Little Bird in My Praying Hands: Rainer Maria Rilke and God's Animal Body (original) (raw)

Stability of Einstein-aether cosmological models

Physical Review D, 2013

We use a dynamical systems analysis to investigate the future behaviour of Einstein-Aether cosmological models with a scalar field coupling to the expansion of the aether and a non-interacting perfect fluid. The stability of the equilibrium solutions are analysed and the results are compared with the standard inflationary cosmological solutions and previously studied cosmological Einstein-Aether models.

Inflationary attractors

1993

A generic outcome of theories with scalar-tensor coupling is the existence of inflationary attractors, either power-law or de Sitter. The fluctuations arising during this phase are Gaussian and their spectrum depends on the wavenumber k according to the power-law k 1/(1−p) , where p is the inflationary power-law exponent. We investigate to which extent these properties depend on the coupling function and on the potential. We find the class of models in which viable attractors exist. Within this class, we find that the cosmic expansion and the scaling of the fluctuation spectrum are independent of the coupling function. Further, the analytical solution of the Fokker-Planck equation shows that the deviations from Gaussianity are negligible.

The Einstein-Friedrich-nonlinear scalar field system and the stability of scalar field Cosmologies

A frame representation is used to derive a first order quasi-linear symmetric hyperbolic system for a scalar field minimally coupled to gravity. This procedure is inspired by similar evolution equations introduced by Friedrich to study the Einstein-perfect fluid system. The resulting evolution system is used to show that, for some classes of scalar field potentials, small non-linear perturbations of an expanding Klein-Gordon-Robertson-Walker background decay exponentially to zero or converge to constant values. * sequence is assumed to depend continously on the parameter ε in such a way that the limit ε → 0 renders the reference solutionů. In particular, one can write the full solution to the EFEs as the Ansatz

Attractor universe in the scalar-tensor theory of gravitation

Physical Review D, 2009

In the scalar-tensor theory of gravitation it seems nontrivial to establish if solutions of the cosmological equations in the presence of a cosmological constant behave as attractors independently of the initial values. We develop a general formulation in terms of two-dimensional phase space. We show that there are two kinds of fixed points, one of which is an attractor depending on the coupling constant and equation of state. In the case with a power-law potential in the Jordan frame, we also find new type of inflation caused by the coupling to the matter fluid.

Dynamical System Perspective of Cosmological Models Minimally Coupled with Scalar Field

Advances in High Energy Physics, 2020

The stability criteria for the dynamical system of a homogeneous and isotropic cosmological model are investigated with the interaction of a scalar field in the presence of a perfect fluid. In this paper, we depict the dynamical system perspective to study qualitatively the scalar field cosmology under two special cases, with and without potential. In the absence of potential, we get a two-dimensional dynamical system, and we study the analytical as well as geometrical behavior. For the dynamical system with potential, we analyze different potential forms: simple exponential potential form (Vϕ=Voe−λϕ), double exponential potential form Vϕ=Voexp−Aexp2αϕ, and inverse power law potential form (Vϕ=Voϕ−α). We generate an autonomous system of ordinary differential equations (ASODE) for each case by introducing new dimensionless variables and obtain respective fixed points. We also analyze the type, nature, and stability of the fixed points and how their behavior reflects towards the cosmo...

Dynamical analysis of the covarying coupling constants in scalar-tensor gravity

2022

We consider a scalar-tensor theory of gravity wherein the scalar field φ includes the gravitational coupling G and the speed of light c, both of which are allowed to be functions of the spacetime coordinates. The cosmological coupling Λ turns out to be an emergent phenomenon from a possible behavior of φ. The dynamics of φ is analysed in the phase space where we describe gravity from a precisely specified form of the action. For reasonable assumptions on the potential V (φ) and the matter-energy content, we show that an attractor point can be quickly reached within a period where the Hubble parameter becomes essentially constant. When the system gets to the stable point, the dynamics of φ ceases and the constraintĠ/G = σ (ċ/c) with σ = 3 must be satisfied for the rest of the cosmic evolution. Our findings thus provide a foundation for the phenomenological model used recently to interpret cosmological and astrophysical data. It is shown that cosmic evolution after the equilibrium accommodates radiation-and matter-dominated eras that naturally evolve to an accelerated expansion typical of dark energy. The generalized Brans-Dicke approach developed in this paper results in equations that can be readily tested with observational data.

Inflation as an Attractor in Scalar Cosmology

Modern Physics Letters A, 2013

We study an inflation mechanism based on attractor properties in cosmological evolutions of a spatially flat Friedmann–Robertson–Walker spacetime based on the Einstein-scalar field theory. We find a new way to get the Hamilton–Jacobi equation solving the field equations. The equation relates a solution "generating function" with the scalar potential. We analyze its stability and find a later time attractor which describes a Universe approaching to an eternal-de Sitter inflation driven by the potential energy, V0>0. The attractor exists when the potential is regular and does not have a linear and quadratic terms of the field. When the potential has a mass term, the attractor exists if the scalar field is in a symmetric phase and is weakly coupled, λ<9V0/16. We also find that the attractor property is intact under small modifications of the potential. If the scalar field has a positive mass-squared or is strongly coupled, there exists a quasi-attractor. However, the qu...

Applications of scalar attractor solutions to cosmology

Physical Review D, 2001

We develop a framework to study the phase space of a system consisting of a scalar field rolling down an arbitrary potential with varying slope and a background fluid, in a cosmological setting. We give analytical approximate solutions of the field evolution and discuss applications of its features to the issues of quintessence, moduli stabilisation and quintessential inflation.

On the stability of the Einstein static universe

Classical and Quantum Gravity, 2003

We show using covariant techniques that the Einstein static universe containing a perfect fluid is always neutrally stable against small inhomogeneous vector and tensor perturbations and neutrally stable against adiabatic scalar density inhomogeneities so long as c 2 s > 1 5 , and unstable otherwise. We also show that the stability is not significantly changed by the presence of a self-interacting scalar field source, but we find that spatially homogeneous Bianchi type IX modes destabilize an Einstein static universe. The implications of these results for the initial state of the universe and its pre-inflationary evolution are also discussed.