QCD perturbation theory at large orders with large renormalization scales in the large β0\beta_0 limit

We examine the QCD perturbation series at large orders, for different values of the 'large $\beta_0$ renormalization scale'. It is found that if we let this scale grow exponentially with the order, the divergent series can be turned into an expansion that converges to the Borel integral, with a certain cut off. In the case of the first IR renormalon at $2/\beta_0$, corresponding to a dimension four operator in the operator product expansion, this qualitatively improves the perturbative predictions. Furthermore, our results allow us to establish formulations of the principle of minimal sensitivity and the fastest apparent convergence criterion that result in a convergent expansion.Comment: 14 pages, 5 figures, elaborated conclusion

Avoiding the Landau-pole in perturbative QCD

We propose an alternative perturbative expansion for QCD. All scheme and scale dependence is reduced to one free parameter. Fixing this parameter with a fastest apparent convergence criterion gives sensible results in the whole energy region. We apply the expansion to the calculation of the zero flavor triple gluon vertex, the quark gluon vertex, the gluon propagator and the ghost propagator. A qualitative agreement with the corresponding lattice results is found.Comment: 18 pages, 8 figure

Compactifications of conformal gravity

We study conformal theories of gravity, i.e. those whose action is invariant under the local transformation g_{\mu\nu} -> \omega^2 (x) g_{\mu\nu}. As is well known, in order to obtain Einstein gravity in 4D it is necessary to introduce a scalar compensator with a VEV that spontaneously breaks the conformal invariance and generates the Planck mass. We show that the compactification of extra dimensions in a higher dimensional conformal theory of gravity also yields Einstein gravity in lower dimensions, without the need to introduce the scalar compensator. It is the field associated with the size of the extra dimensions (the radion) who takes the role of the scalar compensator in 4D. The radion has in this case no physical excitations since they are gauged away in the Einstein frame for the metric. In these models the stabilization of the size of the extra dimensions is therefore automatic.Comment: 13 page

The non-perturbative groundstate of Q.C.D and the local composite operator A_mu^2

We investigate the possibility that the dimension 2 condensate A_mu^2 has a non zero non-perturbative value in Yang-Mills theory. We introduce a multiplicatively renormalisable effective potential for this condensate and show through two loop calculations that a non zero condensate is energetically favoured.Comment: 12 page

Description of our cosmological spacetime as a perturbed conformal Newtonian metric and implications for the backreaction proposal for the accelerating universe

It has been argued that the spacetime of our universe can be accurately described by a perturbed conformal Newtonian metric, and hence even large density inhomogeneities in a dust universe can not change the observables predicted by the homogeneous dust model. In this paper we study a spherically symmetric dust model and illustrate conditions under which large spatial variations in the expansion rate can invalidate the argument.Comment: 22 pages, 8 figures; replaced to fit the version accepted for publication in Phys. Rev.

Supernovae data and perturbative deviation from homogeneity

We show that a spherically symmetric perturbation of a dust dominated $\Omega=1$ FRW universe in the Newtonian gauge can lead to an apparent acceleration of standard candles and provide a fit to the magnitude-redshift relation inferred from the supernovae data, while the perturbation in the gravitational potential remains small at all scales. We also demonstrate that the supernovae data does not necessarily imply the presence of some additional non-perturbative contribution by showing that any Lemaitre-Tolman-Bondi model fitting the supernovae data (with appropriate initial conditions) will be equivalent to a perturbed FRW spacetime along the past light cone.Comment: 8 pages, 3 figures; v2: 1 figure added, references added/updated, minor modifications and clarifications, matches published versio

f(R) actions, cosmic acceleration and local tests of gravity

We study spherically symmetric solutions in f(R) theories and its compatibility with local tests of gravity. We start by clarifying the range of validity of the weak field expansion and show that for many models proposed to address the Dark Energy problem this expansion breaks down in realistic situations. This invalidates the conclusions of several papers that make inappropriate use of this expansion. For the stable models that modify gravity only at small curvatures we find that when the asymptotic background curvature is large we approximately recover the solutions of Einstein gravity through the so-called Chameleon mechanism, as a result of the non-linear dynamics of the extra scalar degree of freedom contained in the metric. In these models one would observe a transition from Einstein to scalar-tensor gravity as the Universe expands and the background curvature diminishes. Assuming an adiabatic evolution we estimate the redshift at which this transition would take place for a source with given mass and radius. We also show that models of dynamical Dark Energy claimed to be compatible with tests of gravity because the mass of the scalar is large in vacuum (e.g. those that also include R^2 corrections in the action), are not viable.Comment: 26 page

Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach

We search for spherically symmetric solutions of f(R) theories of gravity via the Noether Symmetry Approach. A general formalism in the metric framework is developed considering a point-like f(R)-Lagrangian where spherical symmetry is required. Examples of exact solutions are given.Comment: 17 pages, to appear in Class. Quant. Gra