Higher harmonics increase LISA's mass reach for supermassive black holes

Current expectations on the signal to noise ratios and masses of supermassive black holes which the Laser Interferometer Space Antenna (LISA) can observe are based on using in matched filtering only the dominant harmonic of the inspiral waveform at twice the orbital frequency. Other harmonics will affect the signal-to-noise ratio of systems currently believed to be observable by LISA. More significantly, inclusion of other harmonics in our matched filters would mean that more massive systems that were previously thought to be {\it not} visible in LISA should be detectable with reasonable SNRs. Our estimates show that we should be able to significantly increase the mass reach of LISA and observe the more commonly occurring supermassive black holes of masses $\sim 10^8M_\odot.$ More specifically, with the inclusion of all known harmonics LISA will be able to observe even supermassive black hole coalescences with total mass $\sim 10^8 M_\odot (10^9M_\odot)$ (and mass-ratio 0.1) for a low frequency cut-off of $10^{-4}{\rm Hz}$ $(10^{-5}{\rm Hz})$ with an SNR up to $\sim 60$ $(\sim 30)$ at a distance of 3 Gpc. This is important from the astrophysical viewpoint since observational evidence for the existence of black holes in this mass range is quite strong and binaries containing such supermassive black holes will be inaccessible to LISA if one uses as detection templates only the dominant harmonic.Comment: minor corrections mad

Dirac phase leptogenesis

I present here a concise summary of the preprint arXiv:0707.3024, written in collaboration with A. Anisimov and P. Di Bari. There we discuss leptogenesis when {\em CP} violation stems exlusively from the Dirac phase in the PMNS mixing matrix. Under this assumption it turns out that the situation is very constrained when a hierarchical heavy right-handed (RH) neutrino spectrum is considered: the allowed regions are small and the final asymmetry depends on the initial conditions. On the other hand, for a quasi-degenerate spectrum of RH neutrinos, the {\em CP} asymmetry can be enhanced and the situation becomes much more favorable, with no dependence on the initial conditions. Interestingly, in the extreme case of resonant leptogenesis, in order to match the observed baryon asymmetry of the Universe, we obtain a lower bound on \sin \q_{13} which depends on the lightest active neutrino mass m_1.Comment: 3 pages, 2 figures, contribution to the proceedings of the TAUP 07 conference, Sep. 11-15, Sendai, Japa

On the Role of Low-Energy CP Violation in Leptogenesis

The link between low-energy CP violation and leptogenesis became more accessible with the understanding of flavor effects. However, a definite well-motivated model where such a link occurs was still lacking. Adjoint SU(5) is a simple grand unified theory where neutrino masses are generated through the Type I and Type III seesaw mechanisms, and the lepton asymmetry is generated by the fermionic triplet responsible for the Type III seesaw. We focus exclusively on the case of inverted hierarchy for neutrinos, and we show that successful flavored leptogenesis in this theory strongly points towards low-energy CP violation. Moreover, since the range of allowed masses for the triplet is very restricted, we find that the discovery at the LHC of new states present in the theory, together with proton decay and unification of gauge couplings, can conspire to provide a hint in favor of leptogenesis.Comment: 12 pages, 6 figure

Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions

Two long-standing problems with the post-Newtonian approximation for isolated slowly-moving systems in general relativity are: (i) the appearance at high post-Newtonian orders of divergent Poisson integrals, casting a doubt on the soundness of the post-Newtonian series; (ii) the domain of validity of the approximation which is limited to the near-zone of the source, and prevents one, a priori, from incorporating the condition of no-incoming radiation, to be imposed at past null infinity. In this article, we resolve the problem (i) by iterating the post-Newtonian hierarchy of equations by means of a new (Poisson-type) integral operator that is free of divergencies, and the problem (ii) by matching the post-Newtonian near-zone field to the exterior field of the source, known from previous work as a multipolar-post-Minkowskian expansion satisfying the relevant boundary conditions at infinity. As a result, we obtain an algorithm for iterating the post-Newtonian series up to any order, and we determine the terms, present in the post-Newtonian field, that are associated with the gravitational-radiation reaction onto an isolated slowly-moving matter system.Comment: 61 pages, to appear in Phys. Rev.

The labour market after age 50: some elements of a Franco-American comparison

This paper examines various supply and demand side aspects of the French labour market for older workers and puts them in perspective by comparing them to the US case. We first consider the supply side incentives (or disincentives) of basic pension schemes for the two countries : for France, we discuss how these incentives have been changed by the 1993 and 2003 pension reforms and we present some projections of the impact of these reforms on labour force participation rates, based on the DESTINIE dynamic microsimulation model. We then discuss, on the demand side, the hypothesis of a wage-productivity gap for older workers which could explain their lower employment rates. Evidence in favor of this hypothesis is not overwhelming. Nevertheless, workers who lose their jobs at older ages probably suffer a large loss of firm-specific and sector-specific human capital. In the US, this does not preclude re-employment, but at the cost of significant drops of wage levels. In France, the collective choice has been made since the 1970s to allow older workers who lose their jobs to completely withdraw from the labour market : these workers have access to preretirement schemes or specific dispositions of unemployment insurance (including an exemption from seeking employment). This system proved difficult to regulate. Due to these difficulties, France has not been able to do more than stabilize the employment rate in the 55-64 age bracket during the 1990s, after 20 years of continuous decline. The key unanswered question is whether it will be possible to increase the employment rate of this age group in the next two decades.Pensions, preretirement, senior workers

Recommendations of the Stiglitz-Sen-Fitoussi Report: A few illustrations

In September 2009 the Stiglitz-Sen-Fitoussi Commission submitted its report on the measurement of economic performance and social progress. The report is based on a large body of applied research work conducted in recent years in various fields of the economic and social sciences. Some of this research work proposes composite well-being indicators more appropriate than GDP. A parallel trend rather favours the construction of dashboards, i.e. sets of indicators designed to provide an understanding of the several facets of economic performance and quality of life. Without neglecting the interest of constructing composite indicators, the commission strongly emphasized the multidimensional nature of well-being. To address this multidimensional nature, it did not propose its own ready-made dashboard. The report must rather be read as providing guidelines to be followed for constructing such a dashboard. This dossier outlines the main lessons to be learned from a comparison between France and a few other countries with the same level of development, as measured against the criteria used by the Stiglitz Commission. The use of alternative standard of living indicators involves a few reclassifications across countries but without really calling into question the apparent advance of the United States. However, living conditions indicators do show far more marked contrasts in the areas of health, education, the risks of unemployment and poverty, and security. Contributions to the problem of climatic sustainability can be up to three times greater from one country to the next. As for economic sustainability, the indicator proposed by the commission suggests that this sustainability remains warranted, although with a fairly small safety margin in several countries.Stiglitz-Sen-Fitoussi report, measurement of well-being, international comparison, quality of life, sustainable development, economic growth

The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant

We derive the conservative part of the Lagrangian and the energy of a gravitationally bound two-body system at fourth post-Newtonian order, up to terms quadratic in the Newton constant. We also show that such terms are compatible with Lorentz invariance and we write an ansatz for the center-of-mass position. The remaining terms carrying higher powers of the Newton constant are currently under investigation.Comment: 24 pages, 2 figures. Typos in formulae corrected, references added, more comments in the conclusion in v

Hadamard Regularization

Motivated by the problem of the dynamics of point-particles in high post-Newtonian (e.g. 3PN) approximations of general relativity, we consider a certain class of functions which are smooth except at some isolated points around which they admit a power-like singular expansion. We review the concepts of (i) Hadamard ``partie finie'' of such functions at the location of singular points, (ii) the partie finie of their divergent integral. We present and investigate different expressions, useful in applications, for the latter partie finie. To each singular function, we associate a partie-finie (Pf) pseudo-function. The multiplication of pseudo-functions is defined by the ordinary (pointwise) product. We construct a delta-pseudo-function on the class of singular functions, which reduces to the usual notion of Dirac distribution when applied on smooth functions with compact support. We introduce and analyse a new derivative operator acting on pseudo-functions, and generalizing, in this context, the Schwartz distributional derivative. This operator is uniquely defined up to an arbitrary numerical constant. Time derivatives and partial derivatives with respect to the singular points are also investigated. In the course of the paper, all the formulas needed in the application to the physical problem are derived.Comment: 50 pages, to appear in Journal of Mathematical Physic

The Statistical Mechanics of Horizons and Black Hole Thermodynamics

Although we know that black holes are characterized by a temperature and an entropy, we do not yet have a satisfactory microscopic ``statistical mechanical'' explanation for black hole thermodynamics. I describe a new approach that attributes the thermodynamic properties to ``would-be gauge'' degrees of freedom that become dynamical on the horizon. For the (2+1)-dimensional black hole, this approach gives the correct entropy. (Talk given at the Pacific Conference on Gravitation and Cosmology, Seoul, February 1996.)Comment: 11 pages, LaTe

Multipole expansion at the level of the action

Sources of long wavelength radiation are naturally described by an effective field theory (EFT) which takes the form of a multipole expansion. Its action is given by a derivative expansion where higher order terms are suppressed by powers of the ratio of the size of the source over the wavelength. In order to determine the Wilson coefficients of the EFT, i.e. the multipole moments, one needs the mapping between a linear source term action and the multipole expansion form of the action of the EFT. In this paper we perform the multipole expansion to all orders by Taylor expanding the field in the source term and then decomposing the action into symmetric trace free tensors which form irreducible representations of the rotation group. We work at the level of the action, and we obtain the action to all orders in the multipole expansion and the exact expressions for the multipole moments for a scalar field, electromagnetism and linearized gravity. Our results for the latter two cases are manifestly gauge invariant. We also give expressions for the energy flux and the (gauge dependent) radiation field to all orders in the multipole expansion. The results for linearized gravity are a component of the EFT framework NRGR and will greatly simplify future calculations of gravitational wave observables in the radiation sector of NRGR.Comment: 39 pages, some typos corrected, published versio