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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, substantial uncertainty about the dense matter equation of state (EoS) remains. In this work, we present a semiparametric equation of state 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 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 Gaussian Process 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. We find that maximum TOV masses above $$3.2 M_{\odot}$$ can be supported by causal EoS compatible with nuclear constraints at low densities. We then combine information from existing observations of heavy pulsar masses, gravitational waves emitted from binary neutron star mergers, and X-ray pulse profile modeling of millisecond pulsars within a Bayesian inference scheme using our semiparametric EoS prior. With information from all public NICER pulsars (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 $$P(2\rho_{\rm nuc}) = 1.98^{+2.13}_{-1.08}\times10^{34}$$ dyn/cm$$^{2}$$, a radius of a $$1.4 M_{\odot}$$ neutron star value of $$R_{1.4} = 11.4^{+0.98}_{-0.60}$$\;km, and $$M_{\rm max} = 2.31_{-0.23}^{+0.35} M_{\odot}$$ at the 90\% credible level. 

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.