Relativistic Hydrodynamic Cosmological Perturbations

Relativistic cosmological perturbation analyses can be made based on several different fundamental gauge conditions. In the pressureless limit the variables in certain gauge conditions show the correct Newtonian behaviors. Considering the general curvature ($K$) and the cosmological constant ($\Lambda$) in the background medium, the perturbed density in the comoving gauge, and the perturbed velocity and the perturbed potential in the zero-shear gauge show the same behavior as the Newtonian ones in general scales. In the first part, we elaborate these Newtonian correspondences. In the second part, using the identified gauge-invariant variables with correct Newtonian correspondences, we present the relativistic results with general pressures in the background and perturbation. We present the general super-sound-horizon scale solutions of the above mentioned variables valid for general $K$, $\Lambda$, and generally evolving equation of state. We show that, for vanishing $K$, the super-sound-horizon scale evolution is characterised by a conserved variable which is the perturbed three-space curvature in the comoving gauge. We also present equations for the multi-component hydrodynamic situation and for the rotation and gravitational wave.Comment: 16 pages, no figure, To appear in Gen. Rel. Gra

Unified Analysis of Cosmological Perturbations in Generalized Gravity

In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the scalar field and the scalar curvature in the Lagrangian, thus includes broad classes of generalized gravity theories resulting from recent attempts for the unification. We analyze both the scalar-type mode and the gravitational wave in analogous ways. For both modes the large scale evolutions are characterized by the same conserved quantities which are valid in the Einstein's gravity. This unified and simple treatment is possible due to our proper choice of the gauges, or equivalently gauge invariant combinations.Comment: 4 pages, revtex, no figure

Atypical protein kinase C (PKCzeta/lambda) is a convergent downstream target of the insulin-stimulated phosphatidylinositol 3-kinase and TC10 signaling pathways.

Insulin stimulation of adipocytes resulted in the recruitment of atypical PKC (PKCzeta/lambda) to plasma membrane lipid raft microdomains. This redistribution of PKCzeta/lambda was prevented by Clostridium difficile toxin B and by cholesterol depletion, but was unaffected by inhibition of phosphatidylinositol (PI) 3-kinase activity. Expression of the constitutively active GTP-bound form of TC10 (TC10Q/75L), but not the inactive GDP-bound mutant (TC10/T31N), targeted PKCzeta/lambda to the plasma membrane through an indirect association with the Par6-Par3 protein complex. In parallel, insulin stimulation as well as TC10/Q75L resulted in the activation loop phosphorylation of PKCzeta. Although PI 3-kinase activation also resulted in PKCzeta/lambda phosphorylation, it was not recruited to the plasma membrane. Furthermore, insulin-induced GSK-3beta phosphorylation was mediated by both PI 3-kinase-PKB and the TC10-Par6-atypical PKC signaling pathways. Together, these data demonstrate that PKCzeta/lambda can serve as a convergent downstream target for both the PI 3-kinase and TC10 signaling pathways, but only the TC10 pathway induces a spatially restricted targeting to the plasma membrane

The Origin of Structures in Generalized Gravity

In a class of generalized gravity theories with general couplings between the scalar field and the scalar curvature in the Lagrangian, we can describe the quantum generation and the classical evolution of both the scalar and tensor structures in a simple and unified manner. An accelerated expansion phase based on the generalized gravity in the early universe drives microscopic quantum fluctuations inside a causal domain to expand into macroscopic ripples in the spacetime metric on scales larger than the local horizon. Following their generation from quantum fluctuations, the ripples in the metric spend a long period outside the causal domain. During this phase their evolution is characterized by their conserved amplitudes. The evolution of these fluctuations may lead to the observed large scale structures of the universe and anisotropies in the cosmic microwave background radiation.Comment: 5 pages, latex, no figur

Third-order cosmological perturbations of zero-pressure multi-component fluids: Pure general relativistic nonlinear effects

Present expansion stage of the universe is believed to be mainly governed by the cosmological constant, collisionless dark matter and baryonic matter. The latter two components are often modeled as zero-pressure fluids. In our previous work we have shown that to the second-order cosmological perturbations, the relativistic equations of the zero-pressure, irrotational, multi-component fluids in a spatially near flat background effectively coincide with the Newtonian equations. As the Newtonian equations only have quadratic order nonlinearity, it is practically interesting to derive the potential third-order perturbation terms in general relativistic treatment which correspond to pure general relativistic corrections. Here, we present pure general relativistic correction terms appearing in the third-order perturbations of the multi-component zero-pressure fluids. We show that, as in a single component situation, the third-order correction terms are quite small (~ 5 x10^{-5} smaller compared with the relativistic/Newtonian second-order terms) due to the weak level anisotropy of the cosmic microwave background radiation. Still, there do exist pure general relativistic correction terms in third-order perturbations which could potentially become important in future development of precision cosmology. We include the cosmological constant in all our analyses.Comment: 20 pages, no figur

Infrared divergence of pure Einstein gravity contributions to cosmological density power spectrum

We probe the pure Einstein's gravity contributions to the second-order density power spectrum. In the small-scale, we discover that the Einstein's gravity contribution is negligibly small. This guarantees that Newton's gravity is sufficient to handle the baryon acoustic oscillation scale. In the large scale, however, we discover that the Einstein's gravity contribution to the second-order power spectrum dominates the linear-order power spectrum. Thus, pure Einstein gravity contribution appearing in the third-order perturbation leads to an infrared divergence in the power spectrum.Comment: Changed contents, to appear in Physical Review Letter

Doping dependent optical properties of Bi2201

An experimental study of the in-plane optical conductivity of (Pb$_{x}$,Bi$_{2-x}$)(La$_{y}$Sr$_{2-y}$)CuO$_{6+\delta}$ (Bi2201) is presented for a broad doping and temperature range. The in-plane conductivity is analyzed within a strong coupling formalism. We address the interrelationship between the optical conductivity ($\sigma(\omega)$), the single particle self energy, and the electron-boson spectral function. We find that the frequency and temperature dependence can be well described within this formalism. We present a universal description of optical, ARPES and tunneling spectra. The full frequency and temperature dependence of the optical spectra and single particle self-energy is shown to result from an electron-boson spectral function, which shows a strong doping dependence and weak temperature dependence.Comment: 20 pages, 9 figures. To appear in special focus issue "Superconductors with Exotic Symmetries", New Journal of Physic