Post-Newtonian methods and the gravito-electromagnetic analogy

In theoretical physics there is a well known analogy between general relativity and electrodynamics which is based on a linearization of Einstein's field equation. Such a kind of analogy is interesting since Einstein's equation (on component form) is extremely complicated mathematically and hard to gain physical insight into. It turns out though, that a lot of papers in the rich literature on the topic are in lack of a systematic method. The main purpose of this thesis is to study the analogy in a more consistent way using state of the art perturbative methods. The analysis is based on the socalled post-Newtonian approximation-scheme which provides a systematic way to expand any metric theory of gravity, and which also takes account for non-linear effects. By choosing suitable variables and gauge (coordinate) conditions, the post-Newtonian limit of general relativity is reformulated in a way which is appropriate for the discussion. The same kind of systematic expansion is also applied to electrodynamics. In this way the theories are compared in a consistent way beyond their lowest order approximations. This work, described in chapter 4, is basically just a comparison of the mathematical structure of the considered approximations of the theories. In the following chapter the perspective is extended by exploring the huge conceptual difference between the theories. Based on calculations the geometric significance of curvature in the post-Newtonian approximation of general relativity is investigated. The most interesting finding from this chapter is that the analogy turns out being stronger when gravitational phenomena are evaluated in a so-called local proper reference frame, which is quite interesting since in that case the theories are treated on a more equal footing conceptually

Local Observables in a Landscape of Infrared Gauge Modes

Cosmological local observables are at best statistically determined by the fundamental theory describing inflation. When the scalar inflaton is coupled uniformly to a collection of subdominant massless gauge vectors, rotational invariance is obeyed locally. However, the statistical isotropy of fluctuations is spontaneously broken by gauge modes whose wavelength exceed our causal horizon. This leads to a landscape picture where primordial correlators depend on the position of the observer. We compute the stochastic corrections to the curvature power spectrum, show the existence of a new local observable (the shape of the quadrupole), and constrain the theory using Planck limits.Comment: 5 pages, 3 figures, v2: minor updates, matches version published in Physics Letters

Stability of Horndeski vector-tensor interactions

We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M^2, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M^2>0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordstr\"om-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.Comment: References adde

A study of inhomogeneous massless scalar gauge fields in cosmology

Why is the Universe so homogeneous and isotropic? We summarize a general study of a γ-law perfect fluid alongside an inhomogeneous, massless scalar gauge field (with homogeneous gradient) in anisotropic spaces with General Relativity. The anisotropic matter sector is implemented as a j-form (field-strength level), where j ∈ {1, 3}, and the spaces studied are Bianchi space-times of solvable type. Wald’s no-hair theorem is extended to include the j-form case. We highlight three new self-similar space-times: the Edge, the Rope and Wonderland. The latter solution is so far found to exist in the physical state space of types I,II, IV, VI0, VIh, VII0 and VIIh, and is a global attractor in I and V. The stability analysis of the other types has not yet been performed. This paper is a summary of [1], with some remarks towards new results which will be further laid out in upcoming work.publishedVersio