Effective field theories of gravity and compact binary dynamics: A Snowmass 2021 whitepaper

Abstract

In this whitepaper, I describe modern applications of effective field theory (EFT) techniques to classical and quantum gravity, with relevance to problems in astrophysics and cosmology. As in applications of EFT to high-energy, nuclear, or condensed matter physics, the Wilsonian paradigm based on decoupling of short distance scales via renormalization group evolution remains a powerful organizing principle in the context of gravity. However, the presence of spacetime geometry brings in new elements (e.g. nontrivial time-dependence, cosmological or black hole event horizons) which necessitate the introduction of novel field theoretic methods not usually encountered in applications of EFTs to physics at the energy and intensity frontiers. After a brief overview of recent developments in the application of EFT methods to gravity, I will focus on the EFT description of compact binary dynamics, including an overview of some of its applications to the experimental program in gravitational wave detection at LIGO/VIRGO and other observatories.

Black Hole Tidal Love Numbers and Dissipation Numbers in Worldline Effective Field Theory

“…The effective field theory (EFT) of gravitational wave sources is a theoretical tool for systematic calculations of gravitational waveforms [7][8][9][10][11][12]. Within the EFT each compact object of an inspiraling binary is represented as an effective point particle.…”

Scattering amplitudes and N-body post-Minkowskian Hamiltonians in general relativity and beyond

“…Since finding exact solutions to Einstein's equations for the motion of N compact bodies appears intractable, it is important to consider a broad range of complementary approaches, including analytic methods. This strategy has been quite successful for the 2-body problem where numerical relativity [6][7][8], effective one-body [9,10], and gravitational self-force [11][12][13][14] have been applied in concert with perturbative analyses in post-Newtonian (PN) [15][16][17][18][19][20][21][22], post-Minkowskian (PM) [23][24][25][26][27][28][29][30][31], and non-relativistic general relativity [32][33][34][35][36][37][38][39][40][41][42].…”

“…Recently, new techniques based on powerful tools from theoretical high energy physics, such as scattering amplitudes and effective field theory (EFT), have also been applied to the 2-body problem [43][44][45]. These approaches build on the field theoretic description of gravitons [46][47][48][49][50][51][52][53] by bringing in cutting-edge tools such as the double copy [54][55][56][57][58], on-shell methods [59][60][61][62][63], EFT [32,42,64], and advanced multiloop integration [65][66][67][68][69][70][71][72][73][74]. The program is motivated in large part by advancing the development of highly accurate waveform models for future gravitational wave detectors [75,76]; see e.g.…”

“…The calculation of the 2PN contribution to the 3-body potential was undertaken in [136] and completed in [137]. More recently, by making use of the EFT formalism of [32,42], these results were extended to include 4-body interactions at 2PN order where the result was given in terms of certain un-evaluated Feynman integrals. The 1PM Hamiltonian was calculated in [138], although at this order there are no genuine 3-body interactions.…”

Radiation-reaction in the Effective Field Theory approach to Post-Minkowskian dynamics

“…The successes of current gravitational wave (GW) detectors [2], together with the expected reach of future observatories [3][4][5][6][7][8][9], has reinvigorated various efforts to tackle the perturbative regime of the two-body dynamics in gravity stemming off of "traditional" [10][11][12] as well as those inspired by effective field theory (EFT) techniques [13][14][15][16][17]. In a concerted effort with various other theoretical frameworks, e.g.…”