Gravitational waveform and polarization from binary black hole inspiral in dynamical Chern-Simons gravity: from generation to propagation

Abstract

We calculate the gravitational waveform radiated from spinning black holes (BHs) binary in dynamical Chern-Simons (dCS) gravity. The equation of motion (EOM) of the spinning binary BHs is derived based on the modified Mathisson-Papapetrou-Dixon equation for the spin-aligned circular orbits. The leading-order effects induced by the dCS theory contain spin-spin interaction and monopole-quadrupole interaction, which influences both the EOM of the binary system and corresponding gravitational waveform at the second post-Newtonian (PN) order (i.e., 2PN order). After reporting the waveforms, we investigate the polarization modes of gravitational waves (GWs) in dCS theory. None of the extra modes appears in this theory up to the considered PN order. Moreover, since the time scale of the binary merger is much smaller than that of the cosmological expansion, the parity-violating effect of the dCS theory does not appear in the process of GW generation. However, during the process of GW propagation, amplitude birefringence, a typical parity-violating effect, makes plus and cross modes convert to each other, which modifies the gravitational waveform at 1.5PN order.

Gravitational radiation from eccentric binary black hole system in dynamical Chern-Simons gravity

“…Modified gravitational waveforms have been derived in various extended gravitational theories for quasi-circular [138][139][140][141][142][143][144][145] and quasi-elliptic [146][147][148] binary systems at the leading Newtonian order, that is the leading-order beyond-GR modification and the sub-leading effects are negligible. Unlike the above theories, as a kind of parity-violating theory [133,[149][150][151], dynamical Chern-Simons (DCS) gravity [152,153] modifies the waveform from BBH at 2PN approximation, leaving behind a lower-order waveform that is completely consistent with GR [154][155][156][157]. The template under quasi-circular and spin-aligned assumption has been reported in our previous works [156,157].…”

“…One of the most important predictions is that the amplitude of the left-handed circular polarization mode of GWs increases (or decreases) during the propagation while the amplitude of the right-handed mode decreases (or increases). This phenomenon is always called amplitude birefringence of GWs [133,153,157]. The similar phenomenons (as well as the velocity birefringence) are investigated in other parity-violating theories, such as ghost-free parity-violating theory [159,160], Nieh-Yan gravity [149,150,161,162], Hořava-Lifshitz gravity [163][164][165], parity-violating symmetric teleparallel gravity [151,166,167], spatially covariant gravity [136,168,169], and reviewed by refs.…”

“…Unlike the above theories, as a kind of parity-violating theory [133,[149][150][151], dynamical Chern-Simons (DCS) gravity [152,153] modifies the waveform from BBH at 2PN approximation, leaving behind a lower-order waveform that is completely consistent with GR [154][155][156][157]. The template under quasi-circular and spin-aligned assumption has been reported in our previous works [156,157]. Then, the quasi-Keplerian case is taken into consideration in this JCAP05(2024)073 paper, including the periastron advance but still assuming the spin vectors to be aligned with the orbital angular momentum (OAM).…”

Landau damping for gravitational waves in parity-violating theories

“…In this respect, a possible choice JCAP02(2023)009 is represented by theories of gravity exhibiting parity violation, where the propagation of the two circular polarization modes (left and right handed states [19]), is described by different equations of motion. This leads to the so called gravitational birefringence [52][53][54][55][56][57][58][59][60][61][62], which consists in different behaviour for the amplitude and the phase/group velocity of each polarization state. In particular, phase velocity is usually affected in such a way that its expression for left and right modes differs from GR for corrections of opposite sign.…”

Scalar induced gravitational waves from Chern-Simons gravity during inflation era

“…It was first proposed by embedding the three-dimensional CS term into the four-dimensional GR [80]. Since then, the GWs and cosmology have been studied extensively in the CS gravity [81][82][83][84][85][86][87][88][89][90][91][92][93][94] and other parity-violating gravity theories, such as the Nieh-Yan term [95][96][97][98][99][100][101][102][103][104], as well as in more general models with non-vanishing torsion and/or non-metricity tensors [105][106][107][108][109][110][111][112]. Interestingly, the GWs in PV gravity show diverse features that are different from GR, such as the velocity and amplitude birefringence phenomena of GWs [113][114][115][116][117][118][119].…”