energy model, but the entire general class of viable models comprising a single scalar field? This paper bears both good and bad news. On one hand, we find that the goal of reconstructing dark energy models is fundamentally limited by the unobservability of the present values of the matter density Omega_m0, the perturbation normalization sigma_8 as well as the present matter power spectrum. On the other, we find that, under certain conditions, cosmological observations can nonetheless rule out the entire class of the most general single scalar-field models, i.e. those based on the Horndeski Lagrangian.

Journal of Cosmology and Astroparticle Physics, 2009

We perform a detailed phase-space analysis of Hořava-Lifshitz cosmology, with and without the detailed-balance condition. Under detailed-balance we find that the universe can reach a bouncingoscillatory state at late times, in which dark-energy, behaving as a simple cosmological constant, is dominant. In the case where the detailed-balance condition is relaxed, we find that the universe reaches an eternally expanding, dark-energy-dominated solution, with the oscillatory state preserving also a small probability. Although this analysis indicates that Hořava-Lifshitz cosmology can be compatible with observations, it does not enlighten the discussion about its possible conceptual and theoretical problems.

The Astrophysical Journal, 1995

We investigate the local non{linear dynamics of irrotational dust with vanishing magnetic part of the Weyl tensor, H ab . Once coded in the initial conditions, this dynamical restriction is respected by the relativistic evolution equations. Thus, the outcome of the latter are exact solutions for special initial conditions with H ab = 0, but with no symmetries: they describe inhomogeneous triaxial dynamics generalizing that of a uid element in a Tolman{Bondi, Kantowski{Sachs or Szekeres geometry. A subset of these solutions may be seen as (special) perturbations of Friedmann models, in the sense that there are trajectories in phase{space that pass arbitrarily close to the isotropic ones. We nd that the nal fate of ever{expanding con gurations is a spherical void, locally corresponding to a Milne universe. For collapsing con gurations we nd a whole family of triaxial attractors, with vanishing local density parameter . These attractors locally correspond to Kasner vacuum solutions: there is a single physical con guration collapsing to a degenerate pancake, while the generic con guration collapses to a triaxial spindle singularity. These silent universe models may provide a fair representation of the universe on super horizon scales. Moreover, one might conjecture that the non{local information carried by H ab becomes negligible during the late highly non{linear stages of collapse, so that the attractors we nd may give all of the relevant expansion or collapse con gurations of irrotational dust. Subject headings: cosmology: theory | large{scale structure of the universe | analytical methods | gravitation | relativity Ref. SISSA 85/94/A