On Higher Derivatives as Constraints in Field Theory: a Geometric Perspective

We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.Comment: 7 page

Critical phenomena of thick branes in warped spacetimes

We have investigated the effects of a generic bulk first-order phase transition on thick Minkowski branes in warped geometries. As occurs in Euclidean space, when the system is brought near the phase transition an interface separating two ordered phases splits into two interfaces with a disordered phase in between. A remarkable and distinctive feature is that the critical temperature of the phase transition is lowered due to pure geometrical effects. We have studied a variety of critical exponents and the evolution of the transverse-traceless sector of the metric fluctuations.Comment: revtex4, 4 pages, 4 figures, some comments added, typos corrected, published in PR

Noise Kernel in Stochastic Gravity and Stress Energy Bi-Tensor of Quantum Fields in Curved Spacetimes

The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bi-tensor which describes the fluctuations of a quantum field in curved spacetimes. It plays the role in stochastic semiclassical gravity based on the Einstein-Langevin equation similar to the expectation value of the stress-energy tensor in semiclassical gravity based on the semiclassical Einstein equation. According to the stochastic gravity program, this two point function (and by extension the higher order correlations in a hierarchy) of the stress energy tensor possesses precious statistical mechanical information of quantum fields in curved spacetime and, by the self-consistency required of Einstein's equation, provides a probe into the coherence properties of the gravity sector (as measured by the higher order correlation functions of gravitons) and the quantum nature of spacetime. It reflects the low and medium energy (referring to Planck energy as high energy) behavior of any viable theory of quantum gravity, including string theory. It is also useful for calculating quantum fluctuations of fields in modern theories of structure formation and for backreaction problems in cosmological and black holes spacetimes. We discuss the properties of this bi-tensor with the method of point-separation, and derive a regularized expression of the noise-kernel for a scalar field in general curved spacetimes. One collorary of our finding is that for a massless conformal field the trace of the noise kernel identically vanishes. We outline how the general framework and results derived here can be used for the calculation of noise kernels for Robertson-Walker and Schwarzschild spacetimes.Comment: 22 Pages, RevTeX; version accepted for publication in PR

Effective Field Theory Approach to String Gas Cosmology

We derive the 4D low energy effective field theory for a closed string gas on a time dependent FRW background. We examine the solutions and find that although the Brandenberger-Vafa mechanism at late times no longer leads to radion stabilization, the radion rolls slowly enough that the scenario is still of interest. In particular, we find a simple example of the string inspired dark matter recently proposed by Gubser and Peebles.Comment: 19 pages, 2 figures, comments adde

Adiabatic decaying vacuum model for the universe

We study a model that the entropy per particle in the universe is constant. The sources for the entropy are the particle creation and a lambda decaying term. We find exact solutions for the Einstein field equations and show the compatibilty of the model with respect to the age and the acceleration of the universe.Comment: 10 pages, 2 figure

Black Hole Formation with an Interacting Vacuum Energy Density

We discuss the gravitational collapse of a spherically symmetric massive core of a star in which the fluid component is interacting with a growing vacuum energy density. The influence of the variable vacuum in the collapsing core is quantified by a phenomenological \beta-parameter as predicted by dimensional arguments and the renormalization group approach. For all reasonable values of this free parameter, we find that the vacuum energy density increases the collapsing time but it cannot prevent the formation of a singular point. However, the nature of the singularity depends on the values of \beta. In the radiation case, a trapped surface is formed for \beta<1/2 whereas for \beta>1/2, a naked singularity is developed. In general, the critical value is \beta=1-2/3(1+\omega), where the \omega-parameter describes the equation of state of the fluid component.Comment: 9 pages, 8 figure

Stochastic semiclassical fluctuations in Minkowski spacetime

The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the ground state of semiclassical gravity, namely, Minkowski spacetime and a scalar field in its vacuum state. The relevant equations are explicitly derived for massless and massive fields arbitrarily coupled to the curvature. In doing so, some semiclassical results, such as the expectation value of the stress-energy tensor to linear order in the metric perturbations and particle creation effects, are obtained. We then solve the equations and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. In the conformal field case, explicit results are obtained. These results hint that gravitational fluctuations in stochastic semiclassical gravity have a ``non-perturbative'' behavior in some characteristic correlation lengths.Comment: 28 pages, RevTeX, no figure