In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian.The EFT also systematically captures "post-Minkowskian" corrections to the multipole expansion due to non-linear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from non-relativistic binaries, including long distance effects up to 3PN (v 6 ) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.

We use the effective field theory (EFT) framework to calculate the tail effect in gravitational radiation reaction, which enters at the fourth post-Newtonian order in the dynamics of a binary system. The computation entails a subtle interplay between the near (or potential) and far (or radiation) zones. In particular, we find that the tail contribution to the effective action is nonlocal in time and features both a dissipative and a "conservative" term. The latter includes a logarithmic ultraviolet (UV) divergence, which we show cancels against an infrared (IR) singularity found in the (conservative) near zone. The origin of this behavior in the long-distance EFT is due to the point-particle limit-shrinking the binary to a pointwhich transforms a would-be infrared singularity into an ultraviolet divergence. This is a common occurrence in an EFT approach, which furthermore allows us to use renormalization group (RG) techniques to resum the resulting logarithmic contributions. We then derive the RG evolution for the binding potential and total mass/energy, and find agreement with the results obtained imposing the conservation of the (pseudo) stress-energy tensor in the radiation theory. While the calculation of the leading tail contribution to the effective action involves only one diagram, five are needed for the one-point function. This suggests logarithmic corrections may be easier to incorporate in this fashion. We conclude with a few remarks on the nature of these IR/UV singularities, the (lack of) ambiguities recently discussed in the literature, and the completeness of the analytic post-Newtonian framework.

We use the effective field theory for gravitational bound states, proposed by Goldberger and Rothstein, to compute the interaction Lagrangian of a binary system at the second post-Newtonian order. Throughout the calculation, we use a metric parametrization based on a temporal Kaluza-Klein decomposition and test the claim by Kol and Smolkin that this parametrization provides important calculational advantages. We demonstrate how to use the effective field theory method efficiently in precision calculations, and we reproduce known results for the second post-Newtonian order equations of motion in harmonic gauge in a straightforward manner. I. INTRODUCTIONIn the last two decades, significant progress has been made towards the detection of gravitational waves (GWs) via laser interferometry. Currently, the ground-based experiments LIGO [1], VIRGO [2], GEO [3], and TAMA [4] are actively searching for GWs [5]. Moreover, the proposed LISA experiment [6], due to be the first space-based GW detector, will search for GWs in a complementary frequency band to the ground-based experiments and is expected to achieve high event rates at an unprecedented signal-to-noise ratio [7].A particularly interesting source of GWs, which is expected to be detected, is the compact binary system undergoing coalescence, with neutron star (NS) and/or black hole (BH) constituents. Current experiments have yet to detect the binary inspiral signal. However, Advanced LIGO [8], an upgrade of LIGO scheduled to come online in 2014, may allow for routine detection of such events. This is due to a ∼ 10-fold increase in sensitivity over LIGO, which will in turn result in an increase of the accessible event rate by a factor ∼ 1000. Current estimates for the number of expected NS/NS, BH/BH, and BH/NS events in Advanced LIGO are roughly 10 − 100, 1 − 500, and 1 − 30 per year, respectively [9,10].All three stages of the binary coalescence, inspiral, merger, and ringdown, are potentially detectable. The inspiral phase, where the characteristic orbital velocity is v 2 ≪ 1 (in units where c = 1), can be computed analytically using an expansion in v 2 ∼ Gm/r. The merger is computed numerically [11], and there has been significant recent progress in this area [12]. The ringdown can be treated analytically using quasinormal modes [13].The perturbative calculation of the inspiral phase has been performed with a variety of methods [14,15]. Because of the phase evolution of the inspiral signal and the ability to measure the total orbital phase to ∼ 10 −3 over the LIGO bandwidth [16], these perturbation expansions must be calculated to high order. If we consider a circular orbit in the adiabatic approximation, the signal phase Φ(ω) is related to the orbital energy E(ω) and the radiated power P (ω) through the relation d 2 Φ/dω 2 ∼ (dE/dω)/P . An accuracy of ∼ 10 −3 in the cumulative orbital phase, over the LIGO bandwidth, can be achieved if the perturbation expansion is calculated to O(v 6 ) beyond Newtonian dynamics i.e., at third post-Newtonian order (3PN) [9,17]....

Using effective field theory techniques we calculate the source multipole moments needed to obtain the spin contributions to the power radiated in gravitational waves from inspiralling compact binaries to third Post-Newtonian order (3PN). The multipoles depend linearly and quadratically on the spins and include both spin (1)spin(2) and spin (1)spin(1) components.The results in this paper provide the last missing ingredient required to determine the phase evolution to 3PN including all spin effects which we will report in a separate paper.