Lee-Yang zero analysis for the study of QCD phase structure

We comment on the Lee-Yang zero analysis for the study of the phase structure of QCD at high temperature and baryon number density by Monte-Carlo simulations. We find that the sign problem for non-zero density QCD induces a serious problem in the finite volume scaling analysis of the Lee-Yang zeros for the investigation of the order of the phase transition. If the sign problem occurs at large volume, the Lee-Yang zeros will always approach the real axis of the complex parameter plane in the thermodynamic limit. This implies that a scaling behavior which would suggest a crossover transition will not be obtained. To clarify this problem, we discuss the Lee-Yang zero analysis for SU(3) pure gauge theory as a simple example without the sign problem, and then consider the case of non-zero density QCD. It is suggested that the distribution of the Lee-Yang zeros in the complex parameter space obtained by each simulation could be more important information for the investigation of the critical endpoint in the $(T, \mu_q)$ plane than the finite volume scaling behavior.Comment: 16 pages, 3 figures, 2 tables, minor change

Multiple time scales hidden in heterogeneous dynamics of glass-forming liquids

A multi-time probing of density fluctuations is introduced to investigate hidden time scales of heterogeneous dynamics in glass-forming liquids. Molecular dynamics simulations for simple glass-forming liquids are performed, and a three-time correlation function is numerically calculated for general time intervals. It is demonstrated that the three-time correlation function is sensitive to the heterogeneous dynamics and that it reveals couplings of correlated motions over a wide range of time scales. Furthermore, the time scale of the heterogeneous dynamics $\tau_{\rm hetero}$ is determined by the change in the second time interval in the three-time correlation function. The present results show that the time scale of the heterogeneous dynamics $\tau_{\rm hetero}$ becomes larger than the $\alpha$-relaxation time at low temperatures and large wavelengths. We also find a dynamical scaling relation between the time scale $\tau_{\rm hetero}$ and the length scale $\xi$ of dynamical heterogeneity as $\tau_{\rm hetero} \sim \xi^{z}$ with $z=3$.Comment: 4 pages, 5 figures, to appear in Phys. Rev. E (Rapid Communications

Solar system and equivalence principle constraints on f(R) gravity by chameleon approach

We study constraints on f(R) dark energy models from solar system experiments combined with experiments on the violation of equivalence principle. When the mass of an equivalent scalar field degree of freedom is heavy in a region with high density, a spherically symmetric body has a thin-shell so that an effective coupling of the fifth force is suppressed through a chameleon mechanism. We place experimental bounds on the cosmologically viable models recently proposed in literature which have an asymptotic form f(R)=R-lambda R_c [1-(R_c/R)^{2n}] in the regime R >> R_c. From the solar-system constraints on the post-Newtonian parameter gamma, we derive the bound n>0.5, whereas the constraints from the violations of weak and strong equivalence principles give the bound n>0.9. This allows a possibility to find the deviation from the LambdaCDM cosmological model. For the model f(R)=R-lambda R_c(R/R_c)^p with 0<p<1 the severest constraint is found to be p<10^{-10}, which shows that this model is hardly distinguishable from the LambdaCDM cosmology.Comment: 5 pages, no figures, version to appear in Physical Review

On the scalar graviton in n-DBI gravity

n-DBI gravity is a gravitational theory which yields near de Sitter inflation spontaneously at the cost of breaking Lorentz invariance by a preferred choice of foliation. We show that this breakdown endows n-DBI gravity with one extra physical gravitational degree of freedom: a scalar graviton. Its existence is established by Dirac's theory of constrained systems. Firstly, studying scalar perturbations around Minkowski space-time, we show that there exists one scalar degree of freedom and identify it in terms of the metric perturbations. Then, a general analysis is made in the canonical formalism, using ADM variables. It is useful to introduce an auxiliary scalar field, which allows recasting n-DBI gravity in an Einstein-Hilbert form but in a Jordan frame. Identifying the constraints and their classes we confirm the existence of an extra degree of freedom in the full theory, besides the two usual tensorial modes of the graviton. We then argue that, unlike the case of (the original proposal for) Horava-Lifschitz gravity, there is no evidence that the extra degree of freedom originates pathologies, such as vanishing lapse, instabilities and strong self-coupling at low energy scales.Comment: 30 pages, 1 figur

Matter instabilities in general Gauss-Bonnet gravity

We study the evolution of cosmological perturbations in f(G) gravity, where the Lagrangian is the sum of a Ricci scalar R and an arbitrary function f in terms of a Gauss-Bonnet term G. We derive the equations for perturbations assuming matter to be described by a perfect fluid with a constant equation of state w. We show that density perturbations in perfect fluids exhibit negative instabilities during both the radiation and the matter domination, irrespective of the form of f(G). This growth of perturbations gets stronger on smaller scales, which is difficult to be compatible with the observed galaxy spectrum unless the deviation from General Relativity is very small. Thus f(G) cosmological models are effectively ruled out from this Ultra-Violet instability, even though they can be compatible with the late-time cosmic acceleration and local gravity constraints.Comment: 9 pages, 2 figures, published PRD versio

Density perturbations in general modified gravitational theories

We derive the equations of linear cosmological perturbations for the general Lagrangian density $f (R,\phi, X)/2+L_c$, where $R$ is a Ricci scalar, $\phi$ is a scalar field, and $X=-(\nabla \phi)^2/2$ is a field kinetic energy. We take into account a nonlinear self-interaction term $L_c$ recently studied in the context of "Galileon" cosmology, which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasi-static approximation on sub-horizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds. Our analysis includes most of modified gravity models of dark energy proposed in literature and thus it is convenient to test the viability of such models from both theoretical and observational points of view.Comment: 17 pages, no figure

Generalized Galileon cosmology

We study the cosmology of a generalized Galileon field $\phi$ with five covariant Lagrangians in which $\phi$ is replaced by general scalar functions $f_{i}(\phi)$ (i=1,...,5). For these theories, the equations of motion remain at second-order in time derivatives. We restrict the functional forms of $f_{i}(\phi)$ from the demand to obtain de Sitter solutions responsible for dark energy. There are two possible choices for power-law functions $f_{i}(\phi)$, depending on whether the coupling $F(\phi)$ with the Ricci scalar $R$ is independent of $\phi$ or depends on $\phi$. The former corresponds to the covariant Galileon theory that respects the Galilean symmetry in the Minkowski space-time. For generalized Galileon theories we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar and tensor perturbations as well as the condition for the stability of de Sitter solutions. We also carry out detailed analytic and numerical study for the cosmological dynamics in those theories.Comment: 24 pages, 10 figures, version to appear in Physical Review

Large N reduction on coset spaces

As an extension of our previous work concerning the large N reduction on group manifolds, we study the large N reduction on coset spaces. We show that large N field theories on coset spaces are described by certain corresponding matrix models. We also construct Chern-Simons-like theories on group manifolds and coset spaces, and give their reduced models.Comment: 22 pages, typos correcte