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In the coming decades, the space-based gravitational-wave (GW) detectors such as Taiji, TianQin, and LISA are expected to form a network capable of detecting millihertz GWs emitted by the mergers of massive black hole binaries (MBHBs). In this work, we investigate the potential of GW standard sirens from the Taiji-TianQin-LISA network in constraining cosmological parameters. For the optimistic scenario in which electromagnetic (EM) counterparts can be detected, we predict the number of detectable bright sirens based on three different MBHB population models, i.e., pop III, Q3d, and Q3nod. Our results show that the Taiji-TianQin-LISA network alone could achieve a constraint precision of 0.9% for the Hubble constant, meeting the standard of precision cosmology. Moreover, the Taiji-TianQin-LISA network could effectively break the cosmological parameter degeneracies generated by the CMB data, particularly in the dynamical dark energy models. When combined with the CMB data, the joint CMB+Taiji-TianQin-LISA data offer σ ( w ) = 0.036 in the w CDM model, which is close to the latest constraint result obtained from the CMB+SN data. We also consider a conservative scenario in which EM counterparts are not available. Due to the precise sky localizations of MBHBs by the Taiji-TianQin-LISA network, the constraint precision of the Hubble constant is expected to reach 1.2%. In conclusion, the GW standard sirens from the Taiji-TianQin-LISA network will play a critical role in helping solve the Hubble tension and shedding light on the nature of dark energy.

Gravitational waves (GWs) from compact binary coalescences encode the absolute luminosity distances of GW sources. Once the redshifts of GW sources are known, one can use the distance-redshift relation to constrain cosmological parameters. One way to obtain the redshifts is to localize GW sources by GW observations and then use galaxy catalogs to determine redshifts from a statistical analysis of redshift information of the potential host galaxies, commonly referred to as the dark siren method. The third-generation (3G) GW detectors are planned to work in the 2030s and will observe numerous compact binary coalescences. Using these GW events as dark sirens requires high-quality galaxy catalogs from future sky survey projects. The China Space Station Telescope (CSST) will be launched in 2024 and will observe billions of galaxies within a 17500 deg 2 survey area with redshift up to z ∼ 4, providing photometric and spectroscopic galaxy catalogs. In this work, we simulate the CSST galaxy catalogs and the 5-year GW data from the 3G GW detectors and combine them to infer the Hubble constant ( H 0 ). Our results show that the measurement precision of H 0 could reach the sub-percent level, meeting the standard of precision cosmology. We conclude that the synergy between CSST and the 3G GW detectors is of great significance in measuring the Hubble constant.

We present a forecast of the cosmological parameter estimation using fast radio bursts (FRBs) from the upcoming Square Kilometre Array (SKA), focusing on the issues of dark energy, the Hubble constant, and baryon density. We simulate 10 5 and 10 6 localized FRBs from a 10-year SKA observation, and find that: (1) using 10 6 FRB data alone can tightly constrain dark-energy equation of state parameters better than CMB+BAO+SNe, providing an independent cosmological probe to explore dark energy; (2) combining the FRB data with gravitational-wave standard siren data from 10-year observation with the Einstein Telescope, the Hubble constant can be constrained to a sub-percent level, serving as a powerful low-redshift probe; (3) using 10 6 FRB data can constrain the baryon density Ω b h to a precision of ∼0.1%. Our results indicate that SKA-era FRBs will provide precise cosmological measurements to shed light on both dark energy and the missing baryon problem, and help resolve the Hubble tension.

We investigate the possibility of phantom crossing in the dark energy sector and the solution for the Hubble tension between early and late universe observations. We use robust combinations of different cosmological observations, namely the Cosmic Microwave Background (CMB), local measurement of Hubble constant (H0), Baryon Acoustic Oscillation (BAO) and SnIa for this purpose. For a combination of CMB+BAO data that is related to early universe physics, phantom crossing in the dark energy sector was confirmed at a 95% confidence level and we obtained the constraint H0=71.0−3.8+2.9 km/s/Mpc at a 68% confidence level, which is in perfect agreement with the local measurement by Riess et al. We show that constraints from different combinations of data are consistent with each other and all of them are consistent with phantom crossing in the dark energy sector. For the combination of all data considered, we obtained the constraint H0=70.25±0.78 km/s/Mpc at a 68% confidence level and the phantom crossing happening at the scale factor am=0.851−0.031+0.048 at a 68% confidence level.

The ΛCDM model provides a good fit to most astronomical observations but harbors large areas of phenomenology and ignorance. With the improvements in the precision and number of observations, discrepancies between key cosmological parameters of this model have emerged. Among them, the most notable tension is the 4σ to 6σ deviation between the Hubble constant (H0) estimations measured by the local distance ladder and the cosmic microwave background (CMB) measurement. In this review, we revisit the H0 tension based on the latest research and sort out evidence from solutions to this tension that might imply new physics beyond the ΛCDM model. The evidence leans more towards modifying the late-time universe.

In the era of precision cosmology, it is essential to determine the Hubble constant empirically with an accuracy of one per cent or better 1 . At present, the uncertainty on this constant is dominated by the uncertainty in the calibration of the Cepheid period–luminosity relationship 2 , 3 (also known as the Leavitt law). The Large Magellanic Cloud has traditionally served as the best galaxy with which to calibrate Cepheid period–luminosity relations, and as a result has become the best anchor point for the cosmic distance scale 4 , 5 . Eclipsing binary systems composed of late-type stars offer the most precise and accurate way to measure the distance to the Large Magellanic Cloud. Currently the limit of the precision attainable with this technique is about two per cent, and is set by the precision of the existing calibrations of the surface brightness–colour relation 5 , 6 . Here we report a calibration of the surface brightness–colour relation with a precision of 0.8 per cent. We use this calibration to determine a geometrical distance to the Large Magellanic Cloud that is precise to 1 per cent based on 20 eclipsing binary systems. The final distance is 49.59 ± 0.09 (statistical) ± 0.54 (systematic) kiloparsecs. A new calibration of the surface brightness–colour relation of eclipsing binary stars gives a distance to the Large Magellanic Cloud that is precise to one per cent.

Gravitational-wave detections provide a novel way to determine the Hubble constant 1 – 3 , which is the current rate of expansion of the Universe. This ‘standard siren’ method, with the absolute distance calibration provided by the general theory of relativity, was used to measure the Hubble constant using the gravitational-wave detection of the binary neutron-star merger, GW170817, by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo 4 , combined with optical identification of the host galaxy 5 , 6 NGC 4993. This independent measurement is of particular interest given the discrepancy between the value of the Hubble constant determined using type Ia supernovae via the local distance ladder (73.24 ± 1.74 kilometres per second per megaparsec) and the value determined from cosmic microwave background observations (67.4 ± 0.5 kilometres per second per megaparsec): these values differ 7 , 8 by about 3 σ . Local distance ladder observations may achieve a precision of one per cent within five years, but at present there are no indications that further observations will substantially reduce the existing discrepancies 9 . Here we show that additional gravitational-wave detections by LIGO and Virgo can be expected to constrain the Hubble constant to a precision of approximately two per cent within five years and approximately one per cent within a decade. This is because observing gravitational waves from the merger of two neutron stars, together with the identification of a host galaxy, enables a direct measurement of the Hubble constant independent of the systematics associated with other available methods. In addition to clarifying the discrepancy between existing low-redshift (local ladder) and high-redshift (cosmic microwave background) measurements, a precision measurement of the Hubble constant is of crucial value in elucidating the nature of dark energy 10 , 11 . Gravitational-wave observations of binary neutron-star mergers will enable precision measurements of the Hubble constant within five years.

The present rate of the expansion of our Universe, the Hubble constant, can be predicted from the cosmological model using measurements of the early Universe, or more directly measured from the late Universe. But as these measurements improved, a surprising disagreement between the two appeared. In 2019, a number of independent measurements of the late Universe using different methods and data provided consistent results, making the discrepancy with the early Universe predictions increasingly hard to ignore.The Hubble constant can be estimated from measurements of both the early and late Universe, but the two estimates disagree. In 2019 a number of independent measurements using different methods made this discrepancy harder to ignore.

The difference from 4 to 6 σ in the Hubble constant (H0) between the values observed with the local (Cepheids and Supernovae Ia, SNe Ia) and the high-z probes (Cosmic Microwave Background obtained by the Planck data) still challenges the astrophysics and cosmology community. Previous analysis has shown that there is an evolution in the Hubble constant that scales as f(z)=H0/(1+z)η, where H0 is H0(z=0) and η is the evolutionary parameter. Here, we investigate if this evolution still holds by using the SNe Ia gathered in the Pantheon sample and the Baryon Acoustic Oscillations. We assume H0=70kms−1Mpc−1 as the local value and divide the Pantheon into three bins ordered in increasing values of redshift. Similar to our previous analysis but varying two cosmological parameters contemporaneously (H0, Ω0m in the ΛCDM model and H0, wa in the w0waCDM model), for each bin we implement a Markov-Chain Monte Carlo analysis (MCMC) obtaining the value of H0 assuming Gaussian priors to restrict the parameters spaces to values we expect from our prior knowledge of the current cosmological models and to avoid phantom Dark Energy models with w<−1. Subsequently, the values of H0 are fitted with the model f(z). Our results show that a decreasing trend with η∼10−2 is still visible in this sample. The η coefficient reaches zero in 2.0 σ for the ΛCDM model up to 5.8 σ for w0waCDM model. This trend, if not due to statistical fluctuations, could be explained through a hidden astrophysical bias, such as the effect of stretch evolution, or it requires new theoretical models, a possible proposition is the modified gravity theories, f(R). This analysis is meant to further cast light on the evolution of H0 and it does not specifically focus on constraining the other parameters. This work is also a preparatory to understand how the combined probes still show an evolution of the H0 by redshift and what is the current status of simulations on GRB cosmology to obtain the uncertainties on the Ω0m comparable with the ones achieved through SNe Ia.

The astronomical event GW170817, detected in gravitational and electromagnetic waves, is used to determine the expansion rate of the Universe, which is consistent with and independent of existing measurements. Hubble constant from colliding neutron stars The gravitational-wave signature of merging black holes or neutron stars yields the distance to the merger. If a counterpart is observed and its recession velocity arising from the Hubble flow is known, then a calibration of the Hubble constant that is entirely independent of the usual 'distance ladder' is possible. The gravitational-wave event of 17 August 2017 (GW170817) corresponded to the merger of two neutron stars, and an associated 'kilonova' was seen. Daniel Holz and the LIGO–Virgo collaboration, along with a group of astronomers involved with the search for the counterpart, have determined that the Hubble constant calculated this way is about 70 kilometres per second per megaparsec. This is consistent with other determinations, but independent of them. On 17 August 2017, the Advanced LIGO 1 and Virgo 2 detectors observed the gravitational-wave event GW170817—a strong signal from the merger of a binary neutron-star system 3 . Less than two seconds after the merger, a γ-ray burst (GRB 170817A) was detected within a region of the sky consistent with the LIGO–Virgo-derived location of the gravitational-wave source 4 , 5 , 6 . This sky region was subsequently observed by optical astronomy facilities 7 , resulting in the identification 8 , 9 , 10 , 11 , 12 , 13 of an optical transient signal within about ten arcseconds of the galaxy NGC 4993. This detection of GW170817 in both gravitational waves and electromagnetic waves represents the first ‘multi-messenger’ astronomical observation. Such observations enable GW170817 to be used as a ‘standard siren’ 14 , 15 , 16 , 17 , 18 (meaning that the absolute distance to the source can be determined directly from the gravitational-wave measurements) to measure the Hubble constant. This quantity represents the local expansion rate of the Universe, sets the overall scale of the Universe and is of fundamental importance to cosmology. Here we report a measurement of the Hubble constant that combines the distance to the source inferred purely from the gravitational-wave signal with the recession velocity inferred from measurements of the redshift using the electromagnetic data. In contrast to previous measurements, ours does not require the use of a cosmic ‘distance ladder’ 19 : the gravitational-wave analysis can be used to estimate the luminosity distance out to cosmological scales directly, without the use of intermediate astronomical distance measurements. We determine the Hubble constant to be about 70 kilometres per second per megaparsec. This value is consistent with existing measurements 20 , 21 , while being completely independent of them. Additional standard siren measurements from future gravitational-wave sources will enable the Hubble constant to be constrained to high precision.