The Generalized Uncertainty Principle (GUP), which has been predicted by various theories of quan... more The Generalized Uncertainty Principle (GUP), which has been predicted by various theories of quantum gravity near the Planck scale is implemented on deriving the thermodynamics of ideal Quark-Gluon Plasma (QGP) consisting of two massless quark flavors at the hadron-QGP phase equilibrium and at a vanishing chemical potential. The effective degrees of freedom and MIT bag pressure are utilized to distinguish between the hadronic and partonic phases. We find that GUP makes a non-negligible contribution to all thermodynamic quantities, especially at high temperatures. The asymptotic behavior of corresponding QGP thermodynamic quantities characterized by the Stephan-Boltzmann limit would be approached, when the GUP approach is taken into consideration.
In 1948, Koppe formulated an almost complete recipe for statistical-thermal models including part... more In 1948, Koppe formulated an almost complete recipe for statistical-thermal models including particle production, formation and decay of resonances, temporal and thermal evolution of the interacting system, statistical approaches, and equilibrium condition in final state of the nuclear interaction. As the rate of particle production was one of the basic assumptions, recalling Koppe’s work would be an essential input to be involved in the statistical prediction of non-equilibrium particle production in recent and future ultra-relativistic collisions.
The SU(4) Polyakov linear sigma model (PLSM) is extended towards characterizing the chiral conden... more The SU(4) Polyakov linear sigma model (PLSM) is extended towards characterizing the chiral condensates, σ l , σ s and σ c of light, strange and charm quarks, respectively and the deconfinement order-parameters φ and φ at finite temperatures and densities (chemical potentials). The PLSM is considered to study the QCD equation of state in the presence of the chiral condensate of charm for different finite chemical potentials. The PLSM results are in a good agreement with the recent lattice QCD simulations. We conclude that, the charm condensate is likely not affected by the QCD phase-transition, where the corresponding critical temperature is greater than that of the light and strange quark condensates.
Recently, there has been much attention devoted to resolving the quantum corrections to the Beken... more Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein–Hawking (black hole) entropy, which relates the entropy to the cross-sectional area of the black hole horizon. Using generalized uncertainty principle (GUP), corrections to the geometric entropy and thermodynamics of black hole will be introduced. The impact of GUP on the entropy near the horizon of three types of black holes: Schwarzschild, Garfinkle–Horowitz–Strominger and Reissner–Nordstrom is determined. It is found that the logarithmic divergence in the entropy-area relation turns to be positive. The entropy S, which is assumed to be related to horizon's two-dimensional area, gets an additional terms, for instance , where α is the GUP parameter.
The quantum entropy at finite temperatures is analyzed by using models for colored quarks making ... more The quantum entropy at finite temperatures is analyzed by using models for colored quarks making up the physical states of the hadrons. We explicitly work out some special models for the structure of the states of SU(2) and SU(3) relating to the effects of the temperature on the quantum entropy. We show that the entropy of the singlet states monotonically decreases meaning that the mixing of these states continually diminishes with the temperature. It has been found that the structure of the octet states is more complex so that it can be best characterized by two parts. One part is very similar to that of the singlet states. The other one reflects the existence of strong correlations between two of the three color states. Furthermore, we work out the entropy for the {\it classical} Ising and the {\it quantum} XY spin chains. In Ising model the quantum (ground state) entropy does not directly enter into the canonical partition function. It also does not depend on the number of spatia...
The hadron ratios measured in central Au-Au collisions are analysed by means of Hadron Resonance ... more The hadron ratios measured in central Au-Au collisions are analysed by means of Hadron Resonance Gas (HRG) model over a wide range of nucleon-nucleon center-of-mass energies, √ sNN = 7.7 − 200 GeV as offered by the STAR Beam Energy Scan I (BES-I). We restrict the discussion on STAR BES-I, because of large statistics and over all homogeneity of STAR measurements (one detector) against previous experiments. Over the last three decades, various heavy-ion experiments utilizing different detectors (different accuracies) have been carried out. Regularities in produced particles at different energies haven been studied. The temperature and baryon chemical potential are deduced from fits of experimental ratios to thermal model calculations assuming chemical equilibrium. We find that the resulting freeze- out parameters using single hard-core value and point-like constituents of HRG are identical. This implies that the excluded-volume comes up with no effect on the extracted parameters. We c...
The successive stages of a high-energy collision are conjectured to end up with chemical and ther... more The successive stages of a high-energy collision are conjectured to end up with chemical and thermal freezeout of the produced particles. We utilize generic (non)extensive statistics which is believed to determine the degree of (non)extensivity through two critical exponents due to possible phase-space modifications. This statistical approach likely manifests various types of correlations and fluctuations and also possible interactions among the final-state produced particles. We study the baryon-to-pion ratios at top RHIC and LHC energies including the so-called proton anomaly.
Based on quantum mechanics and general relativity, Karolyhazy proposed a generalization to the we... more Based on quantum mechanics and general relativity, Karolyhazy proposed a generalization to the well-known Heisenberg uncertainty relation in which the energy density of quantum fluctuations of space-time plays a crucial role. Later on, various holographic DE models were suggested, in which the Hubble scale (size) and the age of the universe were assumed as measures for the largest infrared cutoff satisfying the holographic principle and energy bounds assuring applicability of quantum field theory. We review various models based on the holographic principle and the Karolyhazy relation and compare these to the space-time foam and superconducting DE models. We analyze their (in)stability against cosmological perturbation.
In framework of linear $\sigma$-model (LSM) with three quark flavors, the chiral phase-diagram at... more In framework of linear $\sigma$-model (LSM) with three quark flavors, the chiral phase-diagram at finite temperature and density is investigated. At temperatures higher than the critical temperature ($ T_c $), we added to LSM the gluonic sector from the quasi-particle model (QPM), which assumes that the interacting gluons in the strongly interacting matter, the quark-gluon plasma (QGP), are phenomenologically the same as non-interacting massive quasi-particles. The dependence of the chiral condensates of strange and non-strange quarks on temperature and chemical potential is analysed. Then, we have calculated the thermodynamics in the new approach (combination of LSM and QPM). Confronting the results with recent lattice QCD simulations shows an excellent agreement in almost all thermodynamic quantities. The first and second order moments of particle multiplicity are studied in dependence on the chemical potential but at fixed temperature and on the chemical potential but at fixed te...
In mean field approximation, the grand canonical potential of SU(3) Polyakov linear-σ model (PLSM... more In mean field approximation, the grand canonical potential of SU(3) Polyakov linear-σ model (PLSM) is analyzed for chiral phase transition, σl and σs and for deconfinement order-parameters, ϕ and ϕ∗ of light- and strange-quarks, respectively. Various PLSM parameters are determined from the assumption of global minimization of the real part of the potential. Then, we have calculated the subtracted condensates (Δl,s). All these results are compared with recent lattice QCD simulations. Accordingly, essential PLSM parameters are determined. The modeling of the relaxation time is utilized in estimating the conductivity properties of the QCD matter in thermal medium, namely electric [σel(T)] and heat [κ(T)] conductivities. We found that the PLSM results on the electric conductivity and on the specific heat agree well with the available lattice QCD calculations. Also, we have calculated bulk and shear viscosities normalized to the thermal entropy, ξ/s and η/s, respectively, and compared th...
The linear-sigma model, in which information about confining gluons is included through the Polya... more The linear-sigma model, in which information about confining gluons is included through the Polyakov-loop potential (PLSM), is considered in order to perform a systematic study for various magnetic properties of QCD matter under extreme conditions of high temperatures and densities and finite magnetic field strengths. The introduction of magnetic field to the PLSM Lagrangian requires suitable utilization of Landau quantization, modification in the dispersion relations, and momentum-space dimension-reduction. We observed that increasing the magnetic field leads to filling-up lower Landau levels first and decreasing the number of occupied levels. We conclude that the population of Landau levels is most sensitive to the magnetic field and to the quark charges. The influences of finite magnetic field on the temperature dependence of chiral and deconfinement order-parameter(s) are studied. We present estimations for the magnetization, the magnetic susceptibility, the permeability, and th...
AbstractIt was argued that the Raychaudhuri equation with a quantum correction term seems to avoi... more AbstractIt was argued that the Raychaudhuri equation with a quantum correction term seems to avoid the Big Bang singularity and to characterize an everlasting Universe (Ali and Das in Phys Lett B 741:276, 2015). Critical comments on both conclusions and on the correctness of the key expressions of this work were discussed in literature (Lashin in Mod Phys Lett 31:1650044, 2016). In the present work, we have analyzed the perturbative (in)stability conditions in the inflationary era of the early Universe. We conclude that both unstable and stable modes are incompatible with the corresponding ones obtained in the standard FLRW Universe. We have shown that unstable modes do exist at small (an)isotropic perturbation and for different equations of state. Inequalities for both unstable and stable solutions with the standard FLRW space were derived. They reveal that in the FLRW flat Universe both perturbative instability and stability are likely. While negative stability modes have been obt...
It is conjectured that in cosmological applications the particle current is not modified but fini... more It is conjectured that in cosmological applications the particle current is not modified but finite heat or energy flow. Therefore, comoving Eckart frame is a suitable choice, as it merely ceases the charge and particle diffusion and conserves charges and particles. The cosmic evolution of viscous hadron and parton epochs in casual and non-casual Eckart frame is analyzed. By proposing equations of state deduced from recent lattice QCD simulations including pressure p, energy density ρ, and temperature T, the Friedmann equations are solved. We introduce expressions for the temporal evolution of the Hubble parameter H˙, the cosmic energy density ρ˙, and the share η˙ and the bulk viscous coefficient ζ˙. We also suggest how the bulk viscous pressure Π could be related to H. We conclude that the relativistic theory of fluids, the Eckart frame, and the finite viscous coefficients play essential roles in the cosmic evolution, especially in the hadron and parton epochs.
The QCD phase-diagram is studied, at finite magnetic field. Our calculations are based on the QCD... more The QCD phase-diagram is studied, at finite magnetic field. Our calculations are based on the QCD effective model, the SU(3) Polyakov linear-sigma model (PLSM), in which the chiral symmetry is integrated in the hadron phase and in the parton phase, the up-, down- and strange-quark degrees of freedom are incorporated besides the inclusion of Polyakov loop potentials in the pure gauge limit, which are motivated by various underlying QCD symmetries. The Landau quantization and the magnetic catalysis are implemented. The response of the QCD matter to an external magnetic field such as magnetization, magnetic susceptibility and permeability has been estimated. We conclude that the parton phase has higher values of magnetization, magnetic susceptibility, and permeability relative to the hadron phase. Depending on the contributions to the Landau levels, we conclude that the chiral magnetic field enhances the chiral quark condensates and hence the chiral QCD phase-diagram, i.e. the hadron-p...
For temperatures [Formula: see text] ranging from a few MeV up to TeV and energy density [Formula... more For temperatures [Formula: see text] ranging from a few MeV up to TeV and energy density [Formula: see text] up to [Formula: see text][Formula: see text]GeV/fm3, the bulk viscosity [Formula: see text] is calculated in nonperturbation (up, down, strange, charm and bottom) and perturbation theories with up, down, strange, charm, bottom and top quark flavors, at vanishing baryon-chemical potential. To these calculations, results deduced from the effective QCD-like model, the Polyakov linear-sigma model (PLSM), are also integrated in. The PLSM merely comes up with essential contributions for the vacuum and thermal condensations of the gluons and the quarks (up, down, strange and charm flavors). Furthermore, the thermal contributions of the photons, neutrinos, charged leptons, electroweak particles and scalar Higgs boson are found very significant along the entire range of [Formula: see text] and [Formula: see text] and therefore could be well integrated in. We present the dimensionless ...
The particle ratios [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see ... more The particle ratios [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] measured at AGS, SPS and RHIC energies are compared with large statistical ensembles of 100,000 events deduced from the CRMC EPOS [Formula: see text] and the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) hybrid model. In the UrQMD hybrid model two types of phase transitions are taken into account. All these data are then confronted with the ideal Hadron Resonance Gas Model. The two types of phase transitions are apparently indistinguishable. Apart from [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the UrQMD hybrid model agrees well with the CRMC EPOS [Formula: see text]. We also conclude that the CRMC EPOS [Formula: see text] seems to largely under...
Based on recent perturbative and non-perturbative lattice calculations with almost quark flavors ... more 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 equation...
The Generalized Uncertainty Principle (GUP), which has been predicted by various theories of quan... more The Generalized Uncertainty Principle (GUP), which has been predicted by various theories of quantum gravity near the Planck scale is implemented on deriving the thermodynamics of ideal Quark-Gluon Plasma (QGP) consisting of two massless quark flavors at the hadron-QGP phase equilibrium and at a vanishing chemical potential. The effective degrees of freedom and MIT bag pressure are utilized to distinguish between the hadronic and partonic phases. We find that GUP makes a non-negligible contribution to all thermodynamic quantities, especially at high temperatures. The asymptotic behavior of corresponding QGP thermodynamic quantities characterized by the Stephan-Boltzmann limit would be approached, when the GUP approach is taken into consideration.
In 1948, Koppe formulated an almost complete recipe for statistical-thermal models including part... more In 1948, Koppe formulated an almost complete recipe for statistical-thermal models including particle production, formation and decay of resonances, temporal and thermal evolution of the interacting system, statistical approaches, and equilibrium condition in final state of the nuclear interaction. As the rate of particle production was one of the basic assumptions, recalling Koppe’s work would be an essential input to be involved in the statistical prediction of non-equilibrium particle production in recent and future ultra-relativistic collisions.
The SU(4) Polyakov linear sigma model (PLSM) is extended towards characterizing the chiral conden... more The SU(4) Polyakov linear sigma model (PLSM) is extended towards characterizing the chiral condensates, σ l , σ s and σ c of light, strange and charm quarks, respectively and the deconfinement order-parameters φ and φ at finite temperatures and densities (chemical potentials). The PLSM is considered to study the QCD equation of state in the presence of the chiral condensate of charm for different finite chemical potentials. The PLSM results are in a good agreement with the recent lattice QCD simulations. We conclude that, the charm condensate is likely not affected by the QCD phase-transition, where the corresponding critical temperature is greater than that of the light and strange quark condensates.
Recently, there has been much attention devoted to resolving the quantum corrections to the Beken... more Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein–Hawking (black hole) entropy, which relates the entropy to the cross-sectional area of the black hole horizon. Using generalized uncertainty principle (GUP), corrections to the geometric entropy and thermodynamics of black hole will be introduced. The impact of GUP on the entropy near the horizon of three types of black holes: Schwarzschild, Garfinkle–Horowitz–Strominger and Reissner–Nordstrom is determined. It is found that the logarithmic divergence in the entropy-area relation turns to be positive. The entropy S, which is assumed to be related to horizon's two-dimensional area, gets an additional terms, for instance , where α is the GUP parameter.
The quantum entropy at finite temperatures is analyzed by using models for colored quarks making ... more The quantum entropy at finite temperatures is analyzed by using models for colored quarks making up the physical states of the hadrons. We explicitly work out some special models for the structure of the states of SU(2) and SU(3) relating to the effects of the temperature on the quantum entropy. We show that the entropy of the singlet states monotonically decreases meaning that the mixing of these states continually diminishes with the temperature. It has been found that the structure of the octet states is more complex so that it can be best characterized by two parts. One part is very similar to that of the singlet states. The other one reflects the existence of strong correlations between two of the three color states. Furthermore, we work out the entropy for the {\it classical} Ising and the {\it quantum} XY spin chains. In Ising model the quantum (ground state) entropy does not directly enter into the canonical partition function. It also does not depend on the number of spatia...
The hadron ratios measured in central Au-Au collisions are analysed by means of Hadron Resonance ... more The hadron ratios measured in central Au-Au collisions are analysed by means of Hadron Resonance Gas (HRG) model over a wide range of nucleon-nucleon center-of-mass energies, √ sNN = 7.7 − 200 GeV as offered by the STAR Beam Energy Scan I (BES-I). We restrict the discussion on STAR BES-I, because of large statistics and over all homogeneity of STAR measurements (one detector) against previous experiments. Over the last three decades, various heavy-ion experiments utilizing different detectors (different accuracies) have been carried out. Regularities in produced particles at different energies haven been studied. The temperature and baryon chemical potential are deduced from fits of experimental ratios to thermal model calculations assuming chemical equilibrium. We find that the resulting freeze- out parameters using single hard-core value and point-like constituents of HRG are identical. This implies that the excluded-volume comes up with no effect on the extracted parameters. We c...
The successive stages of a high-energy collision are conjectured to end up with chemical and ther... more The successive stages of a high-energy collision are conjectured to end up with chemical and thermal freezeout of the produced particles. We utilize generic (non)extensive statistics which is believed to determine the degree of (non)extensivity through two critical exponents due to possible phase-space modifications. This statistical approach likely manifests various types of correlations and fluctuations and also possible interactions among the final-state produced particles. We study the baryon-to-pion ratios at top RHIC and LHC energies including the so-called proton anomaly.
Based on quantum mechanics and general relativity, Karolyhazy proposed a generalization to the we... more Based on quantum mechanics and general relativity, Karolyhazy proposed a generalization to the well-known Heisenberg uncertainty relation in which the energy density of quantum fluctuations of space-time plays a crucial role. Later on, various holographic DE models were suggested, in which the Hubble scale (size) and the age of the universe were assumed as measures for the largest infrared cutoff satisfying the holographic principle and energy bounds assuring applicability of quantum field theory. We review various models based on the holographic principle and the Karolyhazy relation and compare these to the space-time foam and superconducting DE models. We analyze their (in)stability against cosmological perturbation.
In framework of linear $\sigma$-model (LSM) with three quark flavors, the chiral phase-diagram at... more In framework of linear $\sigma$-model (LSM) with three quark flavors, the chiral phase-diagram at finite temperature and density is investigated. At temperatures higher than the critical temperature ($ T_c $), we added to LSM the gluonic sector from the quasi-particle model (QPM), which assumes that the interacting gluons in the strongly interacting matter, the quark-gluon plasma (QGP), are phenomenologically the same as non-interacting massive quasi-particles. The dependence of the chiral condensates of strange and non-strange quarks on temperature and chemical potential is analysed. Then, we have calculated the thermodynamics in the new approach (combination of LSM and QPM). Confronting the results with recent lattice QCD simulations shows an excellent agreement in almost all thermodynamic quantities. The first and second order moments of particle multiplicity are studied in dependence on the chemical potential but at fixed temperature and on the chemical potential but at fixed te...
In mean field approximation, the grand canonical potential of SU(3) Polyakov linear-σ model (PLSM... more In mean field approximation, the grand canonical potential of SU(3) Polyakov linear-σ model (PLSM) is analyzed for chiral phase transition, σl and σs and for deconfinement order-parameters, ϕ and ϕ∗ of light- and strange-quarks, respectively. Various PLSM parameters are determined from the assumption of global minimization of the real part of the potential. Then, we have calculated the subtracted condensates (Δl,s). All these results are compared with recent lattice QCD simulations. Accordingly, essential PLSM parameters are determined. The modeling of the relaxation time is utilized in estimating the conductivity properties of the QCD matter in thermal medium, namely electric [σel(T)] and heat [κ(T)] conductivities. We found that the PLSM results on the electric conductivity and on the specific heat agree well with the available lattice QCD calculations. Also, we have calculated bulk and shear viscosities normalized to the thermal entropy, ξ/s and η/s, respectively, and compared th...
The linear-sigma model, in which information about confining gluons is included through the Polya... more The linear-sigma model, in which information about confining gluons is included through the Polyakov-loop potential (PLSM), is considered in order to perform a systematic study for various magnetic properties of QCD matter under extreme conditions of high temperatures and densities and finite magnetic field strengths. The introduction of magnetic field to the PLSM Lagrangian requires suitable utilization of Landau quantization, modification in the dispersion relations, and momentum-space dimension-reduction. We observed that increasing the magnetic field leads to filling-up lower Landau levels first and decreasing the number of occupied levels. We conclude that the population of Landau levels is most sensitive to the magnetic field and to the quark charges. The influences of finite magnetic field on the temperature dependence of chiral and deconfinement order-parameter(s) are studied. We present estimations for the magnetization, the magnetic susceptibility, the permeability, and th...
AbstractIt was argued that the Raychaudhuri equation with a quantum correction term seems to avoi... more AbstractIt was argued that the Raychaudhuri equation with a quantum correction term seems to avoid the Big Bang singularity and to characterize an everlasting Universe (Ali and Das in Phys Lett B 741:276, 2015). Critical comments on both conclusions and on the correctness of the key expressions of this work were discussed in literature (Lashin in Mod Phys Lett 31:1650044, 2016). In the present work, we have analyzed the perturbative (in)stability conditions in the inflationary era of the early Universe. We conclude that both unstable and stable modes are incompatible with the corresponding ones obtained in the standard FLRW Universe. We have shown that unstable modes do exist at small (an)isotropic perturbation and for different equations of state. Inequalities for both unstable and stable solutions with the standard FLRW space were derived. They reveal that in the FLRW flat Universe both perturbative instability and stability are likely. While negative stability modes have been obt...
It is conjectured that in cosmological applications the particle current is not modified but fini... more It is conjectured that in cosmological applications the particle current is not modified but finite heat or energy flow. Therefore, comoving Eckart frame is a suitable choice, as it merely ceases the charge and particle diffusion and conserves charges and particles. The cosmic evolution of viscous hadron and parton epochs in casual and non-casual Eckart frame is analyzed. By proposing equations of state deduced from recent lattice QCD simulations including pressure p, energy density ρ, and temperature T, the Friedmann equations are solved. We introduce expressions for the temporal evolution of the Hubble parameter H˙, the cosmic energy density ρ˙, and the share η˙ and the bulk viscous coefficient ζ˙. We also suggest how the bulk viscous pressure Π could be related to H. We conclude that the relativistic theory of fluids, the Eckart frame, and the finite viscous coefficients play essential roles in the cosmic evolution, especially in the hadron and parton epochs.
The QCD phase-diagram is studied, at finite magnetic field. Our calculations are based on the QCD... more The QCD phase-diagram is studied, at finite magnetic field. Our calculations are based on the QCD effective model, the SU(3) Polyakov linear-sigma model (PLSM), in which the chiral symmetry is integrated in the hadron phase and in the parton phase, the up-, down- and strange-quark degrees of freedom are incorporated besides the inclusion of Polyakov loop potentials in the pure gauge limit, which are motivated by various underlying QCD symmetries. The Landau quantization and the magnetic catalysis are implemented. The response of the QCD matter to an external magnetic field such as magnetization, magnetic susceptibility and permeability has been estimated. We conclude that the parton phase has higher values of magnetization, magnetic susceptibility, and permeability relative to the hadron phase. Depending on the contributions to the Landau levels, we conclude that the chiral magnetic field enhances the chiral quark condensates and hence the chiral QCD phase-diagram, i.e. the hadron-p...
For temperatures [Formula: see text] ranging from a few MeV up to TeV and energy density [Formula... more For temperatures [Formula: see text] ranging from a few MeV up to TeV and energy density [Formula: see text] up to [Formula: see text][Formula: see text]GeV/fm3, the bulk viscosity [Formula: see text] is calculated in nonperturbation (up, down, strange, charm and bottom) and perturbation theories with up, down, strange, charm, bottom and top quark flavors, at vanishing baryon-chemical potential. To these calculations, results deduced from the effective QCD-like model, the Polyakov linear-sigma model (PLSM), are also integrated in. The PLSM merely comes up with essential contributions for the vacuum and thermal condensations of the gluons and the quarks (up, down, strange and charm flavors). Furthermore, the thermal contributions of the photons, neutrinos, charged leptons, electroweak particles and scalar Higgs boson are found very significant along the entire range of [Formula: see text] and [Formula: see text] and therefore could be well integrated in. We present the dimensionless ...
The particle ratios [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see ... more The particle ratios [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] measured at AGS, SPS and RHIC energies are compared with large statistical ensembles of 100,000 events deduced from the CRMC EPOS [Formula: see text] and the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) hybrid model. In the UrQMD hybrid model two types of phase transitions are taken into account. All these data are then confronted with the ideal Hadron Resonance Gas Model. The two types of phase transitions are apparently indistinguishable. Apart from [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the UrQMD hybrid model agrees well with the CRMC EPOS [Formula: see text]. We also conclude that the CRMC EPOS [Formula: see text] seems to largely under...
Based on recent perturbative and non-perturbative lattice calculations with almost quark flavors ... more 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 equation...
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