A design study is currently in progress for a third-generation gravitational-wave (GW) detector called the Einstein Telescope (ET). An important kind of source for ET will be the inspiral and merger of binary neutron stars up to $z\sim 2$. If binary neutron star mergers are the progenitors of short-hard $\gamma$-ray bursts, then some fraction of them will be seen both electromagnetically and through GW, so that the luminosity distance and the redshift of the source can be determined separately. An important property of these “standard sirens” is that they are self-calibrating: the luminosity distance can be inferred directly from the GW signal, with no need for a cosmic distance ladder. Thus, standard sirens will provide a powerful independent check of the $\Lambda \mathrm{CDM}$ model. In previous work, estimates were made of how well ET would be able to measure a subset of the cosmological parameters (such as the dark energy parameter $w_0$) it will have access to, assuming that the others had been determined to great accuracy by alternative means. Here we perform a more careful analysis by explicitly using the potential Planck cosmic microwave background data as prior information for these other parameters. We find that ET will be able to constrain $w_0$ and $w_a$ with accuracies $\Delta w_0=0.099$ and $\Delta w_a=0.302$, respectively. These results are compared with projected accuracies for the JDEM baryon acoustic oscillations project and the SNAP type Ia supernovae observations.

In this paper, we investigate a kind of special quintom model, which is made of a quintessence field ${\varphi }_1$ and a phantom field ${\varphi }_2$, and the potential function has the form of $V({\varphi }_1^2-{\varphi }_2^2)$. This kind of quintom field can be separated into two kinds: the hessence model, which has the state of ${\varphi }_1^2>{\varphi }_2^2$, and the hantom model with the state ${\varphi }_1^2<{\varphi }_2^2$. We discuss the evolution of these models in the $\omega \mathrm{\text{−}}{\omega }^{\prime }$ plane ($\omega$ is the state equation of the dark energy, and ${\omega }^{\prime }$ is its time derivative in units of Hubble time), and find that according to $\omega >-1$ or $<-1$, and the potential of the quintom being climbed up or rolled down, the $\omega \mathrm{\text{−}}{\omega }^{\prime }$ plane can be divided into four parts. The late time attractor solution, if existing, is always quintessencelike or $\Lambda$-like for hessence field, so the big rip does not exist. But for hantom field, its late time attractor solution can be phantomlike or $\Lambda$-like, and sometimes, the big rip is unavoidable. Then we consider two special cases: one is the hessence field with an exponential potential, and the other is with a power law potential. We investigate their evolution in the $\omega \mathrm{\text{−}}{\omega }^{\prime }$ plane. We also develop a theoretical method of constructing the hessence potential function directly from the effective equation-of-state function $\omega (z)$. We apply our method to five kinds of parametrizations of equation-of-state parameter, where $\omega$ crossing $-1$ can exist, and find they all can be realized. At last, we discuss the evolution of the perturbations of the quintom field, and find the perturbations of the quintom ${\delta }_Q$ and the metric $\Phi$ are all finite even at the state of $\omega =-1$ and ${\omega }^{\prime }\ne 0$.

We use the Fisher information matrix to investigate the angular resolution and luminosity distance uncertainty for coalescing binary neutron stars (BNSs) and neutron star-black hole binaries (NSBHs) detected by the third-generation (3G) gravitational-wave (GW) detectors. Our study focuses on an individual 3G detector and a network of up to four 3G detectors at different locations including the United States, Europe, China, and Australia for the proposed Einstein Telescope (ET) and Cosmic Explorer (CE) detectors. In particular, we examine the effect of the Earth’s rotation, as GW signals from BNS and low-mass NSBH systems could be hours long for 3G detectors. In this case, an individual detector can be effectively treated as a detector network with long baselines formed by the trajectory of the detector as it rotates with the Earth. Therefore, a single detector or two-detector networks could also be used to localize the GW sources effectively. We find that a time-dependent antenna beam-pattern function can help better localize BNS and NSBH sources, especially edge-on ones. The medium angular resolution for one ET-D detector is around $150{\mathrm{deg}}^2$ for BNSs at a redshift of $z=0.1$, which improves rapidly with a decreasing low-frequency cutoff $f_{\mathrm{low}}$ in sensitivity. The medium angular resolution for a network of two CE detectors in the United States and Europe, respectively, is around $20{\mathrm{deg}}^2$ at $z=0.2$ for the simulated BNS and NSBH samples. While for a network of two ET-D detectors, the similar angular resolution can be achieved at a much higher redshift of $z=0.5$. The angular resolution of a network of three detectors is mainly determined by the baselines between detectors regardless of the CE or ET detector type. The medium angular resolution of BNS for a network of three detectors of the ET-D or CE type in the United States, Europe, and Australia is around $10{\mathrm{deg}}^2$ at $z=2$. We discuss the implications of our results for multimessenger astronomy and, in particular, for using GW sources as independent tools to constrain the Hubble constant $H_0$, the deceleration parameter $q_0$, and the equation-of-state (EoS) of dark energy. We find that, in general, if 10 BNSs or NSBHs at $z=0.1$ with known redshifts are detected by 3G networks consisting of two ET-like detectors, $H_0$ can be measured with an accuracy of 0.9%. If 1000 face-on BNSs at $z<2$ are detected with known redshifts, we are able to achieve $\mathrm{\Delta }{q}_0=0.002$ for the deceleration parameter, or $\mathrm{\Delta }{w}_0=0.03$ and $\mathrm{\Delta }{w}_a=0.2$ for EoS of dark energy, respectively.

As an extension of our previous work [J. Qiao , arXiv:1909.03815.], in this article, we calculate the effects of parity violation on gravitational-wave (GW) waveforms during their propagation in the most general parity-violating gravities, including Chern-Simons modified gravity, ghost-free scalar-tensor gravity, the symmetric teleparallel equivalence of General Relativity theory, Hořava-Lifshitz gravity, and so on. For this purpose, we consider the GWs generated by the coalescence of compact binaries and concentrate on the imprints of the parity violation in the propagation of GWs. With a unified description of GW in the theories of parity-violating gravity, we study the effects of velocity and amplitude birefringence on the GW waveforms. Decomposing the GWs into the circular polarization modes, the two birefringence effects exactly correspond to the modifications in phase and amplitude of GW waveforms, respectively. We find that, for each circular polarization mode, the amplitude, phase, and velocity of GW can be modified by both the parity-violating terms and parity-conserving terms in gravity. Therefore, in order to test the parity symmetry in gravity, we should compare the difference between two circular polarization modes, rather than measure an individual mode. Combining two circular modes, we obtain the GW waveforms in the Fourier domain and obtain the deviations from those in General Relativity. The GW waveforms derived in this paper are also applicable to the theories of parity-conserving gravity, which have the modified dispersion relations (e.g., massive gravity, double special relativity theory, extra-dimensional theories, etc.) or/and have the modified friction terms (e.g., nonlocal gravity, gravitational theory with time-dependent Planck mass, etc.).

We study primordial gravitational waves in the Horava-Lifshitz theory of quantum gravity, in which high-order spatial derivative operators, including the ones violating parity, generically appear in order for the theory to be power-counting renormalizable and ultraviolet complete. Because of both parity violation and the nonadiabatic evolution of the modes due to a modified dispersion relationship, a large polarization of primordial gravitational waves becomes possible, and it could be well within the range of detection of the BB, TB and EB power spectra of the forthcoming cosmic microwave background observation, where T, E, and B stand, respectively, the different components of the polarization of the cosmic microwave background radiation.

Measurement of pulsar timing residuals provides a direct way to detect relic gravitational waves at the frequency $f\sim 1/\mathrm{yr}$. In this paper, we investigate the constraints on the inflationary parameters, the tensor-to-scalar ratio $r$, and the tensor spectral index $n_t$, by the current and future pulsar timing arrays. We find that the Five-hundred-meter Aperture Spherical Radio Telescope in China and the planned Square Kilometre Array projects have fairly strong abilities to test the phantomlike inflationary models. If $r=0.1$, then Five-hundred-meter Aperture Spherical Radio Telescope could give the constraint on the spectral index $n_t<0.56$ and Square Kilometre Array could give $n_t<0.32$, while an observation with total time $T=20\mathrm{yr}$, pulsar noise level ${\sigma }_w=30\mathrm{ns}$, and monitored pulsar number $n=200$ could even constrain $n_t<0.07$. These are much tighter than those inferred from the current results of the Parkes Pulsar Timing Array, European Pulsar Timing Array, and North American Nanohertz Observatory for Gravitational Waves. By studying the effects of various observational factors on the sensitivities of pulsar timing arrays, we find that compared with ${\sigma }_w$ and $n$, the total observation time $T$ has the most significant effect.