85 research outputs found
A new approach to the analysis of the phase space of f(R)-gravity
We propose a new dynamical system formalism for the analysis of f(R)
cosmologies. The new approach eliminates the need for cumbersome inversions to
close the dynamical system and allows the analysis of the phase space of
f(R)-gravity models which cannot be investigated using the standard technique.
Differently form previously proposed similar techniques, the new method is
constructed in such a way to associate to the fixed points scale factors, which
contain four integration constants (i.e. solutions of fourth order differential
equations). In this way a new light is shed on the physical meaning of the
fixed points. We apply this technique to some f(R) Lagrangians relevant for
inflationary and dark energy models.Comment: 32 pages, 13 figures, typos corrected, updated bibliograph
Covariant gauge invariant theory of Scalar Perturbations in -gravity: a brief review
I review the state of the art of the investigation on the structure formation
in -gravity based on the Covariant and Gauge Invariant approach to
perturbations. A critical analysis of the results, in particular the presence
of characteristic signature of these models, together with their meaning and
their implication is given.Comment: 23 pages, 12 figures, to appear on The Open Astronomy Journa
A first-order secular theory for the post-Newtonian two-body problem with spin -- I: The restricted case
We revisit the relativistic restricted two-body problem with spin employing a
perturbation scheme based on Lie series. Starting from a post-Newtonian
expansion of the field equations, we develop a first-order secular theory that
reproduces well-known relativistic effects such as the precession of the
pericentre and the Lense-Thirring and geodetic effects. Additionally, our
theory takes into full account the complex interplay between the various
relativistic effects, and provides a new explicit solution of the averaged
equations of motion in terms of elliptic functions. Our analysis reveals the
presence of particular configurations for which non-periodical behaviour can
arise. The application of our results to real astrodynamical systems (such as
Mercury-like and pulsar planets) highlights the contribution of relativistic
effects to the long-term evolution of the spin and orbit of the secondary body.Comment: 14 pages, 3 figures, Published in MNRA
On the Anisotropic Interior Solutions in Ho\v{r}ava Gravity and Einstein-{\ae}ther Theory
We find a reconstruction algorithm able to generate all the static
spherically symmetric interior solutions in the framework of Ho\v{r}ava gravity
and Einstein-\ae ther theory in presence of anisotropic fluids. We focus for
simplicity on the case of a static \ae ther finding a large class of possible
viable interior star solutions which present a very rich phenomenology. We
study one illustrative example in more detail.Comment: v1: 5 pages, 1 figure; v2: 6 pages, 1 figure. Matches published
version in EP
The 1+1+2 formalism for Scalar-Tensor gravity
We use the 1+1+2 covariant approach to clarify a number of aspects of
spherically symmetric solutions of non-minimally coupled scalar tensor
theories. Particular attention is focused on the extension of Birkhoff's
theorem and the nature of quasi-local horizons in this context.Comment: 27 pages, accepted versio
On dynamical systems approaches and methods in cosmology
We discuss dynamical systems approaches and methods applied to flat
Robertson-Walker models in -gravity. We argue that a complete description
of the solution space of a model requires a global state space analysis that
motivates globally covering state space adapted variables. This is shown
explicitly by an illustrative example, , ,
for which we introduce new regular dynamical systems on global compactly
extended state spaces for the Jordan and Einstein frames. This example also
allows us to illustrate several local and global dynamical systems techniques
involving, e.g., blow ups of nilpotent fixed points, center manifold analysis,
averaging, and use of monotone functions. As a result of applying dynamical
systems methods to globally state space adapted dynamical systems formulations,
we obtain pictures of the entire solution spaces in both the Jordan and the
Einstein frames. This shows, e.g., that due to the domain of the conformal
transformation between the Jordan and Einstein frames, not all the solutions in
the Jordan frame are completely contained in the Einstein frame. We also make
comparisons with previous dynamical systems approaches to cosmology and
discuss their advantages and disadvantages.Comment: 36 pages, 7 figures. v2: references added, matches published versio
Reconstructing exact scalar-tensor cosmologies via conformal transformations
We propose a new reconstruction method for scalar--tensor gravity based on
the use of conformal transformations. The new method allows the derivation of a
set of interesting exact cosmological solutions in brans Dicke gravity as well
as other extensions of General Relativity.Comment: 8 pages, 2 figure
An analysis of the phase space of Horava-Lifshitz cosmologies
Using the dynamical system approach, properties of cosmological models based
on the Horava-Lifshitz gravity are systematically studied. In particular, the
cosmological phase space of the Horava-Lifshitz model is characterized. The
analysis allows to compare some key physical consequences of the imposition (or
not) of detailed balance. A result of the investigation is that in the detailed
balance case one of the attractors in the theory corresponds to an oscillatory
behavior. Such oscillations can be associated to a bouncing universe, as
previously described by Brandenberger, and will prevent a possible evolution
towards a de Sitter universe. Other results obtained show that the cosmological
models generated by Horava-Lifshitz gravity without the detailed balance
assumption have indeed the potential to describe the transition between the
Friedmann and the dark energy eras. The whole analysis leads to the plausible
conclusion that a cosmology compatible with the present observations of the
universe can be achieved only if the detailed balance condition is broken.Comment: 12 pages, some typos corrected, some references adde
A new approach to reconstruction methods in gravity
We present a new approach of the reconstruction method based on the use of
the cosmic parameters instead of a time law for the scale factor. This allows
the derivation and analysis of a set of new non-trivial cosmological solutions
for -gravity. A number of simple examples are given.Comment: 5 pages, Revtex
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