Cosmology

The Effective Field Theory (EFT) approach can be employed to perform high PN order calculations of the Hamiltonian of a binary system. We show how we reproduced the 3PN dynamics by means of an algorithm implemented in Mathematica and our progress towards the computation of the 4PN Hamiltonian. We also show the EFT computation of the tail term affecting the conservative dynamics at 4PN order, first derived using traditional methods by Blanchet and Damour.

Based on tetrad-generalized canonical formalism by Arnowitt, Deser, and Misner most recent achievements in analytic calculations of higher order post-Newtonian Hamiltonians for spinning binary black holes and neutron stars are presented. The results of the generalized ADM formalism are put into mathematical relationship with those obtained within the Effective Field Theory approach.

The advent of large spectroscopic surveys of galaxies in the early 1980s has shown us that galaxies assemble in large scale structures. Recently, cosmic voids have received more attention through the availability wide and deep galaxy surveys. Voids have a simple phase space structure and thus are easier to model than cluster of galaxies. I will present two important applications of the precise analysis of voids in the context of constraining the equation of state of dark energy. First I will discuss how they could be used to have a much better determination of the expansion factor than using traditional methods, like Baryonic Acoustic Oscillations. Second, I will show that voids is maybe the only large-scale structure for which the dynamics can be finely modelled, notably through the use of the Monge-Ampere-Kantorovitch orbit reconstruction method. For the two above cases, I will present how we can mathematically define cosmic voids, the methods that have been developed to find them and some results based on N-body simulations for constraining the Dark Energy equation of state.

High-accuracy templates predicted by general relativity for the gravitational waves generated by inspiralling compact binaries (binary star systems composed of neutron stars and/or black holes) have been developed using a mixed multipolar and post-Newtonian (MPN) formalism. In this talk we shall review the foundations of this formalism and its main results, including the equations of motion and radiation from compact binaries up to 3.5PN order. We shall also present some recent work on the comparison between post-Newtonian approximations and black hole perturbations applied to compact binaries in the small mass ratio limit.

In my talk I will discuss the static subsector of the black hole effective action in an arbitrary dimension. In particular, the derivation of the induced mass multipoles as a result of an external (static) gravitational field will be elucidated. In 4d these constants vanish, however in general they are non-vanishing in higher dimensions. Moreover, in certain cases they exhibit a (classical) renormalization group flow consistent with the divergences of the effective field theory.

Recent years have seen the paradigm of effective field theory (EFT) successfully applied to an increasing number of classical systems that range from the gravitational inspiral of compact binaries to hydrodynamics. Many of these systems exhibit dissipation in one form or another, such as radiation reaction or viscous fluid flow, that naturally results from the system being open. This "openness" can manifest as energy leaving the dynamical variables of interest via radiation or heat transfer, for example. As the EFT approach typically utilizes the action, and hence Hamilton's Principle of Extremal Action, it is crucial to determine how generally and consistently to accommodate dissipative effects in a variational principle. In this talk, I discuss why Hamilton's Principle fails to incorporate dissipation. I then provide a reformulation that has been used successfully to confirm well-established results as well as to provide new predictions regarding dissipative systems. I show specific examples drawn from EFT applications. Finally, I show how this reformulation of Hamilton's Principle turns out to correspond to the classical limit of quantum theories based on the so-called "in-in" or "closed-time-path" approaches.

After the first landmark gravitational-wave (GW) detection, GW astronomy will turn to the study of detector data to identify the physical properties of GW sources. The science payoff of GW observations must therefore depend critically on the accurate knowledge of the shapes of waveforms as functions of the source parameters. Effective-field-theory techniques have advanced and continue to advance the state of the art for the modeling of inspiraling-binary dynamics. But how far do we have to push our calculations to satisfy the needs of observations? I review current attempts to answer this question for different detectors and sources, and for the delicate problem of matching post-Newtonian and numerical-relativity waveforms.