Perturbative Equation Of State Research Articles

Dark sector evolution in Horndeski models

We use the Equation of State (EoS) approach to study the evolution of the dark sector in Horndeski models, the most general scalar-tensor theories with second order equations of motion. By including the effects of the dark sector into our code EoS_class, we demonstrate the numerical stability of the formalism and excellent agreement with results from other publicly available codes for a range of parameters describing the evolution of the function characterising the perturbations for Horndeski models, αx, with x = K, B, M, T. After demonstrating that on sub-horizon scales (k≳ 10−3 Mpc−1 at z=0) velocity perturbations in both the matter and the dark sector are typically subdominant with respect to density perturbations in the equation of state for perturbations, we find an attractor solution for the dark sector gauge-invariant density perturbation Δds by neglecting its time derivatives in the equation describing its time evolution, as commonly done in the well-known quasi-static approximation. Using this result, we provide simplified expressions for the equation-of-state functions: the dark sector entropy perturbations wdsΓds and anisotropic stress wdsΠds. From this we derive a growth factor-like equation for both matter and dark sector and are able to capture the relevant physics for several observables with great accuracy. We finally present new analytical expressions for the well-known modified gravity phenomenological functions μ, η and Σ for a generic Horndeski model as functions of αx. We show that on small scales they reproduce expressions presented in previous works, but on large scales, we find differences with respect to other works.

Cosmological perturbation theory in generalized Einstein-Aether models

We investigate the evolution of cosmological perturbations in models of dark energy described by a timelike unit normalized vector field specified by a general function $\mathcal{F}(\mathcal{K})$, so-called generalized Einstein-Aether models. First we study the background dynamics of such models via a designer approach in an attempt to model this theory as dark energy. We find that only one specific form of this designer approach matches $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ at background order, and we also obtain a differential equation which $\mathcal{F}(\mathcal{K})$ must satisfy for general $w\mathrm{CDM}$ cosmologies, where CDM refers to cold dark matter. We also present the equations of state for perturbations in generalized Einstein-Aether models, which completely parametrize these models at the level of linear perturbations. A generic feature of modified gravity models is that they introduce new degrees of freedom. By fully eliminating these we are able to express the gauge invariant entropy perturbation and the scalar, vector, and tensor anisotropic stresses in terms of the perturbed fluid variables and metric perturbations only. These can then be used to study the evolution of perturbations in the scalar, vector, and tensor sectors, and we use these to evolve the Newtonian gravitational potentials.

Slowly rotating thin shell gravastars

We construct the solutions of slowly rotating gravastars with a thin shell. In the zero-rotation limit, we consider the gravastar composed of a de Sitter core, a thin shell, and Schwarzschild exterior spacetime. The rotational effects are treated as small axisymmetric and stationary perturbations. The perturbed internal and external spacetimes are matched with a uniformly rotating thin shell. We assume that the angular velocity of the thin shell, Ω, is much smaller than the Keplerian frequency of the nonrotating gravastar, The solutions within an accuracy up to the second order of are obtained. The thin shell matter is assumed to be described by a perfect fluid and to satisfy the dominant energy condition in the zero-rotation limit. In this study, we assume that the equation of state for perturbations is the same as that of the unperturbed solution. The spherically symmetric component of the energy density perturbations, is assumed to vanish independently of the rotation rate. Based on these assumptions, we obtain many numerical solutions and investigate properties of the rotational corrections to the structure of the thin shell gravastar.

Material models of dark energy

A new class of “dark energy” models is reviewed and developed, in which the relativistic theory of solids is used to construct material models of dark energy. These are models which include the effects of a continuous medium with well defined physical properties at the level of linearized perturbations. The formalism is constructed for a medium with arbitrary symmetry, and then specialised to isotropic media (which will be the case of interest for the majority of cosmological applications). The theory of relativistic isotropic viscoelastic media is developed whilst keeping in mind that we ultimately want to observationally constrain the allowed properties of the material model. This is done by obtaining the viscoelastic equations of state for perturbations (the entropy and anisotropic stress), as well as identifying the consistent corner of the theory which has constant equation of state parameter . A connection to the non‐relativistic theory of solids is obtained by identifying the two quadratic invariants that are needed to construct the energy‐momentum tensor, namely the Rayleigh dissipation function and Lagrangian for perturbations. Finally, the notion is developed that the viscoelastic behavior of the medium can be thought of as a non‐minimally coupled massive gravity theory. This also provides a tool‐kit for constructing consistent generalizations of coupled dark energy theories.

Computing model independent perturbations in dark energy and modified gravity

We present a methodology for computing model independent perturbations in dark energy and modified gravity. This is done from the Lagrangian for perturbations, by showing how field content, symmetries, and physical principles are often sufficient ingredients for closing the set of perturbed fluid equations. The fluid equations close once ``equations of state for perturbations'' are identified: these are linear combinations of fluid and metric perturbations which construct gauge invariant entropy and anisotropic stress perturbations for broad classes of theories. Our main results are the proof of the equation of state for perturbations presented in a previous paper, and the development of the required calculational tools.

A model study of the equation of state, quark-number susceptibility and scalar susceptibility of QCD at finite chemical potential and zero temperature

In this article, we try to calculate the equation of state (EOS) of quantum chromodynamics (QCD) at finite chemical potential and zero temperature in the framework of a nonperturbative QCD model. Compared with the cold, perturbative EOS of QCD proposed by Fraga et al., our EOS approaches more fastly to the free quark gas result at large chemical potential. It is expected that our EOS can provide a possible new tool for the study of neutron star. We also try to provide a direct approach for calculating quark number susceptibility and scalar susceptibility at finite chemical potential and zero temperature.

Understanding physical properties of hydrocarbon polymers using an equation of state developed from semi soft core potential function

A semi-soft core intermolecular potential function for hydrocarbon molecules has been developed that expands the Boltzmann angle average of the van der Waals type-interaction. The logarithmic form simplifies the many thermodynamic derivatives related to Boltzmann statistics and clarifies the concept of the collision diameter. Second and third virial coefficients were derived as closed expressions and both the additive and non-additive terms were derived, especially for the third virial coefficient. A virial equation of state (EOS) was derived using the newly developed virial coefficients and compared to experimentally observed compressibility factors of natural gases. A perturbation EOS is derived to obtain vapor–liquid equilibrium (VLE) using the present potential function and the method of statistical mechanics. The EOS was employed to explain the VLE of pure hydrocarbon molecules. To expand the applicable range from small molecules to long chain polymers, the perturbation EOS was modified to a polymer EOS by introducing chain terms. Despite the relatively short expressions, each of the developed EOSs developed in this study were comparable in accuracy to well-known EOSs for each field, which demonstrates the advantage of applying these EOSs to multicomponent mixtures and long chain molecules.

THE EQUATION OF STATE OF QUASI-PARTICLE MODEL OF QUARK–GLUON PLASMA AT FINITE CHEMICAL POTENTIAL

In this letter we propose a new method of calculating the equation of state (EOS) of quasi-particle model of quark–gluon plasma at finite chemical potential. In the quasi-particle model the quark propagator has the form of a free quark propagator with a temperature and density dependent effective mass. From this quark propagator the EOS at finite chemical potential is calculated using the model-independent formula proposed in Refs. 16 and 17. A comparison between our EOS and the cold, perturbative EOS of QCD proposed in Ref. 23 is made.

The equation of state of QCD under hard-dense-loop approximation

Based on the method proposed by Zong et al., we calculate the equation of state (EOS) of QCD at zero temperature and finite quark chemical potential under the hard-dense-loop (HDL) approximation. A comparison between the EOS under HDL approximation and the cold, perturbative EOS of QCD proposed by Fraga, Pisarski and Schaffner-Bielich is made. It is found that when µ is less than 4.7 GeV, the pressure density calculated using HDL approximation is much larger than that calculated using perturbation theory. This enhancement of the obtained pressure density with respect to that of perturbation theory can be regarded as a possible explanation for the strong coupled QGP. It is also expected that the obtained EOS can be applied in the study of neutron stars.

Comment on “An Alternative Approach for CO2 Flux Correction Caused by Heat and Water Vapour Transfer” by Liu

The need and methodology to correct open-path eddy covariance estimates and determine surface exchange were documented in a landmark article a quarter of a century ago (Webb et al., 1980). Interest in these ‘Webb corrections’ is increasing, as seen in both their widespread application and recent articles re-examining their use (Paw U et al., 2000; Fuehrer and Friehe, 2002; Liebethal and Foken, 2003). Indeed, hundreds of eddy covariance tower sites now form a global network (Baldocchi et al., 2001), many employing open-path sensors to measure CO2 and water vapour densities. Regrettably, the recent article of Liu (2005) represents a flawed interpretation, of both the basic equation of state and the Webb corrections, whose publication obscures the open-path correction issue. The essential first step in deriving the Webb corrections is to define an equation of state for turbulent perturbations. This can take various forms including those shown by Equation (9b) of Webb et al., (1980), and Equations (4) and (6) of Liu (2005). To demonstrate clearly Liu’s error in interpretation, the perturbation equation of state is reproduced here in the form most relevant to the correction of open-path eddy covariance. Open-path gas analysers detect extinction targets in a constant sensing volume, and thus respond to molar density (n). Partitioning the molar density of air (n= nv + na) yields components representing water vapour (nv) and all other gases (‘dry air’, na) including trace amounts of CO2 (nc). In molar density terms, Equation (4) of Liu (2005) may be simplified to an equally valid expression of the perturbation equation of state

Equation of state of a mixture of hard spheres with non-additive diameters

The equation of state of a mixture of hard spheres with non-additive diameters has been found by molecular dynamical simulation. The mixture undergoes a fluid-fluid phase transition at high densities. A perturbation equation of state using a multicomponent reference fluid was found to give good agreement with the simulation results.