It has been revealed recently that, in the scale free range, i.e. from the scale of the onset of nonlinear evolution to the scale of dissipation, the velocity and mass density fields of cosmic baryon fluid are extremely well described by the self-sim
ilar log-Poisson hierarchy. As a consequence of this evolution, the relations among various physical quantities of cosmic baryon fluid should be scale invariant, if the physical quantities are measured in cells on scales larger than the dissipation scale, regardless the baryon fluid is in virialized dark halo, or in pre-virialized state. We examine this property with the relation between the Compton parameter of the thermal Sunyaev-Zeldovich effect, $y(r)$, and X-ray luminosity, $L_{rm x}(r)$, where $r$ being the scale of regions in which $y$ and $L_{rm x}$ are measured. According to the self-similar hierarchical scenario of nonlinear evolution, one should expect that 1.) in the $y(r)$-$L_x(r)$ relation, $y(r)=10^{A(r)}[L_{rm x}(r)]^{alpha(r)}$, the coefficients $A(r)$ and $alpha(r)$ are scale-invariant; 2.) The relation $y(r)=10^{A(r)}[L_{rm x}(r)]^{alpha(r)}$ given by cells containing collapsed objects is also available for cells without collapsed objects, only if $r$ is larger than the dissipation scale. These two predictions are well established with a scale decomposition analysis of observed data, and a comparison of observed $y(r)$-$L_x(r)$ relation with hydrodynamic simulation samples. The implication of this result on the characteristic scales of non-gravitational heating is also addressed.
In this work, we use observations of the Hubble parameter from the differential ages of passively evolving galaxies and the recent detection of the Baryon Acoustic Oscillations (BAO) at $z_1=0.35$ to constrain the Dvali-Gabadadze-Porrati (DGP) univer
se. For the case with a curvature term, we set a prior $h=0.73pm0.03$ and the best-fit values suggest a spatially closed Universe. For a flat Universe, we set $h$ free and we get consistent results with other recent analyses.
