Cosmology with Love

The field of gravitational waves (GWs) has moved swiftly after the 2015 direct discovery by the Laser Interferometer Gravitational-wave Observatory (LIGO). The number of GW events have since increased by more than an order of magnitude. Another milestone was reached in 2017 when GWs from a binary neutron star (BNS) inspiral was followed by a short gamma-ray burst (sGRB), and the optical counterpart called a kilonova. The science output of this joint observation was rich with implications for strong-field gravity, astrophysics, fundamental physics, and cosmology.

Thus far, traditional probes of cosmology have been limited to those of electromagnetic (EM) origin. The ones that have been most constraining include the measurements done using type Ia supernovae (SNe Ia) and the cosmic microwave background (CMB). The above mentioned joint observation of GWs and the host galaxy of the kilonova led to an independent measurement of the Hubble constant and the birth of GW cosmology. Having multiple probes measure the same cosmological parameters is important, since it gives confidence in the correctness of the models, and consistency in the impacts on different probes. In addition, it also puts tighter constraints compared to measurements from individual probes. One important cosmological parameter that determines the rate of expansion of the Universe is the Hubble constant. Unfortunately, today the state-of-the-art measurements of the Hubble constant find a discrepancy in the value inferred from SNe Ia versus that from the CMB. While the difference is small, under 10% of either measurement, it is an open debate whether the difference is a failure of the cosmological model or a systematic effect in the measurement that is unaccounted for. At this juncture, measurements of the Hubble constant using a third independent probe of GWs could provide an answer to the discrepancy.

Strong constraints on cosmology using GWs is, however, only possible in the case of a coincident EM counterpart. Discovering the counterpart is a challenge, and these joint detections will likely not become commonplace any time soon. The first joint detection in 2017 remains the only one, although the number of GW events has been steadily growing. Thus, a procedure to do this measurement without the criterion of joint detection is desired going ahead. 

To this end, we have shown that the tidal deformation of inspiralling neutron stars in the moments before their merger encodes the information about the Hubble constant. The GW waveform from BNS systems has a tidal deformability parameter that is dictated by the fundamental composition of the neutron stars. An otherwise analogous binary black hole waveform lacks this feature. But the problem is further complicated because the tidal deformability depends on the internal composition of the stars, and there are several models that relate the mass and the tidal deformability of a neutron star. However, Yagi and Yunes have shown that there are certain parameterizations of this relation that are independent of the details of the microscopic model. In this new work, we demonstrate the use of these relations in the context of measuring the Hubble constant.

We use a relation between the mass and tidal deformability that dramatically reduces the complexity of the problem of using different microscopic models, and we show for the first time that measurement of the Hubble constant is possible. Using several synthetic signals we show that in the next generation of GW detectors, when BNSs are detected in much greater numbers and to much farther distances than today, our prescription will lead to a 2% constraint in Hubble constant, which is comparable with the established EM probes today. This result is relevant for future research, because kilanovae that are farther away will become progressively harder to detect, making the currently used technique of joint detection more difficult to use.

This work is published in Phys. Rev. D 104, October 19, 2021.