44 research outputs found
f(R) gravity, torsion and non-metricity
For both f(R) theories of gravity with an independent symmetric connection
(no torsion), usually referred to as Palatini f(R) gravity theories, and for
f(R) theories of gravity with torsion but no non-metricity, called U4 theories,
it has been shown that the independent connection can actually be eliminated
algebraically, as long as this connection does not couple to matter.
Remarkably, the outcome in both case is the same theory, which is dynamically
equivalent with an \omega_0=-3/2 Brans--Dicke theory. It is shown here that
even for the most general case of an independent connection with both
non-metricity and torsion one arrives at exactly the same theory as in the more
restricted cases. This generalizes the previous results and explains why
assuming that either the torsion or the the non-metricity vanishes ultimately
leads to the same theory. It also demonstrates that f(R) actions cannot support
an independent connection which carries dynamical degrees of freedom,
irrespectively of how general this connection is, at least as long as there is
no connection-matter coupling.Comment: v2: slightly shortened version published in CQG as a Fast Track
Communicatio
Curvature singularities, tidal forces and the viability of Palatini f(R) gravity
In a previous paper we showed that static spherically symmetric objects
which, in the vicinity of their surface, are well-described by a polytropic
equation of state with 3/2<Gamma<2 exhibit a curvature singularity in Palatini
f(R) gravity. We argued that this casts serious doubt on the validity of
Palatini f(R) gravity as a viable alternative to General Relativity. In the
present paper we further investigate this characteristic of Palatini f(R)
gravity in order to clarify its physical interpretation and consequences.Comment: 15 pages. CQG in press. Part of the material moved to an appendix,
discussion on the meV scale predictions of Palatini f(R) gravity adde
Cosmological perturbations in Palatini modified gravity
Two approaches to the study of cosmological density perturbations in modified
theories of Palatini gravity have recently been discussed. These utilise,
respectively, a generalisation of Birkhoff's theorem and a direct linearization
of the gravitational field equations. In this paper these approaches are
compared and contrasted. The general form of the gravitational lagrangian for
which the two frameworks yield identical results in the long-wavelength limit
is derived. This class of models includes the case where the lagrangian is a
power-law of the Ricci curvature scalar. The evolution of density perturbations
in theories of the type is investigated numerically. It is
found that the results obtained by the two methods are in good agreement on
sufficiently large scales when the values of the parameters (b,c) are
consistent with current observational constraints. However, this agreement
becomes progressively poorer for models that differ significantly from the
standard concordance model and as smaller scales are considered
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
Filtering out the cosmological constant in the Palatini formalism of modified gravity
According to theoretical physics the cosmological constant (CC) is expected
to be much larger in magnitude than other energy densities in the universe,
which is in stark contrast to the observed Big Bang evolution. We address this
old CC problem not by introducing an extremely fine-tuned counterterm, but in
the context of modified gravity in the Palatini formalism. In our model the
large CC term is filtered out, and it does not prevent a standard cosmological
evolution. We discuss the filter effect in the epochs of radiation and matter
domination as well as in the asymptotic de Sitter future. The final expansion
rate can be much lower than inferred from the large CC without using a
fine-tuned counterterm. Finally, we show that the CC filter works also in the
Kottler (Schwarzschild-de Sitter) metric describing a black hole environment
with a CC compatible to the future de Sitter cosmos.Comment: 22 pages, 1 figure, discussion extended, references added, accepted
by Gen.Rel.Gra
New Cases of Universality Theorem for Gravitational Theories
The "Universality Theorem" for gravity shows that f(R) theories (in their
metric-affine formulation) in vacuum are dynamically equivalent to vacuum
Einstein equations with suitable cosmological constants. This holds true for a
generic (i.e. except sporadic degenerate cases) analytic function f(R) and
standard gravity without cosmological constant is reproduced if f is the
identity function (i.e. f(R)=R). The theorem is here extended introducing in
dimension 4 a 1-parameter family of invariants R' inspired by the
Barbero-Immirzi formulation of GR (which in the Euclidean sector includes also
selfdual formulation). It will be proven that f(R') theories so defined are
dynamically equivalent to the corresponding metric-affine f(R) theory. In
particular for the function f(R)=R the standard equivalence between GR and
Holst Lagrangian is obtained.Comment: 10 pages, few typos correcte
Cosmological Constraints from Hubble Parameter on f(R) Cosmologies
Modified gravity in the Palatini approach has been presently applied
to Cosmology as a realistic alternative to dark energy. In this concern, a
number of authors have searched for observational constraints on several
gravity functional forms using mainly data of type Ia supenovae (SNe Ia),
Cosmic Microwave Background ({\rm CMB}) radiation and Large Scale Structure
({\rm LSS}). In this paper, by considering a homogeneous and isotropic flat
universe, we use determinations of the Hubble function , which are based
on differential age method, to place bounds on the free parameters of the functional form. We also combine the data with
constraints from Baryon Acoustic Oscillations ({\rm BAO}) and {\rm CMB}
measurements, obtaining ranges of values for and in agreement with
other independent analyses. We find that, for some intervals of and
, models based on gravity in the Palatini
approach, unlike the metric formalism, can produce the sequence of
radiation-dominated, matter-dominated, and accelerating periods without need of
dark energy.Comment: 11 pages, 7 figures, 1 Table, LaTe
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
adde
Stability analysis of f(R)-AdS black holes
We study the stability of f(R)-AdS (Schwarzschild-AdS) black hole obtained
from f(R) gravity. In order to resolve the difficulty of solving fourth order
linearized equations, we transform f(R) gravity into the scalar-tensor theory
by introducing two auxiliary scalars. In this case, the linearized curvature
scalar becomes a dynamical scalaron, showing that all linearized equations are
second order. Using the positivity of gravitational potentials and S-deformed
technique allows us to guarantee the stability of f(R)-AdS black hole if the
scalaron mass squared satisfies the Breitenlohner-Freedman bound. This is
confirmed by computing quasinormal frequencies of the scalaron for large
f(R)-AdS black hole.Comment: 17 pages, 1 figure, version to appear in EPJ
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