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Abstract Over the past decade, an abundance of information from neutron-star observations, nuclear experiments and theory has transformed our efforts to elucidate the properties of dense matter. However, at high densities relevant to the cores of neutron stars (NSs), substantial uncertainty about the dense matter equation of state (EoS) remains. In this work, we present a semiparametric EoS framework aimed at better integrating knowledge across these domains in astrophysical inference. We use a meta-model and realistic crust at low densities, and Gaussian process (GP) extensions at high densities. Comparisons between our semiparametric framework to fully nonparametric EoS representations show that imposing nuclear theoretical and experimental constraints through the meta-model up to nuclear saturation density results in constraints on the pressure up to twice nuclear saturation density. We also show that our GP trained on EoS models with nucleonic, hyperonic, and quark compositions extends the range of EoS explored at high density compared to a piecewise polytropic extension schema, under the requirements of causality of matter and of supporting the existence of heavy pulsars (PSRs). We find that maximum Tolman–Oppenheimer–Volkoff masses above $3.2{\mathrm{M}}_{\odot }$can be supported by causal EoS compatible with nuclear constraints at low densities. We then combine information from existing observations of heavy PSR masses, gravitational waves emitted from binary NS mergers, and x-ray pulse profile modeling of millisecond PSRs within a Bayesian inference scheme using our semiparametric EoS prior. With information from all public NS Interior Composition ExploRer PSRs (including PSR J0030+0451, PSR J0740+6620, PSR J0437–4715, and PSR J0614–3329), we find an astrophysically favored pressure at two times nuclear saturation density of $P\left(2{\rho }_{\mathrm{nuc}}\right)={1.98}_{-1.08}^{+2.13}\times {10}^{34}$dyn cm⁻², a radius of a $1.4{\mathrm{M}}_{\odot }$NS value of $R_{1.4}={11.4}_{-0.60}^{+0.98}$ km, and $M_{\max }={2.31}_{-0.23}^{+0.35}{\mathrm{M}}_{\odot }$at the 90% credible level (C.L). 

The equation of state dependence of a neutron star’s astrophysical features is key to our understanding of isospin asymmetric and dense matter. There exists a series of almost equation of state independent relations reported in the literature, called quasiuniversal relations, that are used to determine neutron star radii and moments of inertia from x-ray and gravitational wave signals. Using sets of equations of state constrained by multimessenger astronomy measurements and nuclear-physics theory, we discuss quasiuniversal relations in the context of future gravitational wave detectors Cosmic Explorer and Einstein Telescope, and the Spectroscopic Time-Resolving Observatory for Broadband Energy X-rays.. We focus on relations that involve the moment of inertia 𝐼, the tidal deformability Λ, and the compactness 𝐶: 𝐶⁡(Λ), 𝐼⁡(Λ), and 𝐼⁡(𝐶). The quasiuniversal fits and their associated errors are constructed with three different microphysics approaches which include state of the art nuclear physics theory and astrophysical constraints. Gravitational-wave and x-ray signals are simulated with the sensitivity of the next generation of detectors. Equation of state inference on those simulated signals is compared to determine if it will offer a better precision on the extraction of a neutron star’s macroscopic parameters than quasiuniversal relations. We confirm that the relation 𝐼⁡(Λ) offers a more pronounced universality than relations involving the compactness regardless of the equation of state set. We show that detections with the third generation of gravitational wave detectors and future x-ray detectors will be sensitive to the fit error marginalization technique. We also find that the sensitivity of those detectors will be sufficient in that using full equation of state distributions leads to significantly better precision on extracted parameters than quasiuniversal relations. We also note that nuclear physics theory offers a more pronounced equation of state invariance of quasiuniversal relations than current astrophysical constraints. 

Abstract We demonstrate how to quantify the frequency-domain amplitude and phase accuracy of waveform models, δ A and δφ , in a form that could be marginalized over in gravitational-wave inference using techniques currently applied for quantifying calibration uncertainty. For concreteness, waveform uncertainties affecting neutron-star inspiral measurements are considered, and post-hoc error estimates from a variety of waveform models are made by comparing time-domain and frequency-domain analytic models with multiple-resolution numerical simulations. These waveform uncertainty estimates can be compared to GW170817 calibration envelopes or to Advanced LIGO and Virgo calibration goals. Signal-specific calibration and waveform uncertainties are compared to statistical fluctuations in gravitational-wave observatories, giving frequency-dependent modeling requirements for detectors such as Advanced LIGO Plus, Cosmic Explorer, or Einstein Telescope. Finally, the distribution of waveform error for the GW170817 posterior is computed from tidal models and compared to the constraints on δφ or δ A from GWTC-1 by Edelman et al. In general, δφ and δ A can also be interpreted in terms of unmodeled astrophysical energy transfer within or from the source system. 

Cosmic Explorer is a next-generation ground-based gravitational-wave observatory that is being designed in the 2020s and is envisioned to begin operations in the 2030s together with the Einstein Telescope in Europe. The Cosmic Explorer concept currently consists of two widely separated L-shaped observatories in the United States, one with 40 km-long arms and the other with 20 km-long arms. This order of magnitude increase in scale with respect to the LIGO-Virgo-KAGRA observatories will, together with technological improvements, deliver an order of magnitude greater astronomical reach, allowing access to gravitational waves from remnants of the first stars and opening a wide discovery aperture to the novel and unknown. In addition to pushing the reach of gravitational-wave astronomy, Cosmic Explorer endeavors to approach the lifecycle of large scientific facilities in a way that prioritizes mutually beneficial relationships with local and Indigenous communities. This article describes the (scientific, cost and access, and social) criteria that will be used to identify and evaluate locations that could potentially host the Cosmic Explorer observatories. 

The ground-based gravitational wave (GW) detectors LIGO and Virgo have enabled the birth of multi-messenger GW astronomy via the detection of GWs from merging stellar-mass black holes (BHs) and neutron stars (NSs). GW170817, the first binary NS merger detected in GWs and all bands of the electromagnetic spectrum, is an outstanding example of the impact that GW discoveries can have on multi-messenger astronomy. Yet, GW170817 is only one of the many and varied multi-messenger sources that can be unveiled using ground-based GW detectors. In this contribution, we summarize key open questions in the astrophysics of stellar-mass BHs and NSs that can be answered using current and future-generation ground-based GW detectors, and highlight the potential for new multi-messenger discoveries ahead. 

Abstract Ground-based gravitational-wave detectors like Cosmic Explorer (CE) can be tuned to improve their sensitivity at high or low frequencies by tuning the response of the signal extraction cavity. Enhanced sensitivity above 2 kHz enables measurements of the post-merger gravitational-wave spectrum from binary neutron star mergers, which depends critically on the unknown equation of state of hot, ultra-dense matter. Improved sensitivity below 500 Hz favors precision tests of extreme gravity with black hole ringdown signals and improves the detection prospects while facilitating an improved measurement of source properties for compact binary inspirals at cosmological distances. At intermediate frequencies, a more sensitive detector can better measure the tidal properties of neutron stars. We present and characterize the performance of tuned CE configurations that are designed to optimize detections across different astrophysical source populations. These tuning options give CE the flexibility to target a diverse set of science goals with the same detector infrastructure. We find that a 40 km CE detector outperforms a 20 km in all key science goals other than access to post-merger physics. This suggests that CE should include at least one 40 km facility. 

Abstract Gravitational-wave observations by the laser interferometer gravitational-wave observatory (LIGO) and Virgo have provided us a new tool to explore the Universe on all scales from nuclear physics to the cosmos and have the massive potential to further impact fundamental physics, astrophysics, and cosmology for decades to come. In this paper we have studied the science capabilities of a network of LIGO detectors when they reach their best possible sensitivity, called A ${}^{♯}$, given the infrastructure in which they exist and a new generation of observatories that are factor of 10 to 100 times more sensitive (depending on the frequency), in particular a pair of L-shaped cosmic explorer (CE) observatories (one 40 km and one 20 km arm length) in the US and the triangular Einstein telescope with 10 km arms in Europe. We use a set of science metrics derived from the top priorities of several funding agencies to characterize the science capabilities of different networks. The presence of one or two A ${}^{♯}$observatories in a network containing two or one next generation observatories, respectively, will provide good localization capabilities for facilitating multimessenger astronomy (MMA) and precision measurement of the Hubble parameter. Two CE observatories are indispensable for achieving precise localization of binary neutron star events, facilitating detection of electromagnetic counterparts and transforming MMA. Their combined operation is even more important in the detection and localization of high-redshift sources, such as binary neutron stars, beyond the star-formation peak, and primordial black hole mergers, which may occur roughly 100 million years after the Big Bang. The addition of the Einstein Telescope to a network of two CE observatories is critical for accomplishing all the identified science metrics including the nuclear equation of state, cosmological parameters, the growth of black holes through cosmic history, but also make new discoveries such as the presence of dark matter within or around neutron stars and black holes, continuous gravitational waves from rotating neutron stars, transient signals from supernovae, and the production of stellar-mass black holes in the early Universe. For most metrics the triple network of next generation terrestrial observatories are a factor 100 better than what can be accomplished by a network of three A ${}^{♯}$observatories. 

This white paper describes the research and development needed over the next decade to realize "Cosmic Explorer," the U.S. node of a future third-generation detector network that will be capable of observing and characterizing compact gravitational-wave sources to cosmological redshifts.