## I-Love-Q Probes of Modied Gravity

*By Toral Gupta, Barun Majumder, Kent Yagi, and Nicolás Yunes*

Although General Relativity has passed all tests carried out so far with flying colors, probes of the *extreme gravity* regime, where the gravitational interaction is simultaneously strong, non-linear and highly dynamical, have only recently began. This is timely because attempts to reconcile general relativity with quantum mechanics, be it in the form of string theory or loop quantum gravity, and attempts to explain cosmological observations, be it in the early or late universe, may require modifications to Einstein’s general theory. New electromagnetic telescopes, like the Neutron Star Interior Composition Explorer, and gravitational wave detectors, like advanced LIGO and Virgo, can now provide the first detailed observations of the extreme gravity regime. These new telescopes herald the era of extreme experimental relativity, allowing for new stringent constraints of deviations from Einstein’s theory, or perhaps, if we are lucky, pointing to signals of departures.

Where do we stand today regarding tests of extreme gravity? The most stringent tests have come from the recent observations of the gravitational waves produced in the merger of black holes and the merger of neutron stars by the LIGO/Virgo collaboration. Perhaps the most striking of this is the confirmation that gravitational waves travel at a speed that (i) is constant (i.e. independent of the frequency of the wave), and (ii) is equal to the speed of light. This test, however, could not constrain the possibility that gravity is parity-violating, a manifestation of which would be that waves of opposite helicity travel at different speeds. A toy model to explore gravitational parity violation is dynamical Chern-Simons gravity, an effective field theory that introduces a parity-violating dynamical scalar field through its coupling to a curvature invariant.

A possible way to constrain gravitational parity violation in the future is to combine gravitational wave observations of neutron star mergers with X-ray, or radio observations of pulsars. Gravitational waves produced by neutron stars encode their Love number, a measure of how much a star tidally deforms when in the presence of the external gravitational field produced by its companion. X-rays produced by hot spots on the surface of rotating neutron stars encode their stellar shape, and in particular their radius, moment of inertia *I,* and perhaps even their quadrupole moment *Q*. Radio observations of binary pulsars can encode spin-orbit precessional effects, which in turn depend on the moment of inertia of the pulsars. Therefore, gravitational wave observations and either X-ray or radio observations can provide the simultaneous measurement of the moment of inertia, the Love number, and maybe even the quadrupole moment.

How do we use these measurements to test gravity? In principle, the moment of inertia, the Love number, and the quadrupole moment depend sensitively on the currently unknown, equation of state of supranuclear matter. Recently, however, two of us showed that these quantities satisfy inter-relations, the so-called *I-Love-Q relations* in General Relativity, that are approximately insensitive to the equation of state. Moreover, we theorised that these relations would remain approximately equation-of-state insensitive in modified gravity, but not necessarily in the same way as in General Relativity. Therefore, the simultaneous measurement of two elements of the I-Love-Q trio would suffice to carry out a null test of Einstein’s theory in an equation-of-state insensitive way.

We confirmed this hypothesis in parity-violating gravity, using dynamical Chern-Simons theory as an effective model, in our recent Classical and Quantum Gravity paper. After calculating the moment of inertia, the Love number and the rotational quadrupole moment in this theory for a wide range of equations of state, we verified that the I-Love-Q relations in this theory remain approximately equation of state independent provided one properly normalizes the dimensional coupling constant of the theory. Moreover, we found that these parity-violating I-Love-Q relations differ from those in General Relativity in a way directly proportional to the normalized coupling constant of the theory. Therefore, the future measurement of two elements of the I-Love-Q trio can be used to constrain parity violation stringently. In particular, a reasonable measurement of the moment of inertia and of the Love number would allow for constraints on parity violation that are millions of times more stringent than current Solar System and table-top constraints; these bounds are in fact not very sensitive to the measurement accuracy of these observables, as shown in the figure above. Our Classical and Quantum Gravity paper therefore shows how powerful the universal I-Love-Q relations can be to probe extreme gravity with neutron star observations.

About the authors;

- Toral Gupta is a graduate student at Indian Institute of Technology Gandhinagar.
- Barun Majumder is a research assistant at Wilfrid Laurier University.
- Kent Yagi is an assistant professor at University of Virginia.
- Nicolás Yunes is an associate professor at Montana State University.

Read the full article “I-Love-Q relations for neutron stars in dynamical Chern Simons gravity” here.

This work is licensed under a Creative Commons Attribution 3.0 Unported License.