Testing and comparing tachyon inflation to single standard field inflation

We compare the standard single scalar field inflationary predictions with those of an inflationary phase driven by a tachyon field. A slow-roll formalism is defined for tachyon inflation and we derive the spectra of scalar and tensor perturbations as well as the consistency relations. At lowest order the predictions of standard and tachyon inflation are the same. Higher order deviations are present and their observational relevance is discussed. We discuss the observational consequences of some typical inflationary tachyon potentials and compare them with recent data. All the models predict a negative and very small running of the scalar spectral index, and they consistently lie within the 1$\sigma$ contour of the data set. However, the regime of blue scalar spectral index and large gravity waves is not explored by these models.Comment: Proceedings of the 10th Marcel Grossmann Meeting, Rio de Janeiro, July 2003, 6 pages, 1 figur

Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model

We study the IIB matrix model, which is conjectured to be a nonperturbative definition of superstring theory, by introducing an integer deformation parameter `nu' which couples to the imaginary part of the effective action induced by fermions. The deformed IIB matrix model continues to be well-defined for arbitrary `nu', and it preserves gauge invariance, Lorentz invariance, and the cluster property. We study the model at `nu' = infinity using a saddle-point analysis, and show that ten-dimensional Lorentz invariance is spontaneously broken at least down to an eight-dimensional one. We argue that it is likely that the remaining eight-dimensional Lorentz invariance is further broken, which can be checked by integrating over the saddle-point configurations using standard Monte Carlo simulation.Comment: 12 pages, latex, no figures, references added, version to appear in JHE

A geometrical approach to nonlinear perturbations in relativistic cosmology

We give a pedagogical review of a covariant and fully non-perturbative approach to study nonlinear perturbations in cosmology. In the first part, devoted to cosmological fluids, we define a nonlinear extension of the uniform-density curvature perturbation and derive its evolution equation. In the second part, we focus our attention on multiple scalar fields and present a nonlinear description in terms of adiabatic and entropy perturbations. In both cases, we show how the formalism presented here enables one to easily obtain equations up to second, third and higher orders.Comment: 16 pages; invited review article for Classical and Quantum Gravity issue on non-linear cosmolog

Effective Field Theory of Cosmological Perturbations

The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry---that allows to write down the most general Lagrangian---and of the Stueckelberg "trick"---that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.Comment: 27 pages, references added, matches published version as special issue article in Classical and Quantum Gravit

The 2007 Personal Income Tax Reform in Italy: Effects on Potential Equity, Horizontal Inequity and Re-ranking

According to Kakwani and Lambert (1998), an equitable income tax should respect three axioms related to each taxpayer’s tax liability, average tax rate and post-tax income: whenever taxation determines unequal tax treatments among equals or modifies pre-tax ordering, it influences the potential vertical effect of the tax through three types of inequity. Following the authors’ measurement system, we investigate changes in axiom violations due to the 2007 Italian personal income tax reform, that introduced significant changes in the tax structure. Our microsimulation model uses as input data those provided by the Bank of Italy in its Survey on Households Income and Wealth in the year 2006; estimates of the distribution of taxpayers are very close to the Ministry of Finance official statistics. The analysis considers both the individual and equivalent household gross income distribution and evaluates the decomposition with and without surtaxes. Main findings suggest that both in the 2006 and 2007 tax system most of the overall violations concern the axiom demanding the average tax rate to be a non decreasing function with respect to the gross income; the axiom requiring richer taxpayers to pay higher tax liabilities than poorer ones and the axiom requiring the tax to do not introduce re-rankings in the pre-tax income order present minor violations. The 2007 reform enhances both the potential redistributive effect, that is the one that could be obtained without axiom violations, and the axiom violations: the net result is a small positive variation of the actual redistributive effect. These phenomena appear more relevant for taxpayers than those for equivalent households. For what concerns taxpayers, the 2007 reform has modified also the composition of the three axiom violations, that remains almost the same whenever equivalent households are considered. Finally, focusing on each decile of the income distribution, regressivities are concentrated in the bottom five deciles of the income distribution both for taxpayers and equivalent households.Personal Income Tax, Redistributive Effect, Horizontal Inequity, Reranking, Microsimulation Models

Prediction of RNA pseudoknots by Monte Carlo simulations

In this paper we consider the problem of RNA folding with pseudoknots. We use a graphical representation in which the secondary structures are described by planar diagrams. Pseudoknots are identified as non-planar diagrams. We analyze the non-planar topologies of RNA structures and propose a classification of RNA pseudoknots according to the minimal genus of the surface on which the RNA structure can be embedded. This classification provides a simple and natural way to tackle the problem of RNA folding prediction in presence of pseudoknots. Based on that approach, we describe a Monte Carlo algorithm for the prediction of pseudoknots in an RNA molecule.Comment: 22 pages, 14 figure

Improved RNA pseudoknots prediction and classification using a new topological invariant

We propose a new topological characterization of RNA secondary structures with pseudoknots based on two topological invariants. Starting from the classic arc-representation of RNA secondary structures, we consider a model that couples both I) the topological genus of the graph and II) the number of crossing arcs of the corresponding primitive graph. We add a term proportional to these topological invariants to the standard free energy of the RNA molecule, thus obtaining a novel free energy parametrization which takes into account the abundance of topologies of RNA pseudoknots observed in RNA databases.Comment: 9 pages, 6 figure