Abstract:
The coincidence problem is studied for the dark energy model of effective Yang-Mills condensate in a flat expanding universe during the matter-dominated stage. The YMC energy $\rho_y(t)$ is taken to represent the dark energy, which is coupled either with the matter, or with both the matter and the radiation components. The effective YM Lagrangian is completely determined by quantum field theory up to 1-loop order. It is found that under very generic initial conditions and for a variety of forms of coupling, the existence of the scaling solution during the early stages and the subsequent exit from the scaling regime are inevitable. The transition to the accelerating stage always occurs around a redshift $z\simeq (0.3\sim 0.5)$. Moreover, when the Yang-Mills condensate transfers energy into matter or into both matter and radiation, the equation of state $w_y$ of the Yang-Mills condensate can cross over -1 around $z\sim 2$, and takes on a current value $\simeq -1.1$. This is consistent with the recent preliminary observations on supernovae Ia. Therefore, the coincidence problem can be naturally solved in the effective YMC dark energy models.

Abstract:
We review the quantum Yang-Mills condensate (YMC) dark energy models. As the effective Yang-Mills Lagrangian is completely determined by the quantum field theory, there is no adjustable parameter in the model except the energy scale. In this model, the equation-of-state (EOS) of the YMC dark energy, $w_y > -1$ and $w_y < -1$, can both be naturally realized. By studying the evolution of various components in the model, we find that, in the early stage of the universe, dark energy tracked the evolution of the radiation, i.e. $w_y \to 1/3$. However, in the late stage, $w_y$ naturally runs to the critical state with $w_y = -1$, and the universe transits from matter-dominated into dark energy dominated stage only at recently $z \sim 0.3$. These characters are independent of the choice of the initial condition, and the cosmic coincidence problem is avoided in the models. We also find that, if the possible interaction between YMC and dust matter is considered, the late time attractor solution may exist. In this case, the EOS of YMC must evolve from $w_y>0$ into $w_y < -1$, which is slightly suggested by the observations. At the same time, the total EOS in the attractor solution is $w_{tot} = -1$, the universe being the de Sitter expansion in the late stage, and the cosmic big rip is naturally avoided. These features are all independent of the interacting forms.

Abstract:
Using the recently released Union2 compilation with 557 Type Ia supernovae, the shift parameter of cosmic microwave background given by the WMAP7 observations, and the baryon acoustic oscillation measurement from the Sloan Digital Sky Survey, we perform the $\chi^2$ analysis on the 1-loop Yang-Mills condensate (YMC) dark energy model. The analysis has been made for both non-coupling and coupling models with $\Omega_{m0}$ and $w_0$ being treated as free parameters. It is found that, $\chi^2_{min}$ = 542.870 at $\Omega_{m0}$ = 0.2701 and $w_0$ = -0.9945 for non-coupling model, and $\chi^2_{min}$ = 542.790 at $\gamma$ = -0.015, $\Omega_{m0}$ = 0.2715 and $w_0$ = -0.9969 for coupling model. Comparing with the $\Lambda$CDM model, the YMC model has a smaller $\chi^2_{min}$, but it has greater values of the Bayesian and Akaike information criteria. Overall, YMC is as robust as $\Lambda$CDM.

Abstract:
The quantum effective Yang-Mills condensate (YMC) dark energy model has some distinguished features that it naturally solves the coincidence problem and, at the same time, is able to give an equation of state $w$ crossing -1. In this work we further employ the Statefinder pair $(r,s)$ introduced by Sahni et al to diagnose the YMC model for three cases: the non-coupling, the YMC decaying into matter only, and the YMC decaying into both matter and radiation. The trajectories $(r,s)$ and $(r,q)$, and the evolutions $r(z)$, $s(z)$ are explicitly presented. It is found that, the YMC model in all three cases has $r\simeq 1$ for $ z < 10$ and $s\simeq 0$ for $z<5$ with only small deviations $\simeq 0.02$, quite close to the cosmological constant model (LCDM), but is obviously differentiated from other dark energy models, such as quiesence, kinessence etc.

Abstract:
This work is a comprehensive investigation of the Yang-Mills condensate (YMC) dark energy (DE) model, which is extended to include the 3-loop quantum corrections. We study its cosmic evolution and the possibility of crossing phantom divide $w=-1$, examine in details the Hubble parameter $H$, the deceleration parameter $q$, the statefinder diagnosis $(r,s)$, and the $w-w^\prime$ diagnosis of the model without and with interaction, and compare our results with other DE models. Besides, by using the observational data of type Ia supernovae (SNIa), the shift parameter from cosmic microwave background (CMB), and the baryon acoustic oscillation (BAO) peak from large scale structures (LSS), we give the cosmological constraints on 3-loop YMC model. It is found that the model can naturally solve the coincidence problem, and its prediction of the afore-mentioned parameter is much closer to the $\Lambda$CDM model than other dynamics DE models; the introduction of the matter-DE interaction will make the YMC model deviating from the $\Lambda$CDM model, and will give an equation of state (EOF) crossing -1. Moreover, it is also found that, to fit the latest SNIa data alone, the $\Lambda$CDM model is slightly better than the 3-loop YMC model; but in fitting of the combination of SNIa, CMB and LSS data, the 3-loop YMC model performs better than the $\Lambda$CDM model.

Abstract:
We study the statefinder parameters in the Yang-Mills condensate dark energy models, and find that the evolving trajectories of these models are different from those of other dark energy models. We also define two eigenfunctions of the Yang-Mills condensate dark energy models. The values of these eigenfunctions are quite close to zero if the equation-of-state of the Yang-Mills condensate is not far from -1, which can be used to simply differentiate between the Yang-Mills condensate models and other dark energy models.

Abstract:
We study the structure of the confining string in Yang-Mills theory using the method of the field strength correlators. The method allows us to demonstrate that both the local fluctuations of the topological charge and the gluon condensate are suppressed in the vicinity of the string axis in agreement with results of lattice simulations.

Abstract:
We investigate the attractor solution in the coupled Yang-Mills field dark energy models with the general interaction term, and obtain the constraint equations for the interaction if the attractor solution exists. The research also shows that, if the attractor solution exists, the equation-of-state of the dark energy must evolve from $w_y>0$ to $w_y\le-1$, which is slightly suggested by the observation. At the same time, the total equation-of-state in the attractor solution is $w_{tot}=-1$, the universe is a de Sitter expansion, and the cosmic big rip is naturally avoided. These features are all independent of the interacting forms.

Abstract:
The Dirac operator describing the coupling of continuum quark fields to SU(2) center vortex world-surfaces composed of elementary squares on a hypercubic lattice is constructed. It is used to evaluate the quenched Dirac spectral density in the random vortex world-surface model, which previously has been shown to quantitatively reproduce both the confinement properties and the topological susceptibility of SU(2) Yang-Mills theory. Under certain conditions on the modeling of the vortex gauge field, a behavior of the quenched chiral condensate as a function of temperature is obtained which is consistent with measurements in SU(2) lattice Yang-Mills theory.