7,875 research outputs found
Dynamics of f(R)-cosmologies containing Einstein static models
We study the dynamics of homogeneous isotropic FRW cosmologies with positive
spatial curvature in -gravity, paying special attention to the existence
of Einstein static models and only study forms of for which these
static models have been shown to exist. We construct a compact state space and
identify past and future attractors of the system and recover a previously
discovered future attractor corresponding to an expanding accelerating model.
We also discuss the existence of universes which have both a past and future
bounce, a phenomenon which is absent in General Relativity.Comment: 14 pages, 6 figure
Fluid observers and tilting cosmology
We study perfect fluid cosmological models with a constant equation of state
parameter in which there are two naturally defined time-like
congruences, a geometrically defined geodesic congruence and a non-geodesic
fluid congruence. We establish an appropriate set of boost formulae relating
the physical variables, and consequently the observed quantities, in the two
frames. We study expanding spatially homogeneous tilted perfect fluid models,
with an emphasis on future evolution with extreme tilt. We show that for
ultra-radiative equations of state (i.e., ), generically the tilt
becomes extreme at late times and the fluid observers will reach infinite
expansion within a finite proper time and experience a singularity similar to
that of the big rip. In addition, we show that for sub-radiative equations of
state (i.e., ), the tilt can become extreme at late times and
give rise to an effective quintessential equation of state. To establish the
connection with phantom cosmology and quintessence, we calculate the effective
equation of state in the models under consideration and we determine the future
asymptotic behaviour of the tilting models in the fluid frame variables using
the boost formulae. We also discuss spatially inhomogeneous models and tilting
spatially homogeneous models with a cosmological constant
Perfect fluids and generic spacelike singularities
We present the conformally 1+3 Hubble-normalized field equations together
with the general total source equations, and then specialize to a source that
consists of perfect fluids with general barotropic equations of state.
Motivating, formulating, and assuming certain conjectures, we derive results
about how the properties of fluids (equations of state, momenta, angular
momenta) and generic spacelike singularities affect each other.Comment: Considerable changes have been made in presentation and arguments,
resulting in sharper conclusion
Global gravitational instability of FLRW backgrounds - interpreting the dark sectors
The standard model of cosmology is based on homogeneous-isotropic solutions
of Einstein's equations. These solutions are known to be gravitationally
unstable to local inhomogeneous perturbations, commonly described as evolving
on a background given by the same solutions. In this picture, the FLRW
backgrounds are taken to describe the average over inhomogeneous perturbations
for all times. We study in the present article the (in)stability of FLRW dust
backgrounds within a class of averaged inhomogeneous cosmologies. We examine
the phase portraits of the latter, discuss their fixed points and orbital
structure and provide detailed illustrations. We show that FLRW cosmologies are
unstable in some relevant cases: averaged models are driven away from them
through structure formation and accelerated expansion. We find support for the
proposal that the dark components of the FLRW framework may be associated to
these instability sectors. Our conclusion is that FLRW cosmologies have to be
considered critically as for their role to serve as reliable models for the
physical background.Comment: 15 pages, 13 figures, 1 table. Matches published version in CQ
Phase Space description of Nonlocal Teleparallel Gravity
We study cosmological solutions in nonlocal teleparallel gravity or
theory, where is the torsion scalar in teleparallel gravity. This is a
natural extenstion of the usual teleparallel gravity with nonlocal terms. In
this work the phase space portrait proposed to describe the dynamics of an
arbitrary flat, homogeneous cosmological background with a number of matter
contents, both in early and late time epochs. The aim was to convert the system
of the equations of the motion to a first order autonomous dynamical system and
to find fixed points and attractors using numerical codes. For this purpose,
firstly we derive effective forms of cosmological field equations describing
the whole cosmic evolution history in a homogeneous and isotropic cosmological
background and construct the autonomous system of the first order dynamical
equations. In addition, we investigate the local stability in the dynamical
systems called "the stable/unstable manifold" by introducing a specific form of
the interaction between matter, dark energy, radiation and a scalar field.
Furthermore, we explore the exact solutions of the cosmological equations in
the case of de Sitter spacetime. In particular, we examine the role of an
auxiliary function called "gauge" in the formation of such cosmological
solutions and show whether the de Sitter solutions can exist or not. Moreover,
we study the stability issue of the de Sitter solutions both in vacuum and
non-vacuum spacetimes. It is demonstrated that for nonlocal gravity, the
stable de Sitter solutions can be produced even in vacuum spacetime.Comment: 14 pages, 3 figures, title changed, version accepted for publication
in European Physical Journal
Exponential stabilization of driftless nonlinear control systems using homogeneous feedback
This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers
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