A new approach to the analysis of the phase space of f(R)-gravity

We propose a new dynamical system formalism for the analysis of f(R) cosmologies. The new approach eliminates the need for cumbersome inversions to close the dynamical system and allows the analysis of the phase space of f(R)-gravity models which cannot be investigated using the standard technique. Differently form previously proposed similar techniques, the new method is constructed in such a way to associate to the fixed points scale factors, which contain four integration constants (i.e. solutions of fourth order differential equations). In this way a new light is shed on the physical meaning of the fixed points. We apply this technique to some f(R) Lagrangians relevant for inflationary and dark energy models.Comment: 32 pages, 13 figures, typos corrected, updated bibliograph

Covariant gauge invariant theory of Scalar Perturbations in f(R)f(R)-gravity: a brief review

I review the state of the art of the investigation on the structure formation in $f(R)$-gravity based on the Covariant and Gauge Invariant approach to perturbations. A critical analysis of the results, in particular the presence of characteristic signature of these models, together with their meaning and their implication is given.Comment: 23 pages, 12 figures, to appear on The Open Astronomy Journa

A first-order secular theory for the post-Newtonian two-body problem with spin -- I: The restricted case

We revisit the relativistic restricted two-body problem with spin employing a perturbation scheme based on Lie series. Starting from a post-Newtonian expansion of the field equations, we develop a first-order secular theory that reproduces well-known relativistic effects such as the precession of the pericentre and the Lense-Thirring and geodetic effects. Additionally, our theory takes into full account the complex interplay between the various relativistic effects, and provides a new explicit solution of the averaged equations of motion in terms of elliptic functions. Our analysis reveals the presence of particular configurations for which non-periodical behaviour can arise. The application of our results to real astrodynamical systems (such as Mercury-like and pulsar planets) highlights the contribution of relativistic effects to the long-term evolution of the spin and orbit of the secondary body.Comment: 14 pages, 3 figures, Published in MNRA

On the Anisotropic Interior Solutions in Ho\v{r}ava Gravity and Einstein-{\ae}ther Theory

We find a reconstruction algorithm able to generate all the static spherically symmetric interior solutions in the framework of Ho\v{r}ava gravity and Einstein-\ae ther theory in presence of anisotropic fluids. We focus for simplicity on the case of a static \ae ther finding a large class of possible viable interior star solutions which present a very rich phenomenology. We study one illustrative example in more detail.Comment: v1: 5 pages, 1 figure; v2: 6 pages, 1 figure. Matches published version in EP

The Massive O(N) Non-linear Sigma Model at High Orders

We extend our earlier work on the massive $O(N)$ nonlinear sigma model to other observables. We derive expressions at leading order in the large $N$ expansion at all orders in the loop expansion for the decay constant, vacuum expectation value, meson-meson scattering and the scalar and vector form factors. This is done using cactus diagram resummation using a generalized gap equation and other recursion relations. For general $N$ we derive the expressions for the $n$-th loop order leading logarithms $\left(M^2/F^2\log(\mu^2/M^2)\right)^n$, up to five-loops for the decay constant and vacuum expectation value (VEV) and up to four-loops for meson-meson scattering, the scalar and vector form factors. We also quote our earlier result for the mass. The large $N$ results do not give a good approximation for the case $N=3$. We use our results to study the convergence of the perturbative series and compare with elastic unitarity.Comment: 39 page

Impact of QED corrections to Higgs decay into four leptons at the LHC

At the LHC a precise measurement of the Higgs boson mass (if discovered), at the level of 0.1-1%, will be possible through the channel g g --> H --> 4l for a wide range of Higgs mass values. To match such an accuracy, the systematic effects induced by QED corrections need to be investigated. In the present study the calculation of O(alpha) and higher order QED corrections is illustrated as well as their impact on the Higgs mass determination, once realistic event selection criteria for charged leptons and photons are considered.Comment: 5 pages, 5 figures, 1 table. Presented at HEP2005 July 21st-27th, 2005, Lisboa, Portugal and at RADCOR 2005, Shonan Village, October 2nd-7th, 2005, Japa

Photon pair production at flavour factories with per mille accuracy

We present a high-precision QED calculation, with 0.1% theoretical accuracy, of two photon production in $e^+ e^-$ annihilation, as required by more and more accurate luminosity monitoring at flavour factories. The accuracy of the approach, which is based on the matching of exact next-to-leading order corrections with a QED Parton Shower algorithm, is demonstrated through a detailed analysis of the impact of the various sources of radiative corrections to the experimentally relevant observables. The calculation is implemented in the latest version of the event generator BabaYaga, available for precision simulations of photon pair production at $e^+ e^-$ colliders of moderately high energies.Comment: 11 pages, 5 figures, 1 tabl

The 1+1+2 formalism for Scalar-Tensor gravity

We use the 1+1+2 covariant approach to clarify a number of aspects of spherically symmetric solutions of non-minimally coupled scalar tensor theories. Particular attention is focused on the extension of Birkhoff's theorem and the nature of quasi-local horizons in this context.Comment: 27 pages, accepted versio