We investigate the constraint ability of the gravitational wave (GW) as the standard siren on the cosmological parameters by using the third-generation gravitational wave detector: the Einstein Telescope. The binary merger of a neutron with either a neutron or black hole is hypothesized to be the progenitor of a short and intense burst of γ rays, some fraction of those binary mergers could be detected both through electromagnetic radiation and gravitational waves. Thus we can determine both the luminosity distance and redshift of the source separately. We simulate the luminosity distances and redshift measurements from 100 to 1000 GW events. We use two different algorithms to constrain the cosmological parameters. For the Hubble constant H0 and dark matter density parameter Ωm, we adopt the Markov chain Monte Carlo approach. We find that with about 500-600 GW events we can constrain the Hubble constant with an accuracy comparable to Planck temperature data and Planck lensing combined results, while for the dark matter density, GWs alone seem not able to provide the constraints as good as for the Hubble constant; the sensitivity of 1000 GW events is a little lower than that of Planck data. It should require more than 1000 events to match the Planck sensitivity. Yet, for analyzing the more complex dynamical property of dark energy, i.e., the equation of state w, we adopt a new powerful nonparametric method: the Gaussian process. We can reconstruct w directly from the observational luminosity distance at every redshift. In the low redshift region, we find that about 700 GW events can give the constraints of w(z) comparable to the constraints of a constant w by Planck data with type Ia supernovae. Those results show that GWs as the standard sirens to probe the cosmological parameters can provide an independent and complementary alternative to current experiments.

The direct detection of gravitational wave by Laser Interferometer Gravitational-Wave Observatory indicates the coming of the era of gravitational-wave astronomy and gravitational-wave cosmology. It is expected that more and more gravitational-wave events will be detected by currently existing and planned gravitational-wave detectors. The gravitational waves open a new window to explore the Universe and various mysteries will be disclosed through the gravitational-wave detection, combined with other cosmological probes. The gravitational-wave physics is not only related to gravitation theory, but also is closely tied to fundamental physics, cosmology and astrophysics. In this review article, three kinds of sources of gravitational waves and relevant physics will be discussed, namely gravitational waves produced during the inflation and preheating phases of the Universe, the gravitational waves produced during the first-order phase transition as the Universe cools down and the gravitational waves from the three phases: inspiral, merger and ringdown of a compact binary system, respectively. We will also discuss the gravitational waves as a standard siren to explore the evolution of the Universe.

We introduce a model-independent approach to the null test of the cosmic curvature which is geometrically related to the Hubble parameter H(z) and luminosity distance dL(z). Combining the independent observations of H(z) and dL(z), we use the model-independent smoothing technique, Gaussian processes, to reconstruct them and determine the cosmic curvature Ω (0) K in the null test relation. The null test is totally geometrical and does not assume any cosmological model. We show that the cosmic curvature Ω (0) K = 0 is consistent with current observational data sets, falling within the 1σ limit. To demonstrate the effect on the precision of the null test, we produce a series of simulated data of the models with different Ω 98.80.Es, 98.80Jk

We present a nonparametric approach to reconstruct the interaction between dark energy and dark matter directly from SNIa Union 2.1 data using Gaussian processes, which is a fully Bayesian approach for smoothing data. In this method, once the equation of state (w) of dark energy is specified, the interaction can be reconstructed as a function of redshift. For the decaying vacuum energy case with w = −1, the reconstructed interaction is consistent with the standard ΛCDM model, namely, there is no evidence for the interaction. This also holds for the constant w cases from −0.9 to −1.1 and for the Chevallier-Polarski-Linder (CPL) parametrization case. If the equation of state deviates obviously from −1, the reconstructed interaction exists at 95% confidence level. This shows the degeneracy between the interaction and the equation of state of dark energy when they get constraints from the observational data.PACS numbers: 95.36.+x, 98.80.Es

Local determinations of the Hubble constant H0 favour a higher value than Planck based on CMB and ΛCDM. Through a model-independent expansion, we show that low redshift (z 0.7) data comprising baryon acoustic oscillations (BAO), cosmic chronometers and Type Ia supernovae has a preference for Quintessence models that lower H0 relative to ΛCDM. In addition, we confirm that an exponential coupling to dark matter cannot alter this conclusion in the same redshift range. Our results leave open the possibility that a coupling in the matter-dominated epoch, potentially even in the dark ages, may yet save H0 from sinking in the string theory Swampland.

We consider a low redshift (z < 0.7) cosmological data set comprising megamasers, cosmic chronometers, type Ia supernovae and baryon acoustic oscillations, which we bin according to their redshift. For each bin, we read the value of H 0 by fitting directly to the flat ΛCDM model. Doing so, we find that H 0 descends with redshift, allowing one to fit a line with a nonzero slope of statistical significance 2.1σ. Our analysis rests on the use of cosmic chronometers to break a degeneracy in baryon acoustic oscillations data and it will be imperative to revisit this feature as data improves. Nevertheless, our results provide the first independent indication of the descending trend reported by the H0LiCOW Collaboration. If substantiated going forward, early Universe solutions to the Hubble tension will struggle explaining this trend.

We perform a forecast analysis of the ability of the LISA space-based interferometer to reconstruct the dark sector interaction using gravitational wave standard sirens at high redshift. We employ Gaussian process methods to reconstruct the distance-redshift relation in a model independent way. We adopt simulated catalogues of standard sirens given by merging massive black hole binaries visible by LISA, with an electromagnetic counterpart detectable by future telescopes. The catalogues are constructed considering three different astrophysical scenarios for the evolution of massive black hole mergers based on the semianalytic model of E. Barausse, Mon. Not. Roy. Astron. Soc. 423 (2012) 2533. We first use these standard siren datasets to assess the potential of LISA in reconstructing a possible interaction between vacuum dark energy and dark matter. Then we combine the LISA cosmological data with supernovae data simulated for the Dark Energy Survey. We consider two scenarios distinguished by the time duration of the LISA mission: 5 and 10 years. Using only LISA standard siren data, the dark sector interaction can be well reconstructed from redshift z ∼ 1 to z ∼ 3 (for a 5 years mission) and z ∼ 1 up to z ∼ 5 (for a 10 years mission), though the reconstruction is inefficient at lower redshift. When combined with the DES datasets, the interaction is well reconstructed in the whole redshift region from z ∼ 0 to z ∼ 3 (5 yr) and z ∼ 0 to z ∼ 5 (10 yr), respectively. Massive black hole binary standard sirens can thus be used to constrain the dark sector interaction at redshift ranges not reachable by usual supernovae datasets which probe only the z 1.5 range. Gravitational wave standard sirens will not only constitute a complementary and alternative way, with respect to familiar electromagnetic observations, to probe the cosmic expansion, but will also provide new tests to constrain possible deviations from the standard ΛCDM dynamics, especially at high redshift.

Hubble tension is routinely presented as a mismatch between the Hubble constant H 0 determined locally and a value inferred from the flat ΛCDM cosmology. In essence, the tension boils down to a disagreement between two numbers. Here, assuming the tension is cosmological in origin, we predict that within flat ΛCDM there should be other inferred values of H 0 , and that a "running of H 0 with redshift" can be expected. These additional determinations of H 0 may be traced to a difference between the effective equation of state (EoS) of the Universe within the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology framework and the current standard model. We introduce a diagnostic that flags such a running of H 0 .