17 research outputs found
Reply to `A comment on `The Cauchy problem of f(R) gravity''
We reply to a comment by Capozziello and Vignolo about the Cauchy problem of
Palatini f(R) gravity.Comment: 3 pages, late
A comment on "The Cauchy problem of f(R)- gravity", Class. Quantum Grav., 24, 5667 (2007), arXiv:0709.4414
A critical comment on [N. Lanahan--Tremblay and V. Faraoni, 2007, {\it Class.
Quantum Grav.}, {\bf 24}, 5667, arXiv:0709.4414] is given discussing the
well-formulation of the Chauchy problem for -gravity in metric-affine
theories.Comment: 3 page
A new approach to cosmological perturbations in f(R) models
We propose an analytic procedure that allows to determine quantitatively the
deviation in the behavior of cosmological perturbations between a given f(R)
modified gravity model and a LCDM reference model. Our method allows to study
structure formation in these models from the largest scales, of the order of
the Hubble horizon, down to scales deeply inside the Hubble radius, without
employing the so-called "quasi-static" approximation. Although we restrict our
analysis here to linear perturbations, our technique is completely general and
can be extended to any perturbative order.Comment: 21 pages, 2 figures; Revised version according to reviewer's
suggestions; Typos corrected; Added Reference
Modified gravity with R-matter couplings and (non-)geodesic motion
We consider alternative theories of gravity with a direct coupling between
matter and the Ricci scalar We study the relation between these theories and
ordinary scalar-tensor gravity, or scalar-tensor theories which include
non-standard couplings between the scalar and matter. We then analyze the
motion of matter in such theories, its implications for the Equivalence
Principle, and the recent claim that they can alleviate the dark matter problem
in galaxies.Comment: typos corrected, minor changes, version published in CQ
Two approaches to testing general relativity in the strong-field regime
Observations of compact objects in the electromagnetic spectrum and the
detection of gravitational waves from them can lead to quantitative tests of
the theory of general relativity in the strong-field regime following two very
different approaches. In the first approach, the general relativistic field
equations are modified at a fundamental level and the magnitudes of the
potential deviations are constrained by comparison with observations. In the
second approach, the exterior spacetimes of compact objects are parametrized in
a phenomenological way, the various parameters are measured observationally,
and the results are finally compared against the general relativistic
predictions. In this article, I discuss the current status of both approaches,
focusing on the lessons learned from a large number of recent investigations.Comment: To appear in the proceedings of the conference New Developments in
Gravit
On the Past Asymptotic Dynamics of Non-minimally Coupled Dark Energy
We apply dynamical systems techniques to investigate cosmological models
inspired in scalar-tensor theories written in the Einstein frame. We prove that
if the potential and the coupling function are sufficiently smooth functions,
the scalar field almost always diverges into the past. The dynamics of two
important invariant sets is investigated in some detail. By assuming some
regularity conditions for the potential and for the coupling function, it is
constructed a dynamical system well suited to investigate the dynamics where
the scalar field diverges, i.e. near the initial singularity. The critical
points therein are investigated and the cosmological solutions associated to
them are characterized. We find that our system admits scaling solutions. Some
examples are taken from the bibliography to illustrate the major results. Also
we present asymptotic expansions for the cosmological solutions near the
initial space-time singularity, which extend in a way previous results of other
researchers.Comment: 38 pages, 2 figures, accepted for publication in CQ
Gibbons-Hawking Boundary Terms and Junction Conditions for Higher-Order Brane Gravity Models
We derive the most general junction conditions for the fourth-order brane
gravity constructed of arbitrary functions of curvature invariants. We reduce
these fourth-order theories to second order theories at the expense of
introducing new scalar and tensor fields - the scalaron and the tensoron. In
order to obtain junction conditions we apply the method of generalized
Gibbons-Hawking boundary terms which are appended to the appropriate actions.
After assuming the continuity of the scalaron and the tensoron on the brane, we
recover junction conditions for such general brane universe models previously
obtained by different methods. The derived junction conditions can serve
studying the cosmological implications of the higher-order brane gravity
models.Comment: REVTEX4, 6 pages, no figures, version to match a JCAP accepted pape
The Cauchy problem of f(R) gravity
The initial value problem of metric and Palatini f(R)gravity is studied by
using the dynamical equivalence between these theories and Brans-Dicke gravity.
The Cauchy problem is well-formulated for metric f(R)gravity in the presence of
matter and well-posed in vacuo. For Palatini f(R)gravity, instead, the Cauchy
problem is not well-formulated.Comment: 16 latex pages, to appear in Class. Quantum Grav; typographical
errors corrected, new references adde
Constraint propagation equations of the 3+1 decomposition of f(R) gravity
Theories of gravity other than general relativity (GR) can explain the
observed cosmic acceleration without a cosmological constant. One such class of
theories of gravity is f(R). Metric f(R) theories have been proven to be
equivalent to Brans-Dicke (BD) scalar-tensor gravity without a kinetic term.
Using this equivalence and a 3+1 decomposition of the theory it has been shown
that metric f(R) gravity admits a well-posed initial value problem. However, it
has not been proven that the 3+1 evolution equations of metric f(R) gravity
preserve the (hamiltonian and momentum) constraints. In this paper we show that
this is indeed the case. In addition, we show that the mathematical form of the
constraint propagation equations in BD-equilavent f(R) gravity and in f(R)
gravity in both the Jordan and Einstein frames, is exactly the same as in the
standard ADM 3+1 decomposition of GR. Finally, we point out that current
numerical relativity codes can incorporate the 3+1 evolution equations of
metric f(R) gravity by modifying the stress-energy tensor and adding an
additional scalar field evolution equation. We hope that this work will serve
as a starting point for relativists to develop fully dynamical codes for valid
f(R) models.Comment: 25 pages, matches published version in CQG, references update
Scalar field mass in generalized gravity
The notions of mass and range of a Brans-Dicke-like scalar field in
scalar-tensor and f(R) gravity are subject to an ambiguity that hides a
potential trap. We spell out this ambiguity and identify a physically
meaningful and practical definition for these quantities. This is relevant when
giving a mass to this scalar in order to circumvent experimental limits on the
PPN parameters coming from Solar System experiments.Comment: 11 pages, no figures, to appear in Class. Quantum Grav. References
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