String cosmology backgrounds from classical string geometry

The dynamics of the Brans-Dicke (BD) cosmology in the Einstein frame is studied. We implement phase-space analysis in order to investigate the role of initial conditions and model parameters in the evolution of the universe. The phase plane algorithm and stability of the model are considered in the Einstein Frame where the cosmological background is described in Λ-Cold Dark Matter (ΛCDM) and is supplemented by a Jordan-Fierz-Brans-Dicke field. Our results show: (1) The model parameter α (the coupling strength of the BD scalar field to matter sources) in the Einstein frame plays an important role in the model stability whereas the initial conditions significantly affect the cosmic dynamics. (2) Using type Ia SNIa data, we fit the parameters of the model with observation and show that the current value of the effective equation of state (EoS) parameter is within the range supported by observations. (3) The phase space analysis implies that the universe approaches an attractor in the near future.

In this paper, we use crossing symmetry and unitarity constraints to put a lower bound on the central charge of conformal field theories in large space-time dimensions D. Specifically, we work with the four-point function of identical scalars ϕ with scaling dimension ∆ϕ, and use a certain class of analytic functionals to show that the OPE coefficient squared {c}_{phi phi {T}^{mu nu}}^2 must be exponentially small in D. For this to hold, we need to make a certain assumption about the nature of the spectrum below 2∆ϕ. Our argument is robust and can be applied to any OPE coefficient squared {c}_{phi phi O}^2 with ∆O< 2∆ϕ. This suggests that conformal field theories in large dimensions (if they exist) must be exponentially close to generalized free field theories.

We explore the properties of a simple analytic equation of state, proposed by Heyes and Woodcock [D. M. Heyes and L. V. Woodcock, Mol. Phys. 59, 1369 (1986)] which is a development of the van der Waals equation of state, improved with an analytically simple yet accurate hard-core component for the compressibility factor. We call this the hard-sphere van der Waals (HSvdW) equation of state. We show, for the first time, that the HSvdW equation of state gives analytic values for the critical parameters and that it gives significantly more realistic values for the critical density than the van der Waals and other cubic equations of state. For single-component square wells of arbitrary well width, the HSvdW equation of state also produces a critical temperature and pressure in agreement with those from a recent Gibbs Monte Carlo simulation study. The chief advantage over a similar equation of state with an alternative form for the hard-core compressibility factor, such as Carnahan–Starling, is that it leads to more tractable analytic expressions for thermodynamic properties without loss of accuracy. Extensive Monte Carlo computer simulations of square-well (SW) and square-shoulder (SS) fluids with variable well width have been performed. We have calculated the compressibility factor, internal energy, pair distribution functions, and coordination number (average number of particles within the soft-shell interaction range). We have also determined the gas–liquid coexistence curve using the particle insertion chemical potential method for the square-well case, λ=1.5σ, where λ is the diameter of the soft interaction shell. This agrees well with the Gibbs ensemble simulation coexistence curve. For the purpose of improving the attractive component of the HSvdW equation of state, we have made use of the SW and SS simulation data and that of other workers to develop another new simple equation of state based on the quasichemical local coordination number approximation (QCA) which is a lattice model of a fluid. The QCA is improved to include the local coordination of the hard-sphere fluid. Present adaptations extend the range of earlier QCA models to arbitrary well width and sign of the well (either attractive well or repulsive shoulder). The simulation coordination numbers are reproduced well by the present model, although there is little improvement in the overall equation of state over the simpler HSvdW.

Perfect fluid generalizations of the parabolic case of Szekeres class I solutions are interpreted as spacetimes whose matter source is a mixture of adiabatically interacting dust (with density rho ) and a homogeneous perfect fluid (with density and pressure mu and p). Simple analytical solutions emerge when the dynamics of mu and p are governed by a Friedmann equation and the equation of state p=( gamma -1) mu holds. The Szafron models correspond to the dynamics of a spatially flat FRW cosmology, admitting a smooth matching with the latter along a suitable timelike hypersurface. New solutions arise for a homogeneous fluid satisfying spatially curved FRW dynamics. For slowly varying p and mu satisfying an arbitrary equation of state, approximate WKB type solutions are derived. Geometric properties and singularities are examined. All solutions are compatible with the existence of a 'regular centre' defined as the regular worldline of privileged isotropic observers. Some of the solutions admit evolution branches along with mu and rho are everywhere positive. These latter cases, under appropriate restrictions, could provide an adequate framework with which to model inhomogeneities in a cosmological background and other situations of astrophysical interest.

We consider conformal and scale-invariant gravities in d dimensions, with a special focus on pure R 2 gravity in the scale-invariant case. In four dimensions, the structure of these theories is well known. However, in dimensions larger than four, the behavior of the modes is so far unclear. In this work, we explore this question, studying the theories in conformally flat spacetimes as well as anisotropic backgrounds. First, we consider the pure theory in d-dimensions. We show that this theory propagates no degrees of freedom for flat space-time. Otherwise, we find the theory in the corresponding Einstein frame and show that it propagates a scalar field and two tensor modes, that arise from Einstein’s gravity. We then consider conformal gravity in d dimensions. We argue on the number of degrees of freedom for conformally flat space-times and show that for d &gt; 4, there exists a frame in which this theory can be written as the Weyl-squared gravity with a cosmological constant, and also generalize this formulation to the f(W)2 theories. Then, we consider the specific model of conformal gravity in five dimensions. We find the analytical and numerical solutions for the anisotropic Universe for this case, which admits super-Hubble and exponential expansions. Finally, we consider the perturbations around these solutions and study the number of the degrees of freedom.

Dark energy: the equation of state description versus scalar-tensor or modified gravity

In a homogeneous and isotropic universe with nonzero spatial curvature we consider the effects of gravitational particle production in the dynamics of the universe. We show that the dynamics of the universe in such a background is characterized by a single nonlinear differential equation which is significantly dependent on the rate of particle creation and whose solutions can be dominated by the curvature effects at early times. For different particle creation rates we apply the singularity test in order to find the analytic solutions of the background dynamics. We describe the behavior of the cosmological solutions for both open and closed universes. We also show how the effects of curvature can be produced by the presence of a second perfect fluid with an appropriate equation of state. By combining that result with the analysis of the critical points we find that our consideration can be related with the preinflationary era. Specifically we find that for negative spatial curvature small changes of the Milne spacetime leads to a de Sitter universe.

In the framework of a general scalar-tensor theory, we investigate the equivalence between two different parametrizations of fields that are commonly used in cosmology - the so-called Jordan frame and Einstein frame. While it is clear that both parametrizations are mathematically equivalent at the level of the classical action, the question about their mathematical equivalence at the quantum level as well as their physical equivalence is still a matter of debate in cosmology. We analyze whether the mathematical equivalence still holds when the first quantum corrections are taken into account. We explicitly calculate the one-loop divergences in both parametrizations by using the generalized Schwinger-DeWitt algorithm and compare both results. We find that the quantum corrections do not coincide off shell and hence induce an off shell dependence on the parametrization. According to the equivalence theorem, the one-loop divergences should however coincide on shell. For a cosmological background, we show explicitly that the on shell equivalence is indeed realized by a nontrivial cancellation.

We explore the possibility that a scalar field with appropriate Lagrangian can mimic a perfect fluid with an affine barotropic equation of state. The latter can be thought of as a generic cosmological dark component evolving as an effective cosmological constant plus a generalized dark matter. As such, it can be used as a simple, phenomenological model for either dark energy or unified dark matter. Furthermore, it can approximate (up to first order in the energy density) any barotropic dark fluid with arbitrary equation of state. We find that two kinds of Lagrangians for the scalar field can reproduce the desired behaviour: a quintessence-like with a hyperbolic potential, or a purely kinetic k-essence one. We discuss the behaviour of these two classes of models from the point of view of the cosmological background, and give some hints on their possible clustering properties.

We study a class of homogeneous and anisotropic geometries with affine equation of state (EoS) for different physically plausible scenarios of the universe evolution using dynamical system technique. We analyze the locally rotationally symmetric Bianchi I (LRS BI), Bianchi III (LRS BIII) and Bianchi V (LRS BV) geometry for the exhibition of the effects of affine EoS in the model. The model exhibits stable attractor which is also isotropic and thus, it may explain the late-time accelerated expansion of the universe. The model also possess stiff matter-, radiation- and matter-dominated phases prior to the dark energy assisted accelerating phase which are confirmed by the behaviours of effective equation of state and deceleration parameters. We use the statefinder diagnostic which is a geometrical diagnostic to explore model independent features of the cosmological dynamical system. The LRS BI, BIII and BV geometry based dynamical systems exhibit r=1,s=0(Lambda cold dark matter model) at late-times, which is compatible with the observations. The dynamical system for the Kantowski–Sachs model yields synchronous bounce on the basis of the model parameters. It also yields a late-time attractor which may explain the accelerated expansion of the universe in the model. The qualitative differences between LRS BIII and BV cosmological dynamical systems have also been discussed.

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We explore the gravitational backreaction of a system consisting in a very large number of elementary fermions at finite temperature, in asymptotically AdS space. We work in the hydrodynamic approximation, and solve the Tolman-Oppenheimer-Volkoff equations with a perfect fluid whose equation of state takes into account both the relativistic effects of the fermionic constituents, as well as its finite temperature effects. We find a novel dense core-diluted halo structure for the density profiles in the AdS bulk, similarly as recently reported in flat space, for the case of astrophysical dark matter halos in galaxies. We further study the critical equilibrium configurations above which the core undergoes gravitational collapse towards a massive black hole, and calculate the corresponding critical central temperatures, for two qualitatively different central regimes of the fermions: the diluted-Fermi case, and the degenerate case. As a probe for the dual CFT, we construct the holographic two-point correlator of a scalar operator with large conformal dimension in the worldline limit, and briefly discuss on the boundary CFT effects at the critical points.

The electron-gas theory of crystals is extended to include the effects of many-body forces that arise from both electrostatic and overlap interactions. These effects are incorporated through a self-consistent spherical relaxation of the ionic charge distributions such that the crystal binding energy is minimized. This variational model is used to compute the elastic constants and equations of state of MgO and CaO, and we compare its results to those derived from earlier electron-gas models. In the variational model, the anion charge distributions are markedly more sensitive to the local crystal environment than they are in the PIB or other electron-gas models. We find that for these oxides the variational model gives the best overall agreement with experiment for lattice constants, equations of state, dissociation energies, and elastic moduli.

The problem of the time evolution of the process of fragment formation is investigated in the framework of expanding periodic systems. We focus on the fragmentation of small (100 constituents) systems. We use a molecular-dynamics method that simulates the behavior of condensed matter under homogeneous adiabatic expansion. Fragment formation is studied using a generalized version of the early cluster formation model (GECFM) which searches for the most bound density fluctuations in phase space. We show that the asymptotic fragment spectra is early realized in phase space not only for the total multiplicity but also for the populations of different mass ranges. In order to map the evolution of the system on the phase diagram of the small cell periodic one, its equation of state is calculated. It is shown that the fragmentation of the system cannot be unambiguously related to spinodal decomposition or nucleation processes. \textcopyright{} 1996 The American Physical Society.

A solution of codimension 2 brane is found for which four-dimensional Friedmann cosmology is recovered on the brane with time-dependent tension, in the Einstein frame. The effective parameter p/ρ of equation of state on the brane can be quintessence like, de Sitter like or phantom like, depending on the integration constants of the solution.