Parametrized tests of general relativity using eccentric compact binaries

Astrophysical population simulations predict that a subset of dynamically formed binary black holes (BBHs) may possess eccentricity $\gtrsim 0.1$ at a gravitational wave (GW) frequency of $10 \,\text{Hz}$. Presently, the LIGO-Virgo-KAGRA (LVK) Collaboration tests general relativity (GR) assuming that the binary eccentricity has decayed well before it enters the detector's frequency band. Previous works have shown that binary eccentricity can bias GR tests if unaccounted for. Here we develop two methods to extend parametrized tests of GR to eccentric binaries. The first method extends the standard null parametrized test for quasicircular binaries by adding fractional deviations at each post-Newtonian (PN) order in the eccentric part of the GW phasing (assuming the small-eccentricity limit). Simultaneous measurement of the circular and eccentric deviation parameters ($\delta\hat{\varphi}, \delta\hat{\varphi}^e$) allows us to constrain deviations from GR for eccentric binaries. While strong constraints on the deviation parameters are not achievable with LIGO's projected sensitivity, the multibanding of LISA and CE observations can constrain these deviations to $|\delta\hat{\varphi}_2| \lesssim 3 \times 10^{-3}$ and $|\delta\hat{\varphi}^e_2|\lesssim 2\times 10^{-2}$. The second method looks for GR deviations in the rate of periastron advance ($\Delta\alpha$). The parameter $\Delta\alpha$ ($\Delta\alpha^{\rm GR} \to 0$) can be constrained with LIGO to $|\Delta\alpha|\lesssim 4 \times 10^{-2}$ (with $1 \sigma$ confidence). Multiband sources observed by LISA and CE provide an improved constraint of $|\Delta\alpha|\lesssim 3\times 10^{-5}$. The space-based detector DECIGO provides the best constraint on $\Delta\alpha$ with $|\Delta\alpha|\lesssim 8 \times 10^{-6}$.