Eckart Theory Research Articles

WIMP Dark Matter in bulk viscous non-standard cosmologies

In this paper, we explore an extension of the classical non-standard cosmological scenario in which the new field, ϕ, which interacts with the radiation component in the early universe, experiences dissipative processes in the form of a bulk viscosity. Assuming an interaction term given by Γ ϕ ρ ϕ , where Γ ϕ accounts for the decay rate of the field and ρ ϕ corresponds to its energy density, and a bulk viscosity according to the expression ξ=ξ 0 ρ ϕ ϕ1/2 in the framework of Eckart's theory, we apply this novel non-standard cosmology to study the parameters space for WIMPs Dark Matter candidate production. This parameter space shows deviations from the classical non-standard cosmological scenario, obtaining new regions to search for this candidate. In particular, for certain combinations of the free parameters, we found large regions in which the model can establish the DM and reproduce the current observable relic density.

Perturbations of a class of locally rotationally symmetric cosmologies with applications to dissipative fluids

A gauge invariant perturbation theory, based on the covariant split of spacetime, is used to study first order perturbations on a class of anisotropic cosmological backgrounds. The perturbations as well as the energy-momentum tensor are kept general, giving a system of equations on which different physical situations may be imposed. Through a harmonic decomposition, the system is then transformed to evolution equations in time and algebraic constraints. This result is then applied to dissipative one-component fluids, and on using the simplified acausal Eckart theory the system is reduced to two closed subsystems, governed by four and eight harmonic coefficients for the odd and even sectors respectively. The system is also seen to close in a simplified causal theory. It is then demonstrated, within the Eckart theory, how vorticity can be generated from viscosity.

Hybrid expansion law in viscous braneworld gravity with Gauss–Bonnet terms

The cosmological model executing hybrid expansion law (HEL) of scale factor in Randall–Sundrum type II (RS) braneworld gravity with Gauss–Bonnet terms in the presence of bulk viscosity described by Eckart theory, Truncated Israel–Stewart (TIS) theory, Full Israel–Stewart (FIS) theory and nonlinear Israel–Stewart (nIS) theory is studied. In the hybrid expansion law, the scale factor of the universe is described by the product of power-law and exponential expansions. In the HEL model, the early inflation and its transition from deceleration phase to present accelerated phase of expansion can be explored. The constraints of hybrid expansion law model parameters are determined using the recent observational data. Thereafter, the estimated parameters are considered to explore the present value of deceleration parameter, jerk parameter and transition epoch from early deceleration to the present accelerating phase.

Thermodynamics of viscous dark energy for the late future time universe

In this work we explore the thermodynamic aspects of dark energy for late future time universe in two different scenarios: as a perfect fluid with constant and variable equation of state parameter; and as dissipative fluid described by a barotropic equation of state with bulk viscosity in the framework of the Eckart theory and the full Israel-Stewart theory.We explore cosmological solutions for a flat, homogeneous and isotropic universe; and we assume the late future time behavior when the dark energy dominates the cosmic evolution.When modeled as a perfect fluid with a dynamical equation of state, $p=w(a)\rho$, the dark energy has an energy density, temperature and entropy well defined and an interesting result is that there is no entropy production even though been dynamical. For dissipative dark energy, in the Eckart theory two cases are studied: $\xi=const.$ and $\xi =(\beta/\sqrt{3}) \rho^{1/2}$; it is found that the entropy grows exponentially for the first case and as a power-law for the second.In the Israel-Stewart theory we consider a $\xi =\xi_0 \rho^{1/2}$ and a relaxation time $\tau = \xi/\rho$; an analytical Big Rip solution is obtained with a power-law entropy.In all cases is obtained a power-law relation between temperature and energy density.In order to maintain the second law of thermodynamics theoretical constraints for the equation of state are found in the different dark energy models studied.A barotropic dark fluid with $w<-1$ is thermodynamically difficult to support, but the overall effect of bulk viscosity in certain cases allows a phantom regime without thermodynamic anomalies.

On the mode structure of imperfect fluids

This paper tries to present a simple picture of several aspects of the mode structure in relativistic non-equilibrium thermodynamics. Its pedagogical focus is on the relation between long-wavelength perturbation modes of the causal Müller-Israel-Stewart (MIS) theory and those of the traditional Eckart theory. Principally, this issue was clarified in a series of papers by Hiscock and Lindblom. Here, I put together some essential features of this topic which do not require the entire formalism of the complete theory.

Singularities and soft-Big Bang in a viscous ΛCDM model

In this paper we explore the different types of singularities that arise in the $\Lambda$CDM model when dissipative processes are considered, in the framework of the Eckart's theory. In particular, we study the late-time behavior of $\Lambda$CDM model with viscous cold dark matter (CDM) and an early-time viscous radiation domination era with cosmological constant (CC). The fluids are described by the barotropic equation of state (EoS) $p=(\gamma-1)\rho$, where $p$ is the equilibrium pressure of the fluid, $\rho$ their energy density, and $\gamma$ is the barotropic index. We explore two particular cases for the bulk viscosity $\xi$, a constant bulk viscosity $\xi=\xi_{0}$, and a bulk viscosity proportional to the energy density of the fluid $\xi=\xi_{0}\rho$. Due to some previous investigations that have explored to describe the behavior of the universe with a negative CC, we extend our analysis to this case. We found that future singularities like Big-Rip are allowed but without having a phantom EoS associated to the DE fluid. Big-Crunch singularities also appears when a negative CC is present, but also de Sitter and even Big-Rip types are allowed due to the negative pressure of the viscosity, which opens the possibility of an accelerated expansion in AdS cosmologies. We also discuss a very particular solution without Big Bang singularity that arises in the early-time radiation dominant era of our model known as Soft-Big Bang.

Early Universe Thermodynamics and Evolution in Nonviscous and Viscous Strong and Electroweak Epochs: Possible Analytical Solutions

Simple SummaryIn the early Universe, both QCD and EW eras play an essential role in laying seeds for nucleosynthesis and even dictating the cosmological large-scale structure. Taking advantage of recent developments in ultrarelativistic nuclear experiments and nonperturbative and perturbative lattice simulations, various thermodynamic quantities including pressure, energy density, bulk viscosity, relaxation time, and temperature have been calculated up to the TeV-scale, in which the possible influence of finite bulk viscosity is characterized for the first time and the analytical dependence of Hubble parameter on the scale factor is also introduced.Based on recent perturbative and non-perturbative lattice calculations with almost quark flavors and the thermal contributions from photons, neutrinos, leptons, electroweak particles, and scalar Higgs bosons, various thermodynamic quantities, at vanishing net-baryon densities, such as pressure, energy density, bulk viscosity, relaxation time, and temperature have been calculated up to the TeV-scale, i.e., covering hadron, QGP, and electroweak (EW) phases in the early Universe. This remarkable progress motivated the present study to determine the possible influence of the bulk viscosity in the early Universe and to understand how this would vary from epoch to epoch. We have taken into consideration first- (Eckart) and second-order (Israel–Stewart) theories for the relativistic cosmic fluid and integrated viscous equations of state in Friedmann equations. Nonlinear nonhomogeneous differential equations are obtained as analytical solutions. For Israel–Stewart, the differential equations are very sophisticated to be solved. They are outlined here as road-maps for future studies. For Eckart theory, the only possible solution is the functionality, , where is the Hubble parameter and is the scale factor, but none of them so far could to be directly expressed in terms of either proper or cosmic time t. For Eckart-type viscous background, especially at finite cosmological constant, non-singular and are obtained, where diverges for QCD/EW and asymptotic EoS. For non-viscous background, the dependence of is monotonic. The same conclusion can be drawn for an ideal EoS. We also conclude that the rate of decreasing with increasing varies from epoch to epoch, at vanishing and finite cosmological constant. These results obviously help in improving our understanding of the nucleosynthesis and the cosmological large-scale structure.

Observational constraints of bulk viscous Friedmann–Robertson–Walker cosmology with hybrid expansion law

In this work, we study bulk viscous Friedmann–Robertson–Walker cosmologies with hybrid expansion law. The bulk viscous theory of dissipative effects described by Eckart theory, truncated Israel–Stewart theory and full Israel–Stewart theory are implemented here. The hybrid expansion law model of scale factor is a general analytic type of evolution from which one can recover power-law and exponential expansion as a special cases. Hybrid expansion law model are applied to describe the present accelerating phase and early phases of evolution. We have determined the cosmological parameters such as Hubble parameter, deceleration parameter, jerk parameter, energy density, bulk viscous pressure and coefficient of bulk viscosity of the universe to construct physically acceptable cosmological model. We have considered both flat and closed space–time of Friedmann–Robertson–Walker cosmology to implement hybrid expansion law with dissipative effect. The variations of the coefficient of bulk viscosity with cosmic evolution are studied here in Eckart, truncated and full Israel–Stewart theory for flat and closed space–time to obtain physically acceptable hybrid expansion models driven by viscosity. We have also estimated observational constraints of the parameters of hybrid expansion law model by considering recent observational data set. We further reveal possible connections of our models with [Formula: see text] tension problem.

Generic instabilities in the relativistic Chapman–Enskog heat conduction law

We address the well-posedness of the Cauchy problem corresponding to the relativistic fluid equations, when coupled with the heat-flux constitutive relation arising within the relativistic Chapman-Enskog procedure. The resulting system of equations is shown to be non hyperbolic, by considering general perturbations over the whole set of equations written with respect to a generic time direction. The obtained eigenvalues are not purely imaginary and their real part grows without bound as the wave-number increases. Unlike Eckart's theory, this instability is not present when the time direction is aligned with the fluid's direction. However, since in general the fluid velocity is not surface-forming, the instability can only be avoided in the particular case where no rotation is present.

Observational constraints of emergent universe in f(R,T) gravity with bulk viscosity

Emergent universe (EU) cosmological models with viscosity in a modified gravity which contains a general function [Formula: see text], where [Formula: see text] and [Formula: see text] denote the curvature scalar and the trace of the energy–momentum tensor, respectively, are studied in a flat Friedmann–Robertson–Walker metric. Cosmological solutions are obtained in [Formula: see text] theory of gravity, which represented as [Formula: see text] with bulk viscosity that described by Eckart theory, truncated Israel Stewart theory and full Israel Stewart Theory. The physical and geometrical features of the EU models in [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] are coupling parameters, with bulk viscosity are studied in details. Constraints of the EU models parameters in [Formula: see text] gravity with bulk viscosity are estimated from observational data set. The stability analysis of the equilibrium points admitting cosmological solutions of the dynamical system associated with the evolution in the modified gravity is studied in Eckart theory, truncated Israel Stewart theory and full Israel Stewart theory.

Observational constraints of emergent universe in brane-world with Gauss–Bonnet term and dissipative effect

Cosmological solutions in the Randall–Sundrum (RS) type II brane-world model including Gauss–Bonnet (GB) term, in the presence of a bulk viscous cosmological fluid are discussed. Transport equations described by Eckart and Israel Stewart are implemented here. Cosmological models admitting emergent universe (EU) of the early universe is explored here in the presence of imperfect fluid described by Eckart theory and Truncated Israel Stewart (TIS) theory and Full Israel Stewart (FIS) theory. We also study the permitted values of the EU model parameters by considering cosmological observational dataset. The stability analysis of the equilibrium points of the dynamical system associated with the evolution in the RS brane including GB term are studied in Eckart theory, TIS theory and FIS theory.

Irreversible thermodynamics of the universe in $$\varvec{f}(R)$$ gravity

In this study, the irreversible thermodynamics of the universe in the framework of f(R) gravity has been studied following standard Eckart theory of non-equilibrium thermodynamics. For a spatially flat universe, validity of GSLT and thermodynamic equilibrium have been examined both for apparent and event horizon as bounding horizons.The general result has been verified for exponential models of f(R) gravity and it is shown that GSLT holds on both apparent and event horizon, but thermodynamic equilibrium does not hold on event horizon.

Extended ΛCDM model and viscous dark energy: a Bayesian analysis

We propose an approach considering the nonextensive effects in the context of the Verlinde theory in order to address an extended cosmological model in the context of viscous dark energy. Specifically, this model leads to a tiny perturbation in the dynamics of the expansion of the universe through the generalized Friedmann equations so-called the extended ΛCDM model. From the observational test standpoint, we make a Bayesian analysis of the models of bulk viscosity for dark energy which follows the Eckart theory of bulk viscosity. These models are investigated through the context of both models ΛCDM and extended ΛCDM. The Bayesian analysis is performed using the data of CMB Distance priors, Baryon Acoustic Oscillations Measurements, Cosmic Chronometers, and SNe Ia distance measurements.

Bulk viscous cosmological model in f(R,T) theory of gravity

In this paper, we have presented bulk viscous cosmological model of the universe in the modified gravity theory in which the Lagragian of the gravitational action contains a general function [Formula: see text], where [Formula: see text] and [Formula: see text] denote the curvature scalar and the trace of the energy–momentum tensor, respectively, in the framework of a flat Friedmann–Robertson–Walker model with isotropic fluid. We obtain cosmological solution in [Formula: see text] theory of gravity, specially of particular choice [Formula: see text], where [Formula: see text] is a constant, in the presence of bulk viscosity that are permitted in Eckart theory, Truncated Israel Stewart (TIS) theory and Full Israel Stewart (FIS) theory. The physical and geometrical properties of the models in Eckart, TIS theory and FIS theory are studied in detail. The analysis of the variation of bulk viscous pressure, energy density, scale factor, Hubble parameter and deceleration parameter with cosmic evolution is done in the respective theories. The models are analyzed by comparison with recent observational data. The cosmological models are compatible with observations.

Extended ΛCDM model

In this work we discuss a general approach for the dissipative dark matter considering a nonextensive bulk viscosity and taking into account the role of generalized Friedmann equations. This generalized ΛCDM model encompasses a flat universe with a dissipative nonextensive viscous dark matter component, following the Eckart theory of bulk viscosity. In order to compare models and constrain cosmological parameters, we perform Bayesian analysis using one of the most recent observations of Type Ia Supernova, baryon acoustic oscillations, and cosmic microwave background data.

Ricci dark energy model with bulk viscosity

In order to explore the possibility of bulk viscosity as a possible candidate of dark energy to explain the accelerating universe, we investigate the dissipative processes in the holographic Ricci dark energy (HRDE) model within the framework of the standard Eckart theory of relativistic thermodynamics. We assume that the flat Friedmann-Robertson-Walker universe is filled with pressureless dark matter and viscous HRDE. We obtain the exact solutions of non-viscous and viscous HRDE models, respectively. We plot the evolution of the scale factor and deceleration parameter to observe the transition phase in the viscous case. We also discuss two geometrical diagnostics, namely the statefinder and Om to discriminate from other existing dark energy models. In the non-viscous HRDE model, the power-law form of expansion is obtained which gives the constant deceleration parameter and statefinder pair. It does not show phase transition. In the viscous HRDE model, we consider all possible forms of bulk viscous coefficient (with constant or general form of viscous terms) and discuss the cosmological evolution in detail. We obtain the exponential expansion of the scale factor which gives the time-dependent deceleration parameter and statefinder pair. The model shows the transition from the decelerated phase to the accelerated phase depending on the values of the viscous term. It starts to accelerate in the past for large values of the viscous term. The trajectory of the statefinder pair shows that for small values of the viscous term, the trajectory is curved and starts from quintessence in early time and approaches to $\Lambda$ CDM model in late time. It is also observed that for large values of the viscous term, it behaves like the Chaplygin gas in early time but approaches to $\Lambda$ CDM model in late time. We also plot the trajectory of the deceleration parameter, statefinder pair and Om with the model parameter to observe the evolutionary behavior of the universe. It also shows a similar behavior except for the fact that it only behaves as quintessence in the past but approaches to $\Lambda$ CDM or the steady state model in late time. The results of viscous HRDE models show that the recent acceleration is well explained with the viscous term.

Unimolecular Decay of Criegee Intermediates to OH Radical Products: Prompt and Thermal Decay Processes.

Alkene ozonolysis is a primary oxidation pathway for anthropogenic and biogenic alkenes emitted into the troposphere. It is also an important source of atmospheric hydroxyl (OH) radicals, often called the atmosphere's detergent. Alkene ozonolysis takes place through a highly exothermic reaction pathway with multiple intermediates and barriers prior to releasing the OH radical products. This Account focuses on a key reaction intermediate with a carbonyl oxide functional group (-COO), known as the Criegee intermediate, which is formed along with a carbonyl coproduct in alkene ozonolysis reactions. Under atmospheric conditions, the initially energized Criegee intermediates may promptly decay to OH products or be collisionally stabilized prior to thermal decay to OH radicals and other products. Alternatively, the stabilized Criegee intermediates may undergo bimolecular reactions with atmospheric species, including water vapor and sulfur dioxide, which can lead to nucleation and growth of aerosols. The dimethyl-substituted Criegee intermediate, (CH3)2COO, is utilized in this Account to showcase recent efforts to experimentally measure and theoretically predict the rates for prompt and thermal unimolecular decay processes of prototypical Criegee intermediates under laboratory and atmospheric conditions. The experimental laboratory studies utilize an alternative synthesis method to efficiently generate Criegee intermediates via the reaction of iodoalkyl radicals with O2. Infrared excitation is then used to prepare the (CH3)2COO Criegee intermediates at specific energies in the vicinity of the transition state barrier or significantly below the barrier for 1,4-hydrogen transfer that leads to OH products. The rate of unimolecular decay is revealed through direct time-domain measurements of the appearance of OH products utilizing ultraviolet laser-induced fluorescence detection under collision-free conditions. Complementary high-level theoretical calculations are carried out to evaluate the transition state barrier and the energy-dependent unimolecular decay rates for (CH3)2COO using Rice-Ramsperger-Kassel-Marcus (RRKM) theory, which are in excellent accord with the experimental measurements. Quantum mechanical tunneling through the barrier, incorporated through Eckart and semiclassical transition state theory models, is shown to make a significant contribution to the unimolecular decay rates at energies in the vicinity of and much below the barrier. Master equation modeling is used to extend the energy-dependent unimolecular rates to thermal decay rates of (CH3)2COO under tropospheric conditions (high pressure limit), which agree well with recent laboratory measurements [ Smith et al. J. Phys. Chem. A 2016 , 120 , 4789 and Chhantyal-Pun et al. J. Phys. Chem. A 2017 , 121 , 4 - 15 ]. Again, tunneling is shown to enhance the thermal decay rate by orders of magnitude. The experimentally validated unimolecular rates are also utilized in modeling the prompt and thermal unimolecular decay of chemically activated (CH3)2COO formed upon ozonolysis of 2,3-dimethyl-2-butene under atmospheric conditions [ Drozd et al. J. Phys. Chem. A 2017 , 121 , 6036 - 6045 ]. Future challenges lie in extension of these spectroscopic and dynamical methods to Criegee intermediates derived from more complex ozonolysis reactions involving biogenic alkenes.

Emergent universe model with dissipative effects

Emergent universe model is presented in general theory of relativity with isotropic fluid in addition to viscosity. We obtain cosmological solutions that permit emergent universe scenario in the presence of bulk viscosity that are described by either Eckart theory or Truncated Israel Stewart (TIS) theory. The stability of the solutions are also studied. In this case, the emergent universe (EU) model is analyzed with observational data. In the presence of viscosity, one obtains emergent universe scenario, which however is not permitted in the absence of viscosity. The EU model is compatible with cosmological observations.

Formula omitted]CDM model with dissipative nonextensive viscous dark matter

Many models in cosmology typically assume the standard bulk viscosity. We study an alternative interpretation for the origin of the bulk viscosity. Using nonadditive statistics proposed by Tsallis, we propose a bulk viscosity component that can only exist by a nonextensive effect through the nonextensive/dissipative correspondence (NexDC). In this paper, we consider a ΛCDM model for a flat universe with a dissipative nonextensive viscous dark matter component, following the Eckart theory of bulk viscosity, without any perturbative approach. In order to analyze cosmological constraints, we use one of the most recent observations of Type Ia Supernova, baryon acoustic oscillations and cosmic microwave background data.

Viscous extended holographic Ricci dark energy in the framework of standard Eckart theory

In this paper, we report a study on the viscous extended holographic Ricci dark energy (EHRDE) model under the assumption of existence of bulk viscosity in the linear barotropic fluid and the EHRDE in the framework of standard Eckart theory of relativistic irreversible thermodynamics and it has been observed that the non-equilibrium bulk viscous pressure is significantly smaller than the local equilibrium pressure. We have studied the equation of state (EoS) parameter and observed that the EoS behaves like “quintom” and is consistent with the constraints set by observational data sets from SNLS3, BAO and Planck + WMAP9 + WiggleZ measurements in [S. Kumar and L. Xu, Phys. Lett. B 737, 244 (2014)]. Analysis of statefinder parameters has shown the possibility of attainment of Lambda cold dark matter ([Formula: see text]CDM) phase under current model and at the same time it has been pointed out that the redshift z = 0, i.e. the current universe, the statefinder pair is different from that of [Formula: see text]CDM and the [Formula: see text]CDM can be attained in a later stage of the universe. An analysis of stability has shown that although the viscous EHRDE along with viscous barotropic is classically unstable in the present epoch, it can lead to a stable universe in very late stage. Considering an universe enveloped by event horizon, we have observed validity of generalized second law (GSL) of thermodynamics.