The effects of generalized uncertainty principle (GUP) on the inflationary dynamics and the thermodynamics of the early universe are studied. Using the GUP approach, the tensorial and scalar density fluctuations in the inflation era are evaluated and compared with the standard case. We find a good agreement with the Wilkinson Microwave Anisotropy Probe data. Assuming that a quantum gas of scalar particles is confined within a thin layer near the apparent horizon of the Friedmann-Lemaitre-Robertson-Walker universe which satisfies the boundary condition, the number and entropy densities and the free energy arising form the quantum states are calculated using the GUP approach. A qualitative estimation for effects of the quantum gravity on all these thermodynamic quantities is introduced.

There are several theoretical indications that the quantum gravity approaches may have predictions for a minimal measurable length, and a maximal observable momentum and throughout a generalization for Heisenberg uncertainty principle. The generalized uncertainty principle (GUP) is based on a momentum-dependent modification in the standard dispersion relation which is conjectured to violate the principle of Lorentz invariance. From the resulting Hamiltonian, the velocity and time of flight of relativistic distant particles at Planck energy can be derived. A first comparison is made with recent observations for Hubble parameter in redshift-dependence in early-type galaxies. We find that LIV has two types of contributions to the time of flight delay ∆t comparable with that observations. Although the wrong OPERA measurement on faster-than-light muon neutrino anomaly, ∆t, and the relative change in the speed of muon neutrino ∆v in dependence on redshift z turn to be wrong, we utilize its main features to estimate ∆v. Accordingly, the results could not be interpreted as LIV. A third comparison is made with the ultra high-energy cosmic rays (UHECR). It is found that an essential ingredient of the approach combining string theory, loop quantum gravity, black hole physics and doubly spacial relativity and the one assuming a perturbative departure from exact Lorentz invariance. Fixing the sensitivity factor and its energy dependence are essential inputs for a reliable confronting of our calculations to UHECR. The sensitivity factor is related to the special time of flight delay and the time structure of the signal. Furthermore, the upper and lower bounds to the parameter, α that characterizes the generalized uncertainly principle, have to be fixed in related physical systems such as the gamma rays bursts.

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Assuming that the background geometry is filled with a free gas consisting of matter and radiation and that no phase transitions are occurring in the early universe, we discuss the thermodynamics of this closed system using classical approaches. We find that essential cosmological quantities, such as the Hubble parameter H, scale factor a, and curvature parameter k, can be derived from this simple model. On one hand, it obeys the laws of thermodynamics entirely. On the other hand, the results are compatible with the FriedmannLemaitreRobertsonWalker model and the Einstein field equations. The inclusion of finite bulk viscosity coefficient derives to important changes in all Of these cosmological quantities. The thermodynamics of the viscous universe is studied and a conservation law is found. Accordingly, our picture of the evolution of the early universe and its astrophysical consequences seems to be the subject of radical revision. We find that the parameter k, for instance, strongly depends on the thermodynamics of the background matter. The time scale at which a negative curvature might take place, depends on the relation between the matter content and the total energy. Using quantum and statistical approaches, we assume that the size of the universe is given by the volume occupied by one particle and one photon. Different types of interactions between matter and photon are taken into account. In this quantum treatment, expressions for H and a are also introduced. Therefore, the expansion of the universe turns out to be accessible.

Oliinychenko, Bugaev and Sorin [arXiv:1204.0103 [hep-ph]] considered the role of conservation laws in discussing possible weaknesses of thermal models which are utilized in describing the hadron multiplicities measured in central nucleus-nucleus collisions. They argued to analyse the criteria for chemical freeze-out and to conclude that none of them were robust. Based on this, they suggested a new chemical freeze-out criterion. They assigned to the entropy per hadron the ad hoc value 7.18 and supposed to remain unchanged over the whole range of the baryo-chemical potentials. Due to unawareness of recent literature, the constant entropy per hadron has been discussed in Ref. [Fizika B18 (2009) 141-150, Europhys.Lett. 75 (2006 420]. Furthermore, it has been shown that the constant entropy per hadron is equivalent to constant entropy normalized to cubic temperature, an earlier criterion for the chemical freeze-out introduced in Ref. [Europhys.Lett. 75 (2006) 420, Nucl.Phys.A764 (2006 387-392]. In this comment, we list out the ignored literature, compare between the entropy-number density ratio and two criteria of averaged energy per averaged particle number and constant entropy per cubic temperature. All these criteria are confronted to the experimental results. The physics of constant entropy per number density is elaborated. It is concluded that this ratio can't remain constant, especially at large chemical potential related to AGS and SIS energies.