Post-Newtonian (PN) theory for inspiraling compact binary systems has been extremely successful in generating waveforms in general relativity (GR). However, if we are interested in testing GR, it would be very useful to have a bank of waveform templates for alternative theories of gravity as well. This program has already begun in a class of massless scalar-tensor theories (equivalent to DEF gravity), which is arguably one of the simplest alternative to GR. Previously, the equations of motion have been computed up to 3PN order [1-3], and the orbital phase has been computed for circular orbits up to 2.5PN beyond the leading dipolar order [4-7]. With the objective of widening the parameter space modeled, I will present in this talk recent advances for the case of elliptic orbits. First, I will present the post-Keplerian parametrization for quasielliptic motion up to 2PN order in scalar-tensor theories [8], and discuss how this can straightforwardly be adapted to other theories. I will show how this easily leads to obtaining the gravitational waveform at 1PN relative order for eccentric orbits [8]. Then, I will present ongoing work [9] aiming at increasing the accuracy of the waveform model. I will focus on the computation of the flux (radiated at infinity) of energy and angular momentum up to 2.5PN order, relatively to the leading dipolar radiation. These quantities exhibit a number of new difficulties, among which the presence of tails and memory contributions. Finally, I will discuss how to combine the post-Keplerian parametrization and these fluxes to deduce the secular evolution of the orbital parameters (e.g. the semimajor axis and eccentricity) through 2.5PN order. These physically correspond to the (modulated) chirp in the waveform frequency, which is a key observable for gravitational wave detectors.
[1] Mirshekari and Will, Phys. Rev. D 87, 084070 (2013), arXiv:1301.4680
[2] Bernard, Phys. Rev. D 98, 044004 (2018), arXiv:1802.10201
[2] Bernard, Phys. Rev. D 99, 044047 (2019), arXiv:1812.04169
[4] Lang, Phys. Rev. D 89, 084014 (2014), arXiv:1310.3320
[5] Lang, Phys. Rev. D 91, 084027 (2015), arXiv:1411.3073
[6] Sennett, Marsat and Buonanno, Phys.Rev.D 94, 084003 (2016), arXiv:1607.01420
[7] Bernard, Blanchet and Trestini, JCAP 08, 008 (2022), arXiv:2201.10924
[8] Trestini, Phys. Rev. D 109, 104003 (2024), arXiv:2401.06844
[9] Trestini (2024), in preparation
Jacopo Mazza
