Bounds on quantum gravity parameter from the SU(2)SU(2) NJL effective model of QCD

Existence of a minimal measurable length, as an effective cutoff in the ultraviolet regime, is a common feature of all approaches to the quantum gravity proposal. It is widely believed that this length scale will be of the order of the Planck length $\lambda=\lambda_0\,l_{_{\rm Pl}}$, where $\lambda_0\sim{\mathcal O}(1)$ is a dimensionless parameter that should be fixed only by the experiments. This issue can be taken into account through the deformed momentum spaces with compact topologies. In this paper, we consider minimum length effects on the physical quantities related to three parameters of the $SU(2)$ Nambu-Jona-Lasinio effective model of QCD by means of the deformed measure which is defined on compact momentum space with ${\mathbf S}^3$ topology. This measure is suggested by the doubly special relativity theories, Snyder deformed spaces, and the deformed algebra that is obtained in the light of the stability theory of Lie algebras. Using the current experimental data of the particle physics collaboration, we constraint quantum gravity parameter $\lambda_0$ and we compare our results with bounds that are arisen from the other experimental setups.Comment: 10 pages, no figure, accepted for publication in Europhysics Letter

Horava-Lifshitz early universe phase transition beyond detailed balance

The early universe is believed to have undergone a QCD phase transition to hadrons at about $10\mu s$ after the big bang. We study such a transition in the context of the non-detailed balance Horava-Lifshitz theory by investigating the effects of the dynamical coupling constant $\lambda$ in a flat universe. The evolution of the relevant physical quantities, namely the energy density $\rho$, temperature $T$, scale factor $a$ and the Hubble parameter $H$ is investigated before, during and after the phase transition, assumed to be of first order. Also, in view of the recent lattice QCD simulations data, we study a cross-over phase transition of the early universe whose results are based on two different sets of lattice data.Comment: 14 pages, 11 figures, to appear in Eur. Phys. J. C. arXiv admin note: text overlap with arXiv:0912.2541, arXiv:0807.3066, arXiv:1005.3508, arXiv:1011.4230 by other author

On the Stability of Einstein Static Universe in Doubly General Relativity Scenario

By presenting a relation between average energy of the ensemble of probe photons and energy density of the Universe, in the context of {\it gravity's rainbow} or {\it doubly general relativity} scenario, we introduce a rainbow FRW Universe model. By analyzing the fixed points in flat FRW model modified by two well known rainbow functions, we find that the finite time singularity avoidance (i.e. Big-Bang) may still remain as a problem. Then, we follow the "Emergent Universe" scenario in which there is no beginning of time and consequently there is no Big-Bang singularity. Moreover, we study the impact of a high energy quantum gravity modifications related to the gravity's rainbow on the stability conditions of an "Einstein static Universe" (ESU). We find that independent of a particular rainbow function, the positive energy condition dictates a positive spatial curvature for the Universe. In fact, without raising a nonphysical energy condition in the quantum gravity regimes, we can address an agreement between gravity's rainbow scenario and basic assumption of modern version of "Emergent Universe". We show that in the absence and presence of an energy-dependent cosmological constant $\Lambda(\epsilon)$, a stable Einstein static solution is available versus the homogeneous and linear scalar perturbations under the variety of obtained conditions. Also, we explore the stability of ESU against the vector and tensor perturbations.Comment: 18 pages, Revisio