Quark-Hadron Phase Transitions in Viscous Early Universe

Based on hot big bang theory, the cosmological matter is conjectured to undergo QCD phase transition(s) to hadrons, when the universe was about $1-10 \mu$s old. In the present work, we study the quark-hadron phase transition, by taking into account the effect of the bulk viscosity. We analyze the evolution of the quantities relevant for the physical description of the early universe, namely, the energy density $\rho$, temperature $T$, Hubble parameter $H$ and scale factor $a$ before, during and after the phase transition. To study the cosmological dynamics and the time evolution we use both analytical and numerical methods. By assuming that the phase transition may be described by an effective nucleation theory (prompt {\it first-order} phase transition), we also consider the case where the universe evolved through a mixed phase with a small initial supercooling and monotonically growing hadronic bubbles. The numerical estimation of the cosmological parameters, $a$ and $H$ for instance, makes it clear that the time evolution varies from phase to phase. As the QCD era turns to be fairly accessible in the high-energy experiments and the lattice QCD simulations, the QCD equation of state is very well defined. In light of this, we introduce a systematic study of the {\it cross-over} quark-hadron phase transition and an estimation for the time evolution of Hubble parameter.Comment: 27 pages, 17 figures, revtex style (To appear in Phys. Rev. D). arXiv admin note: text overlap with arXiv:gr-qc/040404

Particle Ratios in Heavy-Ion Collisions

In framework of statistical models, different particle ratios at energies ranging from $3.5$ to $200$GeV are calculated. Assuming that the particle production takes place along the freeze-out curve, we study the sharp peak in $K^+/\pi^+$ ratio observed at SPS energy. We study the responsibility of non-equilibrium quark occupancy of phase space $\gamma_i$ for particle production. Allowing $\gamma_i$ to take values other than that of equilibrium, we got a very well description for $K^+/\pi^+$ ratio at all energies. Using the resulting parameter set, we analyzed the $K^-/\pi^-$, $\Lambda/\pi^+$ and \hbox{$\Lambda/$} ratios. We found that the corresponding peaks all are located at the same value of energy, $\sqrt{s_{NN}}^{(c)}\simeq7.5$GeV. At this energy, the entropy per particle is singular. The saddle-point in entropy per particle likely refers to critical phenomenon and change in the phase space.Comment: 10 pages, 5 figures and 1 table to be appear in Prog. Theor. Phy

Thermodynamics in the Viscous Early Universe

Assuming that the matter filling the background geometry in the Early Universe was a free gas and no phase transitions took place, we discuss the thermodynamics of this closed system using classical approaches. We found that essential cosmological quantities, such as the Hubble parameter $H$, the scaling factor $a$ and the curvature parameter $k$, can be derived from this simple model. The results are compatible with the Friedmann-Robertson-Walker model and Einstein field equations. Including finite bulk viscosity coefficient leads to important changes in the cosmological quantities. Accordingly, our picture about evolution of the Universe and its astrophysical consequences seems to be a subject of radical revision. We found that $k$ strongly depends on thermodynamics of the cosmic background matter. The time scale, at which negative curvature might take place, depends on the relation between the matter content and the total energy. Using quantum and statistical approaches, we introduced expressions for $H$ and the bulk viscosity coefficient.Comment: 15 pages, 4 eps figures, invited talk given at the "Second IAGA-Symposium", Cairo-Egypt, 4-8 Jan. (2010

Impacts of Generalized Uncertainty Principle on Black Hole Thermodynamics and Salecker-Wigner Inequalities

We investigate the impacts of Generalized Uncertainty Principle (GUP) proposed by some approaches to quantum gravity such as String Theory and Doubly Special Relativity on black hole thermodynamics and Salecker-Wigner inequalities. Utilizing Heisenberg uncertainty principle, the Hawking temperature, Bekenstein entropy, specific heat, emission rate and decay time are calculated. As the evaporation entirely eats up the black hole mass, the specific heat vanishes and the temperature approaches infinity with an infinite radiation rate. It is found that the GUP approach prevents the black hole from the entire evaporation. It implies the existence of remnants at which the specific heat vanishes. The same role is played by the Heisenberg uncertainty principle in constructing the hydrogen atom. We discuss how the linear GUP approach solves the entire-evaporation-problem. Furthermore, the black hole lifetime can be estimated using another approach; the Salecker-Wigner inequalities. Assuming that the quantum position uncertainty is limited to the minimum wavelength of measuring signal, Wigner second inequality can be obtained. If the spread of quantum clock is limited to some minimum value, then the modified black hole lifetime can be deduced. Based on linear GUP approach, the resulting lifetime difference depends on black hole relative mass and the difference between black hole mass with and without GUP is not negligible.Comment: 15 pages, 2 figures with 2 pdf graphs. arXiv admin note: text overlap with arXiv:1208.6584, arXiv:hep-th/9309138 by other author

In-Medium Modifications of Hadron Properties

The in-medium modifications of hadron properties are briefly discussed. We restrict the discussion to the lattice QCD calculations for the hadron masses, screening masses, decay constants and wave functions. We review the progress made so far and describe how to broaden its horizon.Comment: 10 pages, 7 figures \ Talk given at YITP workshop on ``Hadrons ant Finite Density 2006'' Feb. 20-22, 200

Constant Trace Anomaly as a Universal Condition for the Chemical Freeze-Out

Finding out universal conditions describing the freeze-out parameters was a subject of various phenomenological studies. In the present work, we introduce a new condition based on constant trace anomaly (or interaction measure) calculated in the hadron resonance gas (HRG) model. Various extensions to the {\it ideal} HRG which are conjectured to take into consideration different types of interactions have been analysed. When comparing HRG thermodynamics to that of lattice quantum chromodynamics, we conclude that the hard-core radii are practically irrelevant, especially when HRG includes all resonances with masses less than $2~$GeV. It is found that the constant trace anomaly (or interaction measure) agrees well with most of previous conditions.Comment: 15 pages, 3 figures with 4 eps graph

Chemical Freeze-Out and Higher Order Multiplicity Moments

We calculate the non-normalized moments of the particle multiplicity within the framework of the hadron resonance gas (HRG) model. At finite chemical potential $\mu$, a non-monotonic behavior is observed in the thermal evolution of third order moment (skewness $S$) and the higher order ones as well. Among others, this observation likely reflects dynamical fluctuations and strong correlations. The signatures of non-monotonicity in the normalized fourth order moment (kurtosis $\kappa$) and its products get very clear. Based on these findings, we introduce a novel condition characterizing the universal freeze-out curve. The chemical freeze-out parameters $T$ and $\mu$ are described by vanishing $\kappa\, \sigma^2$ or equivalently $m_4=3\,\chi^2$, where $\sigma$, $\chi$ and $m_4$ are the standard deviation, susceptibility and fourth order moment, respectively. The fact that the HRG model is not able to release information about criticality related to the confinement and chiral dynamics should not veil the observations related to the chemical freeze-out. Recent lattice QCD studies strongly advocate the main conclusion of the present paper.Comment: 17 Pages, 5 Figures. arXiv admin note: substantial text overlap with arXiv:1205.176

Screening masses in thermal and dense medium

Screening masses of different hadronic states are studied in thermal and dense medium on lattice. It has been found that screening masses increase with the temperature. In deconfinement phase, chemical potential enhances the screening masses. We use the normalization with respect to lowest Matsubara frequency to characterize dissolving of hadronic bound states at high temperatures. It has been found that different hadronic states have different dissolving temperatures and their survivals are considerably improved at finite chemical potentials.Comment: 2 pages, 1 figure. Talk given at YITP workshop on ''Hadrons at Finite Density 2006'', Yukawa Institute for Theoretical Physics, Kyoto University, February 20-22, 200

Black Box QGP

According to extensive ab initio calculations of lattice QCD, the very large energy density available in heavy-ion collisions at SPS and now at RHIC must be sufficient to generate quark-gluon plasma (QGP), a new state of matter in the form of plasma of free quarks and gluons. The new state of matter discovered at RHIC seems to be perfect fluid rather than free plasma. Its shear viscosity is assumed to be almost zero. In this work, I first considered the theoretical and phenomenological consequences of this discovery and finally asked questions about the nature of phase transition and properties of matter. It is important to answer these questions, otherwise QGP will remain a kind of black box; one sends a signal via new experiments or simulations or models and gets another one from it. I will show that some promising ideas have already been suggested a long time ago. I will also suggest a new phase diagram with separated deconfinement and freeze-out boundaries and a mixed state of thermal quark matter and bubbles of hadron gas.Comment: 11 pages, 6 figure

Dynamical Fluctuations in Baryon--Meson Ratios

The event-by-event dynamical fluctuations in kaon-to-proton and proton-to-pion ratios have been studied in dependence on center--of--mass energies of nucleon--nucleon collisions $\sqrt{s}$. Based on changing phase space volume which apparently is the consequence of phase transition from hadrons to quark--gluon plasma at large $\sqrt{s}$, the single--particle distribution function $f$ is assumed to be rather modified. Varying $f$ and phase space volume are implemented in the grand--canonical partition function, especially at $\sqrt{s}>17$ GeV, so that hadron resonance gas model, when taking into account the experimental acceptance ${\cal A}$ and quark phase space occupation factor $\gamma$, turns to be able to reproduce the dynamical fluctuations in $(K^++K^-)/(p+\overline{p})$ and $(p+\overline{p})/(\pi^++\pi^-)$ ratios over the entire range of $\sqrt{s}$.Comment: 6 pages (revtex4-style), 2 figures with 4 eps graphs and 1 tabl