Gauge Formulation for Higher Order Gravity

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained which includes derivatives of the curvature. We analyze the form of the second field strenght, $G=\partial F +fAF$, in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of $F$ and quadratic contractions of $G$ are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his Generalized Electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behaviour at short distances as well as a meso-large distance modification.Comment: Published versio

On the Transfer of Metric Fluctuations when Extra Dimensions Bounce or Stabilize

In this report, we study within the context of general relativity with one extra dimension compactified either on a circle or an orbifold, how radion fluctuations interact with metric fluctuations in the three non-compact directions. The background is non-singular and can either describe an extra dimension on its way to stabilization, or immediately before and after a series of non-singular bounces. We find that the metric fluctuations transfer undisturbed through the bounces or through the transients of the pre-stabilization epoch. Our background is obtained by considering the effects of a gas of massless string modes in the context of a consistent 'massless background' (or low energy effective theory) limit of string theory. We discuss applications to various approaches to early universe cosmology, including the ekpyrotic/cyclic universe scenario and string gas cosmology.Comment: V2. Minor Clarifications V3. appendix and 2 figures added, typos corrected, conclusions unchanged 12 pages, 6 figure

Aspects of Objectivity in Quantum Mechanics

The purpose of the paper is to explore different aspects of the covariance of (mostly) non-relativistic quantum mechanics. First, doubts are expressed concerning the claim that gauge fields can be 'generated' by way of imposition of (local) gauge covariance of the single-particle wave equation. Then a brief review is given of Galilean covariance in the general case of external fields, and the connection between Galilean boosts and gauge transformations. Under time-dependent translations (and hence non-instantaneous boosts) the geometric phase associated with Schrödinger evolution is non-invariant, and the significance of this result is briefly analysed. The covariance properties of Schrödinger dynamics are then brought to bear on certain versions of the modal interpretation of quantum mechanics. The conclusion that it is only relational properties that can be considered coordinate- or gauge-independent elements of reality is reinforced by appeal to the theory of quantum reference frames due to Aharonov and Kauffher. (This paper appeared in "From Physics to Philosophy", J. Butterfield and C. Pagonis (eds.), Cambridge University Press (1999); pp. 45-70.

Nonholonomic Dynamics

Nonholonomic systems are, roughly speaking, mechanical systems with constraints on their velocity that are not derivable from position constraints. They arise, for instance, in mechanical systems that have rolling contact (for example, the rolling of wheels without slipping) or certain kinds of sliding contact (such as the sliding of skates). They are a remarkable generalization of classical Lagrangian and Hamiltonian systems in which one allows position constraints only. There are some fascinating differences between nonholonomic systems and classical Hamiltonian or Lagrangian systems. Among other things: nonholonomic systems are nonvariational—they arise from the Lagrange-d’Alembert principle and not from Hamilton’s principle; while energy is preserved for nonholonomic systems, momentum is not always preserved for systems with symmetry (i.e., there is nontrivial dynamics associated with the nonholonomic generalization of Noether’s theorem); nonholonomic systems are almost Poisson but not Poisson (i.e., there is a bracket that together with the energy on the phase space defines the motion, but the bracket generally does not satisfy the Jacobi identity); and finally, unlike the Hamiltonian setting, volume may not be preserved in the phase space, leading to interesting asymptotic stability in some cases, despite energy conservation. The purpose of this article is to engage the reader’s interest by highlighting some of these differences along with some current research in the area. There has been some confusion in the literature for quite some time over issues such as the variational character of nonholonomic systems, so it is appropriate that we begin with a brief review of the history of the subject

Naturalness in Cosmological Initial Conditions

We propose a novel approach to the problem of constraining cosmological initial conditions. Within the framework of effective field theory, we classify initial conditions in terms of boundary terms added to the effective action describing the cosmological evolution below Planckian energies. These boundary terms can be thought of as spacelike branes which may support extra instantaneous degrees of freedom and extra operators. Interactions and renormalization of these boundary terms allow us to apply to the boundary terms the field-theoretical requirement of naturalness, i.e. stability under radiative corrections. We apply this requirement to slow-roll inflation with non-adiabatic initial conditions, and to cyclic cosmology. This allows us to define in a precise sense when some of these models are fine-tuned. We also describe how to parametrize in a model-independent way non-Gaussian initial conditions; we show that in some cases they are both potentially observable and pass our naturalness requirement.Comment: 35 pages, 8 figure