Five-dimensional f(R) braneworld models

After incorporating f(R) gravity into the general braneworld sum rules scope, it is shown that some particular class of warped five-dimensional nonlinear braneworld models, which may be interesting for the hierarchy problem solution, still require a negative tension brane. For other classes of warp factors (suitable and not suitable for approaching the hierarchy problem) any negative brane tension in the compactification scheme is not necessary. In this vein, it is argued that, in the bulk f(R) gravity context, some types of warp factors may be useful for approaching the hierarchy problem and for evading the necessity of a negative brane tension in the compactification scheme.

Prediction of R plus R-2 gravity for the deflection of a photon passing close to the Sun

The cross-section for the scattering of a photon by the Sun's gravitational field, treated as an external field, is computed in the framework of R + R-2 gravity. Using this result, we found that for a photon just grazing the Sun's surface the deflection is 1.75 which is exactly the same as that given by Einstein's theory. An explanation for this pseudo-paradox is provided.

Bending of light in the framework of R + R2 gravity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the long standing issue of an R phi(2) coupling between gravity and a massless free scalar field

Using 2-body trees on a flat space background, it is shown that the actions A[g, φ] = (Latin small letter esh) d4x√-g [(R/2K) + (1/2)(gμν ∂μφ∂νφ + λRφ2)] and Ā[ḡ, φ̄] = (Latin small letter esh) d4x√ - ḡ [(R̄/2k) + (1/2) ḡμν∂μφ̄∂ νφ] describe the same theory at the tree-level in this case. We also demonstrate the quantum equivalence (at one-loop) of the barred and unbarred systems for λ == -1/6 (conformal coupling).

Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday

We discuss modified gravity which includes negative and positive powers of curvature and provides gravitational dark energy. It is shown that in GR plus a term containing a negative power of curvature, cosmic speed-up may be achieved while the effective phantom phase (with w less than -1) follows when such a term contains a fractional positive power of curvature. Minimal coupling with matter makes the situation more interesting: even 1/R theory coupled with the usual ideal fluid may describe the (effective phantom) dark energy. The account of the R(2) term (consistent modified gravity) may help to escape cosmic doomsday.

Quadratic gravity theories in 2+1 dimensions and the topological Chern-Simons term

The addition of a topological Chern-Simons term to three-dimensional higher-derivative gravity is not a good therapy to cure the nonunitarity of the aforementioned theory. Moreover, R+R-2 gravity in (2+1)D, which is unitary at the tree level, becomes tree-level nonunitary when it is augmented by the abovementioned topological term. Therefore, unlike what is claimed in the literature, topological higher-derivative gravity in (2+1)D is not tree-level unitary and neither is topological three-dimensional R+R-2 gravity.

Scattering of photons by an external gravitational field in the framework of higher-derivative gravity

The scattering of photons by a static gravitational field, treated as an external field, is discussed in the context of gravity with higher derivatives. It is shown that the R-2 sector of the theory does not contribute to the photon scattering, whereas the R-mu nu(2) sector produces dispersive (energy-dependent) photon propagation.

Unavoidable conflict between massive gravity models and massive topological terms

Massive gravity models in (2 + 1) dimensions, such as those obtained by adding to Einstein's gravity the usual Fierz-Pauli, or the more complicated Ricci scalar squared (R-2), terms, are tree level unitary. Interesting enough these seemingly harmless systems have their unitarity spoiled when they are augmented by a Chern-Simons term. Furthermore, if the massive topological term is added to R + R-munu(2) gravity, or to R + R-munu(2), + R-2 gravity (higher-derivative gravity), which are nonunitary at the tree level, the resulting models remain nonunitary. Therefore, unlike the common belief, as well as the claims in the literature, the coexistence between three-dimensional massive gravity models and massive topological terms is conflicting.

Some remarks on the coupling prescription of teleparallel gravity

By using a nonholonomic moving frame version of the general covariance principle, an active version of the equivalence principle, an analysis of the gravitational coupling prescription of teleparallel gravity is made. It is shown that the coupling prescription determined by this principle is always equivalent with the corresponding prescription of general relativity, even in the presence of fermions. An application to the case of a Dirac spinor is made.

Fierz-Pauli higher derivative gravity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Hamilton-Jacobi formalism for linearized gravity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Cosmic acceleration from second order gauge gravity

We construct a phenomenological theory of gravitation based on a second order gauge formulation for the Lorentz group. The model presents a long-range modification for the gravitational field leading to a cosmological model provided with an accelerated expansion at recent times. We estimate the model parameters using observational data and verify that our estimative for the age of the Universe is of the same magnitude than the one predicted by the standard model. The transition from the decelerated expansion regime to the accelerated one occurs recently (at similar to 9.3 Gyr).

De Sitter Relativity: a New Road to Quantum Gravity?

The Poincar, group generalizes the Galilei group for high-velocity kinematics. The de Sitter group is assumed to go one step further, generalizing Poincar, as the group governing high-energy kinematics. In other words, ordinary special relativity is here replaced by de Sitter relativity. In this theory, the cosmological constant I > is no longer a free parameter, and can be determined in terms of other quantities. When applied to the whole universe, it is able to predict the value of I > and to explain the cosmic coincidence. When applied to the propagation of ultra-high energy photons, it gives a good estimate of the time delay observed in extragalactic gamma-ray flares. It can, for this reason, be considered a new paradigm to approach the quantum gravity problem.

Gauge formulation for higher order gravity

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained that includes derivatives of the curvature. We analyze the form of the second field strength, G=partial derivative F+fAF, in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of F and quadratic contractions of G are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his generalized electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behavior at short distances as well as a meso-large distance modification.

Extended 2D generalized dilaton gravity theories

We show that an anomaly-free description of matter in (1+1) dimensions requires a deformation of the 2D relativity principle, which introduces a non-trivial centre in the 2D Poincare algebra. Then we work out the reduced phase space of the anomaly-free 2D relativistic particle, in order to show that it lives in a noncommutative 2D Minkowski space. Moreover, we build a Gaussian wave packet to show that a Planck length is well defined in two dimensions. In order to provide a gravitational interpretation for this noncommutativity, we propose to extend the usual 2D generalized dilaton gravity models by a specific Maxwell component, which guages the extra symmetry associated with the centre of the 2D Poincare algebra. In addition, we show that this extension is a high energy correction to the unextended dilaton theories that can affect the topology of spacetime. Further, we couple a test particle to the general extended dilaton models with the purpose of showing that they predict a noncommutativity in curved spacetime, which is locally described by a Moyal star product in the low energy limit. We also conjecture a probable generalization of this result, which provides strong evidence that the noncommutativity is described by a certain star product which is not of the Moyal type at high energies. Finally, we prove that the extended dilaton theories can be formulated as Poisson-Sigma models based on a nonlinear deformation of the extended Poincare algebra.