95 research outputs found
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
Flat bidifferential ideals and semihamiltonian PDEs
In this paper we consider a class of semihamiltonian systems characterized by
the existence of a special conservation law.
The density and the current of this conservation law satisfy a second order
system of PDEs which has a natural interpretation in the theory of flat
bifferential ideals. The class of systems we consider contains important
well-known examples of semihamiltonian systems. Other examples, like genus 1
Whitham modulation equations for KdV, are related to this class by a
reciprocal trasformation.Comment: 18 pages. v5: formula (36) corrected; minor change
Two-Dimensional Dilaton-Gravity Coupled to Massless Spinors
We apply a global and geometrically well-defined formalism for
spinor-dilaton-gravity to two-dimensional manifolds. We discuss the general
formalism and focus attention on some particular choices of the dilatonic
potential. For constant dilatonic potential the model turns out to be
completely solvable and the general solution is found. For linear and
exponential dilatonic potentials we present the class of exact solutions with a
Killing vector.Comment: 21 pages, LaTeX, minor changes in text and format, final version to
appear in Classical and Quantum Gravit
Boundary Conditions, Energies and Gravitational Heat in General Relativity (a Classical Analysis)
The variation of the energy for a gravitational system is directly defined
from the Hamiltonian field equations of General Relativity. When the variation
of the energy is written in a covariant form it splits into two (covariant)
contributions: one of them is the Komar energy, while the other is the
so-called covariant ADM correction term. When specific boundary conditions are
analyzed one sees that the Komar energy is related to the gravitational heat
while the ADM correction term plays the role of the Helmholtz free energy.
These properties allow to establish, inside a classical geometric framework, a
formal analogy between gravitation and the laws governing the evolution of a
thermodynamic system. The analogy applies to stationary spacetimes admitting
multiple causal horizons as well as to AdS Taub-bolt solutions.Comment: Latex file, 31 pages; one reference and two comments added, misprints
correcte
Accelerated Cosmological Models in Ricci squared Gravity
Alternative gravitational theories described by Lagrangians depending on
general functions of the Ricci scalar have been proven to give coherent
theoretical models to describe the experimental evidence of the acceleration of
universe at present time. In this paper we proceed further in this analysis of
cosmological applications of alternative gravitational theories depending on
(other) curvature invariants. We introduce Ricci squared Lagrangians in minimal
interaction with matter (perfect fluid); we find modified Einstein equations
and consequently modified Friedmann equations in the Palatini formalism. It is
striking that both Ricci scalar and Ricci squared theories are described in the
same mathematical framework and both the generalized Einstein equations and
generalized Friedmann equations have the same structure. In the framework of
the cosmological principle, without the introduction of exotic forms of dark
energy, we thus obtain modified equations providing values of w_{eff}<-1 in
accordance with the experimental data. The spacetime bi-metric structure plays
a fundamental role in the physical interpretation of results and gives them a
clear and very rich geometrical interpretation.Comment: New version: 26 pages, 1 figure (now included), Revtex
One-loop f(R) gravity in de Sitter universe
Motivated by the dark energy issue, the one-loop quantization approach for a
family of relativistic cosmological theories is discussed in some detail.
Specifically, general gravity at the one-loop level in a de Sitter
universe is investigated, extending a similar program developed for the case of
pure Einstein gravity. Using generalized zeta regularization, the one-loop
effective action is explicitly obtained off-shell, what allows to study in
detail the possibility of (de)stabilization of the de Sitter background by
quantum effects. The one-loop effective action maybe useful also for the study
of constant curvature black hole nucleation rate and it provides the plausible
way of resolving the cosmological constant problem.Comment: 25 pages, Latex file. Discussion enlarged, new references added.
Version accepted in JCA
The Universality of Einstein Equations
It is shown that for a wide class of analytic Lagrangians which depend only
on the scalar curvature of a metric and a connection, the application of the
so--called ``Palatini formalism'', i.e., treating the metric and the connection
as independent variables, leads to ``universal'' equations. If the dimension
of space--time is greater than two these universal equations are Einstein
equations for a generic Lagrangian and are suitably replaced by other universal
equations at bifurcation points. We show that bifurcations take place in
particular for conformally invariant Lagrangians and prove
that their solutions are conformally equivalent to solutions of Einstein
equations. For 2--dimensional space--time we find instead that the universal
equation is always the equation of constant scalar curvature; the connection in
this case is a Weyl connection, containing the Levi--Civita connection of the
metric and an additional vectorfield ensuing from conformal invariance. As an
example, we investigate in detail some polynomial Lagrangians and discuss their
bifurcations.Comment: 15 pages, LaTeX, (Extended Version), TO-JLL-P1/9
Constraining f(R) gravity in the Palatini formalism
Although several models of theories of gravity within the Palatini
approach have been studied already, the interest was concentrated on those that
have an effect on the late-time evolution of the universe, by the inclusion for
example of terms inversely proportional to the scalar curvature in the
gravitational action. However, additional positive powers of the curvature also
provide interesting early-time phenomenology, like inflation, and the presence
of such terms in the action is equally, if not more, probable. In the present
paper models with both additional positive and negative powers of the scalar
curvature are studied. Their effect on the evolution of the universe is
investigated for all cosmological eras, and various constraints are put on the
extra terms in the actions. Additionally, we examine the extent to which the
new terms in positive powers affect the late-time evolution of the universe and
the related observables, which also determines our ability to probe their
presence in the gravitational action.Comment: reference update and minor changes to match published versio
Subset currents on free groups
We introduce and study the space of \emph{subset currents} on the free group
. A subset current on is a positive -invariant locally finite
Borel measure on the space of all closed subsets of consisting of at least two points. While ordinary geodesic currents
generalize conjugacy classes of nontrivial group elements, a subset current is
a measure-theoretic generalization of the conjugacy class of a nontrivial
finitely generated subgroup in , and, more generally, in a word-hyperbolic
group. The concept of a subset current is related to the notion of an
"invariant random subgroup" with respect to some conjugacy-invariant
probability measure on the space of closed subgroups of a topological group. If
we fix a free basis of , a subset current may also be viewed as an
-invariant measure on a "branching" analog of the geodesic flow space for
, whose elements are infinite subtrees (rather than just geodesic lines)
of the Cayley graph of with respect to .Comment: updated version; to appear in Geometriae Dedicat
f(R) theories of gravity in Palatini approach matched with observations
We investigate the viability of f(R) theories in the framework of the
Palatini approach as solutions to the problem of the observed accelerated
expansion of the universe. Two physically motivated popular choices for f(R)
are considered: power law, f(R) = \beta R^n, and logarithmic, f(R) = \alpha
\ln{R}. Under the Palatini approach, both Lagrangians give rise to cosmological
models comprising only standard matter and undergoing a present phase of
accelerated expansion. We use the Hubble diagram of type Ia Supernovae and the
data on the gas mass fraction in relaxed galaxy clusters to see whether these
models are able to reproduce what is observed and to constrain their
parameters. It turns out that they are indeed able to fit the data with values
of the Hubble constant and of the matter density parameter in agreement with
some model independent estimates, but the today deceleration parameter is
higher than what is measured in the concordance LambdaCDM model.Comment: 14 pages, 8 figures, submitted to Physical Review
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