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New insights from the Dark Energy Spectroscopic Instrument (DESI) 2024 baryon acoustic oscillations (BAO) data, in conjunction with cosmic microwave background (CMB) and Type Ia supernova (SN) data, suggest that dark energy may not be a cosmological constant. In this work, we investigate the cosmological implications of holographic dark energy (HDE) and interacting holographic dark energy (IHDE) models, utilizing CMB, DESI BAO, and SN data. By considering the combined DESI BAO and SN data, we determine that in the IHDE model, the parameter $c > 1$ and the dark-energy equation of state $w$ does not cross $-1$ at the $1\sigma$ confidence level, whereas in the HDE model, it marginally falls below this threshold. Upon incorporating CMB data, we observe that in the HDE model, the parameter $c < 1$ and $w$ crosses $-1$ at a level beyond $10\sigma$. Conversely, for the IHDE model, the likelihood of $w$ crossing $-1$ is considerably diminished, implying that the introduction of interaction within the HDE model could potentially resolve or mitigate the cosmic big rip conundrum. Furthermore, our analysis reveals that the HDE and IHDE models are statistically as viable as the $\Lambda$CDM model when assessing Bayesian evidence with DESI BAO data combined with SN data. However, when CMB data are added, the HDE and IHDE models are significantly less favored compared to the $\Lambda$CDM model. Our findings advocate for further exploration of the HDE and IHDE models using forthcoming, more precise late-universe observations., Comment: 13 pages, 5 figures

The Macquart relation and time-delay cosmography are now two promising ways to fast radio burst (FRB) cosmology. In this work, we propose a joint method that combines strongly lensed and unlensed FRBs for improving cosmological parameter estimation by using simulated FRB data from the future sensitive coherent all-sky monitor survey, which is expected to detect a large number of FRBs including galaxy-galaxy strongly lensed events. We find that using a detectable sample of 100,000 localized FRBs including $40$ lensed events can simultaneously constrain the Hubble constant and the equation of state of dark energy, with high precision of $\varepsilon(H_0)=0.4\%$ and $\varepsilon(w)=4.5\%$ in the simplest dynamical dark energy model. The joint analysis of unlensed and lensed FRBs significantly improves the constraint on $H_0$, which could be more effective than combining either the unlensed FRBs with future gravitational wave (GW) standard sirens or the lensed FRBs with CMB. Furthermore, combining the full FRB sample with the CMB+BAO+SNe data yields $\sigma(H_0)=0.29~{\rm km~s^{-1}~Mpc^{-1}}$, $\sigma(w_0)=0.046$, and $\sigma(w_a)=0.15$ in the two-parameter dynamical dark energy model, which outperform the results from the CMB+BAO+SNe+GW data. This reinforces the cosmological implications of a multi-wavelength observational strategy in optical and radio bands. We conclude that the future FRB observations will shed light on the nature of dark energy and also the Hubble tension if enough events with long-duration lensing are incorporated., Comment: 18 pages, 7 figures

The direct detection of gravitational waves by LIGO has confirmed general relativity (GR) and sparked rapid growth in gravitational wave (GW) astronomy. However, subtle post-Newtonian (PN) deviations observed during the analysis of high signal-to-noise ratio events from the observational runs suggest that standard waveform templates, which assume strict adherence to GR, might overlook signals from alternative theories of gravity. Incorporating these exotic signals into traditional search algorithms is computationally infeasible due to the vast template space required. This paper introduces a deep learning framework for detecting exotic GW signals, leveraging neural networks trained on GR-based templates. Through their generalization ability, neural networks learn intricate features from the data, enabling the detection of signals that deviate from GR. We present the first study evaluating the capability of deep learning to detect beyond-GR signals, including a variety of PN orders. Our model achieves rapid and accurate identification of exotic GW signals across different luminosity distances, with performance comparable to GR-based detections. Applying the model to the GW150914 event demonstrates excellent performance, highlighting the potential of AI-driven methods for detecting previously overlooked signals beyond GR. This work paves the way for new discoveries in gravitational wave astronomy, enabling the detection of signals that might escape traditional search pipelines., Comment: 10 pages, 7 figures

Fast radio bursts (FRBs) are enigmatic high-energy events with unknown origins, which are observationally divided into two categories, i.e., repeaters and non-repeaters. However, there are potentially a number of non-repeaters that may be misclassified, as repeating bursts are missed due to the limited sensitivity and observation periods, thus misleading the investigation of their physical properties. In this work, we propose a repeater identification method based on the t-distributed Stochastic Neighbor Embedding (t-SNE) algorithm and apply the classification to the first Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst (CHIME/FRB) catalog. We find that the spectral morphology parameters, specifically spectral running ($r$), represent the key features for identifying repeaters from the non-repeaters. Also, the results suggest that repeaters are more biased towards narrowband emission, whereas non-repeaters are inclined toward broadband emission. We provide a list of 163 repeater candidates, with $5$ of which are confirmed with an updated repeater catalog from CHIME/FRB. Our findings help to the understanding of the various properties underlying repeaters and non-repeaters, as well as guidelines for future FRB detection and categorization., Comment: 15 pages, 7 figures

Sterile neutrinos can influence the evolution of the universe, and thus cosmological observations can be used to detect them. Future gravitational wave (GW) observations can precisely measure absolute cosmological distances, helping to break parameter degeneracies generated by traditional cosmological observations. This advancement can lead to much tighter constraints on sterile neutrino parameters. This work provides a preliminary forecast for detecting sterile neutrinos using third-generation GW detectors in combination with future short $\gamma$-ray burst observations from a THESEUS-like telescope, an approach not previously explored in the literature. Both massless and massive sterile neutrinos are considered within the $\Lambda$CDM cosmology. We find that using GW data can greatly enhance the detection capability for massless sterile neutrinos, reaching 3$\sigma$ level. For massive sterile neutrinos, GW data can also greatly assist in improving the parameter constraints, but it seems that effective detection is still not feasible., Comment: 14 pages, 4 figures

Recently, several pulsar timing array (PTA) projects have detected evidence of the existence of a stochastic gravitational wave background (SGWB) in the nanohertz frequency band, providing confidence in detecting individual supermassive black hole binaries (SMBHBs) in the future. Nanohertz GWs emitted by inspiraling SMBHBs encode the luminosity distances of SMBHBs. They can serve as dark sirens to explore the cosmic expansion history via a statistical method to obtain the redshift information of GW sources' host galaxies using galaxy catalogs. The theoretical analysis of the dark siren method relies on the modeling of the population of SMBHBs. Using a population model consistent with the latest SGWB observations is essential, as the SGWB provides significant information about the distribution of SMBHBs. In this work, we employ a quasar-based model, which can self-consistently account for the SGWB amplitude, to estimate the population of SMBHBs. We constrain the Hubble constant using the mock GW data from different detection cases of PTAs in the future. Our results show that a PTA consisting of 100 pulsars with a white noise level of 20 ns could measure the Hubble constant with a precision close to $1\%$ over a 10-year observation period, and a PTA with 200 pulsars may achieve this goal over a 5-year observation period. The results indicate that modeling the SMBHB population significantly influences the analysis of dark sirens, and SMBHB dark sirens have the potential to be developed as a valuable cosmological probe., Comment: 15 pages, 7 figures

The recent results from the first year baryon acoustic oscillations (BAO) data released by the Dark Energy Spectroscopic Instrument (DESI), combined with cosmic microwave background (CMB) and type Ia supernova (SN) data, have shown a detection of significant deviation from a cosmological constant for dark energy. In this work, we utilize the latest DESI BAO data in combination with the SN data from the full five-year observations of the Dark Energy Survey and the CMB data from the Planck satellite to explore potential interactions between dark energy and dark matter. We consider four typical forms of the interaction term $Q$. Our findings suggest that interacting dark energy (IDE) models with $Q \propto \rho_{\rm de}$ support the presence of an interaction where dark energy decays into dark matter. Specifically, the deviation from $\Lambda$CDM for the IDE model with $Q=\beta H_0\rho_{\rm de}$ reaches the $3\sigma$ level. These models yield a lower value of Akaike information criterion than the $\Lambda$CDM model, indicating a preference for these IDE models based on the current observational data. For IDE models with $Q\propto\rho_{\rm c}$, the existence of interaction depends on the form of the proportionality coefficient $\Gamma$. The IDE model with $Q=\beta H\rho_{\rm c}$ yields $\beta=0.0003\pm 0.0011$, which essentially does not support the presence of the interaction. In general, whether the observational data support the existence of interaction is closely related to the model. Our analysis helps to elucidate which type of IDE model can better explain the current observational data., Comment: 11 pages, 4 figures; published in ApJ

Gravitational wave (GW) detection is of paramount importance in fundamental physics and GW astronomy, yet it presents formidable challenges. One significant challenge is the removal of noise transient artifacts known as ``glitches," which greatly impact the search and identification of GWs. Recent research has achieved remarkable results in data denoising, often using effective modeling methods to remove glitches. However, for glitches from uncertain or unknown sources, current methods cannot completely eliminate them from the GW signal. In this work, we leverage the inherent robustness of machine learning to obtain reliable posterior parameter distributions directly from GW data contaminated by glitches. Our network model provides reasonable and rapid parameter inference even in the presence of glitches, without needing to remove them. We also investigate various factors affecting the rationality of parameter inference in our normalizing flow network, including glitch and GW parameters. The results demonstrate that the normalizing flow can reasonably infer the source parameters of GWs even with unknown contamination. We find that the nature of the glitch itself is the only factor that can affect the rationality of the inferred results. With improvements to our model, we anticipate accelerating the localization of electromagnetic counterparts and providing priors for more accurate deglitching, thereby speeding up subsequent data processing procedures., Comment: 13 pages, 9 figures

Cosmological observations can be used to weigh neutrinos, but this method is model-dependent, with results relying on the cosmological model considered. If we consider interactions between dark energy and dark matter, the neutrino mass constraints differ from those derived under the standard model. On the contrary, gravitational wave (GW) standard siren observations can measure absolute cosmological distances, helping to break parameter degeneracies inherent in traditional cosmological observations, thereby improving constraints on neutrino mass. This paper examines the constraints on neutrino mass within interacting dark energy (IDE) models and explores how future GW standard siren observations could enhance these results. For multi-messenger GW observations, we consider the joint observations of binary neutron star mergers by third-generation ground-based GW detectors and short $\gamma$-ray burst observations by missions similar to the THESEUS satellite project. Using current cosmological observations (CMB+BAO+SN), we obtain an upper limit on the neutrino mass in the IDE models of 0.15 (or 0.16) eV. With the inclusion of GW data, the upper limit on the neutrino mass improves to 0.14 eV. This indicates that in the context of IDE models, the improvement in neutrino mass constraints from GW observations is relatively limited. However, GW observations significantly enhance the constraints on other cosmological parameters, such as matter density parameter, the Hubble constant, and coupling strength between dark energy and dark matter., Comment: 9 pages, 2 figures; published in Chinese Physics C

Multi-band gravitational-wave (GW) standard siren observations are poised to herald a new era in the study of cosmic evolution. These observations offer higher signal-to-noise ratios and improved localizations compared to those achieved with single-band GW detection, which are crucial for the cosmological applications of dark sirens. In this work, we explore the role multi-band GW synergetic observations will play in measuring cosmological parameters, particularly in comparison with single GW observatory data. We used mock multi-band dark siren data from third-generation GW detectors and the baseline Decihertz Interferometer Gravitational-Wave Observatory to infer cosmological parameters. Our analysis was conservative, involving only the 89 actual GW events from the current Gravitational Wave Transient Catalogs in our data simulation, facilitating a direct comparison with existing dark siren results. Multi-band GW observations significantly improve sky localization accuracy by two to three orders of magnitude over single-band observations, although their impact on luminosity distance error remains limited. This results in a substantial improvement in the constraints on matter density and the Hubble constant, enhancing them by $75\%$ to $85\%$ and $65\%$ to $82\%$, respectively. We conclude that the significant potential of multi-band GW synergistic observations for detecting GW signals and resolving the Hubble tension is highly promising and warrants anticipation., Comment: 11 pages, 4 figures

We demonstrate that Debye shielding cannot be employed to constrain the cosmological abundance of magnetic monopoles, contrary to what is stated in the previous literature. Current model-independent bounds on the monopole abundance are then revisited for unit Dirac magnetic charge. We find that the Andromeda Parker bound can be employed to set an upper limit on the monopole flux at the level of $F_M\lesssim 5.3\times 10^{-19}\,\text{cm}^{-2}\text{s}^{-1}\text{sr}^{-1}$ for a monopole mass $10^{13}\,\text{GeV}/c^2\lesssim m\lesssim 10^{16}\,\text{GeV}/c^2$, which is more stringent than the MACRO direct search limit by two orders of magnitude. This translates into stringent constraints on the monopole density parameter $\Omega_M$ at the level of $10^{-7}-10^{-4}$ depending on the mass. For larger monopole masses the scenarios in which magnetic monopoles account for all or the majority of dark matter are disfavored., Comment: 26 pages, 2 figures. Explanations added regarding the fluid approximation. Matching the journal version

Glitches represent a category of non-Gaussian and transient noise that frequently intersects with gravitational wave (GW) signals, exerting a notable impact on the processing of GW data. The inference of GW parameters, crucial for GW astronomy research, is particularly susceptible to such interference. In this study, we pioneer the utilization of temporal and time-spectral fusion normalizing flow for likelihood-free inference of GW parameters, seamlessly integrating the high temporal resolution of the time domain with the frequency separation characteristics of both time and frequency domains. Remarkably, our findings indicate that the accuracy of this inference method is comparable to traditional non-glitch sampling techniques. Furthermore, our approach exhibits greater efficiency, boasting processing times on the order of milliseconds. In conclusion, the application of normalizing flow emerges as pivotal in handling GW signals affected by transient noises, offering a promising avenue for enhancing the field of GW astronomy research., Comment: 13 pages, 10 figures

Gravitational wave (GW) standard siren observations provide a rather useful tool to explore the evolution of the Universe. In this work, we wish to investigate whether dark sirens with neutron star (NS) deformation from third-generation GW detectors could help probe the interaction between dark energy and dark matter. We simulate the GW dark sirens of four detection strategies based on 3 yr observation and consider four phenomenological interacting dark energy (IDE) models to perform cosmological analysis. We find that GW dark sirens could provide tight constraints on $\Omega_{\rm m}$ and $H_0$ in the four IDE models, but do not perform well in constraining the dimensionless coupling parameter $\beta$ in models of the interaction proportional to the energy density of cold dark matter. Nevertheless, the parameter degeneracy orientations of cosmic microwave background (CMB) and GW are almost orthogonal, and thus, the combination of them could effectively break cosmological parameter degeneracies, with the constraint errors of $\beta$ being $0.00068-0.018$. In addition, we choose three typical equations of state (EoSs) of an NS, i.e., SLy, MPA1, and MS1, to investigate the effect of an NS's EoS in cosmological analysis. The stiffer EoS could give tighter constraints than the softer EoS. Nonetheless, the combination of CMB and GW dark sirens (using different EoSs of an NS) shows basically the same constraint results of cosmological parameters. We conclude that the dark sirens from 3G GW detectors would play a crucial role in helping probe the interaction between dark energy and dark matter, and the CMB+GW results are basically not affected by the EoS of an NS., Comment: 13 pages, 9 figures; published in ApJ

In the third-generation (3G) gravitational-wave (GW) detector era, the multi-messenger GW observation for binary neutron star (BNS) merger events can exert great impacts on exploring the cosmic expansion history. In this work, we comprehensively explore the potential of 3G GW standard siren observations in cosmological parameter estimations by considering the 3G GW detectors and the future short $\gamma$-ray burst (GRB) detector THESEUS-like telescope joint observations. Based on the 10-year observation of different detection strategies, we predict that the numbers of detectable GW-GRB events are 334--674 with the redshifts $z<3.5$ and the inclination angles $\iota<15^{\circ}$. For the cosmological analysis, we consider the $\Lambda$CDM, $w$CDM, $w_0w_a$CDM models, and interacting dark energy (IDE) models. We find that GW can tightly constrain the Hubble constant with precisions of $0.345\%-0.065\%$, but perform not well in constraining other cosmological parameters. Fortunately, GW could effectively break the cosmological parameter degeneracies generated by the mainstream EM observations, CMB+BAO+SN (CBS). When combining the mock GW data with the CBS data, CBS+GW can tightly constrain the equation of state of dark energy $w$ with a precision of 1.26\%, close to the standard of precision cosmology. Meanwhile, the addition of GW to CBS could improve constraints on cosmological parameters by $34.2\%-94.9\%$. In conclusion, GW standard siren observations from 3G GW detectors could play a crucial role in helping solve the Hubble tension and probe the fundamental nature of dark energy., Comment: 23 pages, 19 figures; accepted for publication in EPJC

The 2.5-generation (2.5G) ground-based gravitational wave (GW) detectors LIGO Voyager and NEMO are expected to be operational in the late 2020s and early 2030s. In this work, we explore the potential of GW standard sirens observed by the 2.5G GW detectors in measuring cosmological parameters, especially for the Hubble constant. Using GWs to measure cosmological parameters is inherently challenging, especially for 2.5G detectors, given their limited capability, which results in weaker constraints on cosmological parameters from the detected standard sirens. However, the measurement of the Hubble constant using standard siren observations from Voyager and NEMO is still promising. For example, using bright sirens from Voyager and NEMO can measure the Hubble constant with a precision of about $2\%$ and $6\%$ respectively, and using the Voyager-NEMO network can improve the precision to about $1.6\%$. Moreover, bright sirens can be used to break the degeneracy of cosmological parameters generated by CMB data, and to a certain extent, 2.5G detectors can also play a role in this aspect. Observations of dark sirens by 2.5G detectors can achieve relatively good results in measuring the Hubble constant, with a precision of within $2\%$, and if combining observations of bright and dark sirens, the precision of the Hubble constant measurement can reach about $1.4\%$. Finally, we also discussed the impact of the uncertainty in the binary neutron star merger rate on the estimation of cosmological parameters. We conclude that the magnificent prospect for solving the Hubble tension is worth expecting in the era of the 2.5G ground-based GW detectors., Comment: 28 pages, 13 figures

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: (i) 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; (ii) 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; (iii) using $10^6$ FRB data can constrain the baryon density $\Omega_{\rm b}h$ to a precision of $\sim 0.1\%$. 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., Comment: 17 pages, 7 figures; accepted for publication in Science China-Physics, Mechanics & Astronomy

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 $\sigma(w)=0.036$ 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., Comment: 22 pages, 10 figures; published in Science China Physics Mechanics & Astronomy

Recent developments in deep learning techniques have offered an alternative and complementary approach to traditional matched filtering methods for the identification of gravitational wave (GW) signals. The rapid and accurate identification of GW signals is crucial for the progress of GW physics and multi-messenger astronomy, particularly in light of the upcoming fourth and fifth observing runs of LIGO-Virgo-KAGRA. In this work, we use the 2D U-Net algorithm to identify the time-frequency domain GW signals from stellar-mass binary black hole (BBH) mergers. We simulate BBH mergers with component masses from 5 to 80 $M_{\odot}$ and account for the LIGO detector noise. We find that the GW events in the first and second observation runs could all be clearly and rapidly identified. For the third observing run, about $80\%$ GW events could be identified. In particular, GW190814, currently unknown, is a special case that can be identified by the network, while other binary neutron star mergers and neutron star-black hole mergers can not be identified. Compared to the traditional convolutional neural network, the U-Net algorithm can output the time-frequency domain signal images rather than probabilities, providing a more intuitive investigation. Moreover, some of the results through U-Net can provide preliminary inference on the chirp mass information. In conclusion, the U-Net algorithm can rapidly identify the time-frequency domain GW signals from BBH mergers and potentially be helpful for future parameter inferences., Comment: 15 pages, 11 figures

Fast radio bursts (FRBs) have been found in great numbers, but the physical mechanism of these sources is still a mystery. The redshift evolutions of the FRB energy distribution function and the volumetric rate shed light on the origin of FRBs. However, such estimations rely on the dispersion measurement (DM)-redshift ($z$) relationship. A few FRBs that have been detected recently show large excess DMs beyond the expectation from the cosmological and Milky Way contributions, which indicates large spread of DMs from their host galaxies. In this work, we adopt two lognormal-distributed ${\rm DM}_{\rm host}$ models and estimate the energy function using the non-repeating FRBs selected from the Canadian Hydrogen Intensity Mapping Experiment (CHIME)/FRB Catalog 1. By comparing the lognormal-distributed ${\rm DM}_{\rm host}$ models to a constant ${\rm DM}_{\rm host}$ model, the FRB energy function results are consistent within the measurement uncertainty. We also estimate the volumetric rate of the non-repeating FRBs in three different redshift bins. The volumetric rate shows that the trend is consistent with the stellar-mass density redshift evolution. Since the lognormal-distributed ${\rm DM}_{\rm host}$ model increases the measurement errors, the inference of FRBs tracking the stellar-mass density is nonetheless undermined., Comment: 15 pages, 5 figures; published version

In the context of the discrepancies between the early and late universe, we emphasize the importance of independent measurements of the cosmic curvature in the late universe. We present an investigation of the model-independent measurement of the cosmic curvature parameter $\Omega_k$ in the late universe with the latest Hubble parameter $H(z)$ measurements and type Ia supernovae (SNe Ia) data. For that, we use two reconstruction methods, the Gaussian process (GP) and artificial neural network (ANN) methods, to achieve the distance construction from $H(z)$ data. Our analysis reveals that the GP method provides the most precise constraint on $\Omega_k$, with a constraint precision of $\xi(\Omega_k)=0.13$, surpassing recent estimations using similar methods. The GP method consistently indicates a preference for a flat universe at the 2$\sigma$ confidence level. Moreover, we find that the choice of reconstruction method influences the estimation of $\Omega_k$. The ANN reconstruction method exhibits higher sensitivity to the addition of BAO $H(z)$ data, resulting in comparable constraint precision to the GP method. A discrepancy exists between the best-fit values obtained by these two reconstruction methods, indicating their dependence on the reconstruction approach. However, we anticipate that with the improvement of sample size and precision of observational $H(z)$ data, the estimation of $\Omega_k$ using this approach will become more robust and reliable., Comment: 11 pages, 3 figures; accepted for publication in Physical Review D

Gravitational waves (GWs) from the compact binary coalescences can be used as standard sirens to explore the cosmic expansion history. In the next decades, it is anticipated that we could obtain the multi-band GW standard siren data (from nanohertz to a few hundred hertz), which are expected to play an important role in cosmological parameter estimation. In this work, we give for the first time the joint constraints on cosmological parameters using the future multi-band GW standard siren observations. We simulate the multi-band GW standard sirens based on the SKA-era pulsar timing array (PTA), the Taiji observatory, and the Cosmic Explorer (CE) to perform cosmological analysis. In the $\Lambda$CDM model, we find that the joint PTA+Taiji+CE data could provide a tight constraint on the Hubble constant with a $0.5\%$ precision. Moreover, PTA+Taiji+CE could break the cosmological parameter degeneracies generated by CMB, especially in the dynamical dark energy models. When combining the PTA+Taiji+CE data with the CMB data, the constraint precisions of $\Omega_{\rm m}$ and $H_0$ are $1.0\%$ and $0.3\%$, meeting the standard of precision cosmology. The joint CMB+PTA+Taiji+CE data give $\sigma(w)=0.028$ in the $w$CDM model and $\sigma(w_0)=0.11$ and $\sigma(w_a)=0.32$ in the $w_0w_a$CDM model, which are comparable with or close to the latest constraint results by CMB+BAO+SN. In conclusion, it is worth expecting to use the future multi-band GW observations to explore the nature of dark energy and measure the Hubble constant., Comment: 12 pages, 6 figures; accepted for publication in Chinese Physics C

Neutral hydrogen (HI) intensity mapping (IM) surveys are considered a promising tool for investigating the expansion history of the Universe. In this work, we explore the potential of MeerKAT HI IM observations in interferometer mode to estimate the power spectrum and constrain cosmological parameters within typical dark energy models. We employ an approach called the "delay spectrum," which allows us to separate the weak HI signal from foreground contamination in the frequency domain. Our findings indicate that the choice of survey fields significantly impacts the fractional errors on the power spectrum ($\Delta P/P$) within a limited observational time of 10 hours. As the integration time increases from 10 hours to 10,000 hours, $\Delta P/P$ progressively decreases until cosmic variance begins to dominate. For a total observation time of 10,000 hours, the lowest $\Delta P/P$ at low $k$ can be achieved by tracking 100 points for MeerKAT L-band (900-1200 MHz) and 10 points for MeerKAT UHF-band (580-1000 MHz). Next, we assess the performance of HI IM in constraining typical dark energy models. We find that MeerKAT HI IM survey in interferometer mode demonstrates limited capability in constraining the dark-energy equation of state, even when combined with Planck data., Comment: 11 pages, 10 figures; accepted for publication in Monthly Notices of the Royal Astronomical Society

Fast radio bursts (FRBs) can be used to measure cosmological parameters by employing the Macquart relation. However, at present, only a small number of FRB events are localized to host galaxies with known redshifts. Inspired by the dark siren method in gravitational wave cosmology, we develop a Bayesian method to statistically measure the Hubble constant using unlocalized FRBs and galaxy catalog data, which makes it possible to constrain cosmological parameters from a large number of FRB data without known redshifts, meanwhile including the real galaxy information. We assume that the probability for a galaxy to host an FRB is proportional to the luminosity of this galaxy and use the results from the IllustrisTNG simulation as the priors of FRB host galaxy parameters. Ignoring some systematic errors, we obtain the first statistical $H_0$ measurement only using twelve unlocalized FRB events combined with the big bang nucleosynthesis result, i.e., $H_0=80.4^{+24.1}_{-19.4}$ km s$^{-1}$ Mpc$^{-1}$, ($68\%$ highest-density interval). This method can also be refined to constrain other cosmological and FRB parameters. It is applicable to well-localized FRBs that still have several potential hosts., Comment: 13 pages, 5 figures

The 21 cm intensity mapping (IM) technique provides us with an efficient way to observe the cosmic large-scale structure (LSS). From the LSS data, one can use the baryon acoustic oscillation and redshift space distortion to trace the expansion and growth history of the universe, and thus measure the dark energy parameters. In this paper, we make a forecast for cosmological parameter estimation with the synergy of three 21 cm IM experiments. Specifically, we adopt a novel joint survey strategy, FAST ($0

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 $z\sim 4$, 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., Comment: 13 pages, 5 figures; accepted for publication in Science China Physics, Mechanics & Astronomy

With the measurement of the electromagnetic (EM) counterpart, a gravitational wave (GW) event could be treated as a standard siren. As a novel cosmological probe, GW standard sirens will bring significant implications for cosmology. In this paper, by considering the coincident detections of GW and associated $\gamma$ ray burst (GRB), we find that only about 400 GW bright standard sirens from binary neutron star mergers could be detected in a 10-year observation of the Einstein Telescope and the THESEUS satellite mission. Based on this mock sample, we investigate the implications of GW standard sirens on the interaction between dark energy and dark matter. In our analysis, four viable interacting dark energy (IDE) models, with interaction forms $Q=3\beta H \rho_{\mathrm{de}}$ and $Q=3 \beta H \rho_{\mathrm{c}}$, are considered. Compared with the traditional EM observational data such as CMB, BAO, and SN Ia, the combination of both GW and EM observations could effectively break the degeneracies between different cosmological parameters and provide more stringent cosmological fits. We find that the GW data could play a more important role for determining the interaction in the models with $Q=3 \beta H \rho_{\mathrm{c}}$, compared with the models with $Q=3\beta H \rho_{\mathrm{de}}$. We also show that constraining IDE models with mock GW data based on different fiducial $H_0$ values yield different results, indicating that accurate determination of $H_0$ is significant for exploring the interaction between dark energy and dark matter., Comment: 17 pages, 5 figures

Interacting dark energy (IDE) scenario assumes that there exists a direct interaction between dark energy and cold dark matter, but this interaction is hard to be tightly constrained by the current data. Fast radio bursts (FRBs) will be seen in large numbers by future radio telescopes, and thus they have potential to become a promising low-redshift cosmological probe. In this work, we investigate the capability of future FRBs of constraining the dimensionless coupling parameter $\beta$ in four phenomenological IDE models. If we fix the FRB properties, about $10^5$ FRB data can give constraints on $\beta$ tighter than the current cosmic microwave background data in the IDE models with the interaction proportional to the energy density of dark energy. In all the IDE models, about $10^6$ FRB data can achieve the absolute errors of $\beta$ to less than $0.10$, providing a way to precisely measure $\beta$ by only one cosmological probe. Jointly constraining the FRB properties and cosmological parameters would increase the constraint errors of $\beta$ by a factor of about 0.5-2., Comment: 19 pages, 8 figures; accepted for publication in JCAP

Remarkable development of cosmology is benefited from the increasingly improved measurements of cosmic distances including absolute distances and relative distances. In recent years, however, the emerged cosmological tensions motivate us to explore the independent and precise late-universe probes. The two observational effects of strong gravitational lensing (SGL), the velocity dispersions of lens galaxies and the time delays between multiple images, can provide measurements of relative and absolute distances respectively, and their combination is possible to break the degeneracies between cosmological parameters and enable tight constraints on cosmological parameters. In this paper, we combine the observed 130 SGL systems with velocity-dispersion measurements and 7 SGL systems with time-delay measurements to constrain dark-energy cosmological models. It is found that the combination of the two effects does not significantly break the degeneracies between cosmological parameters as expected. However, with the simulations of 8000 SGL systems with well-measured velocity dispersions and 55 SGL systems with well-measured time delays based on the forthcoming LSST survey, we find that the combination of two effects can significantly break the parameter degeneracies, and make the constraint precision of cosmological parameters meet the standard of precision cosmology. We conclude that the observations of SGL will become a useful late-universe probe for precisely measuring cosmological parameters., Comment: 18 pages, 6 figures; to appear in Universe

Using the measurements of tidal deformation in the binary neutron star (BNS) coalescences can obtain the information of redshifts of gravitational wave (GW) sources, and thus actually the cosmic expansion history can be investigated using solely such GW dark sirens. To do this, the key is to get a large number of accurate GW data, which can be achieved with the third-generation (3G) GW detectors. Here we wish to offer an answer to the question of whether the Hubble constant and the equation of state (EoS) of dark energy can be precisely measured using solely GW dark sirens. We find that in the era of 3G GW detectors ${\cal O}(10^5-10^6)$ dark siren data (with the NS tidal measurements) could be obtained in three-year observation if the EoS of NS is perfectly known, and thus using only dark sirens can actually achieve the precision cosmology. Based on a network of 3G detectors, we obtain the constraint precisions of $0.15\%$ and $0.95\%$ for the Hubble constant $H_0$ and the constant EoS of dark energy $w$, respectively; for a two-parameter EoS parametrization of dark energy, the precision of $w_0$ is $2.04\%$ and the error of $w_a$ is 0.13. We conclude that 3G GW detectors would lead to breakthroughs in solving the Hubble tension and revealing the nature of dark energy provided that the EoS of NS is perfectly known., Comment: 23 pages, 6 figures

Strongly lensed type Ia supernovae (SNe Ia) are expected to have some advantages in measuring time delays of multiple images, and so they have a great potential to be developed into a powerful late-universe cosmological probe. In this paper, we simulate a sample of lensed SNe Ia with time-delay measurements in the era of the Legacy Survey of Space and Time (LSST). Based on the distance sum rule, we use lensed SNe Ia to implement model-independent constraints on the Hubble constant $H_0$ and cosmic curvature parameter $\Omega_K$ in the late universe. We find that if 20 lensed SNe Ia could be observed, the constraint on $H_{0}$ is better than the measurement by the SH0ES collaboration. When the event number of lensed SNe Ia increases to 100, the constraint precision of $H_{0}$ is comparable with the result from Planck 2018 data. Considering 200 lensed SNe Ia events as the optimistic estimation, we obtain $\Delta H_0=0.33$ $\rm km\ s^{-1}\ Mpc^{-1}$ and $\Delta\Omega_K=0.053$. In addition, we also simulate lensed quasars in different scenarios to make a comparison and we find that they are still a useful cosmological probe even though the constraint precision from them is much less than that obtained from lensed SNe Ia. In the era of LSST, the measurements of time delay from both lensed SNe Ia and lensed quasars are expected to yield the results of $\Delta H_0=0.26 ~\rm km\ s^{-1}\ Mpc^{-1}$ and $\Delta\Omega_K=0.044$., Comment: 11 pages, 3 figures; accepted for publication in Physical Review D

Although the cosmic curvature has been tightly constrained in the standard cosmological model using observations of cosmic microwave background anisotropies, it is still of great importance to independently measure this key parameter using only late-universe observations in a cosmological model-independent way. The distance sum rule in strong gravitational lensing (SGL) provides such a way, provided that the three distances in the sum rule can be calibrated by other observations. In this paper, we propose that gravitational waves (GWs) can be used to provide the distance calibration in the SGL method, which can avoid the dependence on distance ladder and cover a wider redshift range. Using the simulated GW standard siren observation by the Einstein Telescope as an example, we show that this scheme is feasible and advantageous. We find that $\Delta\Omega_k\simeq 0.17$ with the current SGL data, which is slightly more precise than the case of using SN to calibrate. Furthermore, we consider the forthcoming LSST survey that is expected to observe many SGL systems, and we find that about $10^4$ SGL data could provide the precise measurement of $\Delta\Omega_k\simeq 10^{-2}$ with the help of GWs. In addition, our results confirm that this method of constraining $\Omega_k$ is strongly dependent on lens models. However, obtaining a more accurate phenomenological model for lens galaxies is highly predictable as future massive surveys observe more and more SGL samples, which will significantly improve the constraint of cosmic curvature., Comment: 9 pages, 3 figures

Ultra-low-frequency gravitational waves (GWs) generated by individual inspiraling supermassive black hole binaries (SMBHBs) in the centers of galaxies may be detected by pulsar timing arrays (PTAs) in the future. These GW signals encoding absolute cosmic distances can serve as bright and dark sirens, having potential to be developed into a precise cosmological probe. Here we show that an SKA-era PTA consisting of 100 millisecond pulsars may observe about 25 bright sirens and 41 dark sirens during a 10-year observation. The bright sirens, together with the CMB data, have comparable capabilities to current mainstream data for measuring the equation of state of dark energy. The dark sirens could make the measurement precision of the Hubble constant close to that of current distance-ladder observation. Our results indicate that ultra-low-frequency GWs from individual SMBHBs are of great significance in exploring the nature of dark energy and measuring the Hubble constant., Comment: 44 pages, 10 figures

Sterile neutrinos can affect the evolution of the universe, and thus using the cosmological observations can search for sterile neutrinos. In this work, we use the cosmic microwave background (CMB) anisotropy data from the Planck 2018 release, combined with the latest baryon acoustic oscillation (BAO), type Ia supernova (SN), and Hubble constant ($H_0$) data, to constrain the cosmological models with considering sterile neutrinos. In order to test the influences of the properties of dark energy on the {results} of searching for sterile neutrinos, in addition to the $\Lambda$ cold dark matter ($\Lambda$CDM) model, we also consider the $w$CDM model and the holographic dark energy (HDE) model. We find that the existence of sterile neutrinos {is not preferred} when the $H_0$ local measurement is not included in the data combination. When the $H_0$ measurement is included in the joint constraints, it is found that $\Delta N_{\rm eff}>0$ is {favored} at about 2.7$\sigma$ level for the $\Lambda$CDM model and at about 1-1.7$\sigma$ level for the $w$CDM model. However, $m_{\nu,{\rm{sterile}}}^{\rm{eff}}$ still cannot be well constrained and only upper limits can be given. In addition, we find that the HDE model is definitely ruled out by the current data. We also discuss the issue of the Hubble tension, and we conclude that involving sterile neutrinos in the cosmological models cannot truly resolve the Hubble tension., Comment: 8 pages, 2 figures; accepted for publication in Physics Letters B

Recently, about five hundred fast radio bursts (FRBs) detected by CHIME/FRB Project have been reported. The vast amounts of data would make FRBs a promising low-redshift cosmological probe in the forthcoming years, and thus the issue of how many FRBs are needed for precise cosmological parameter estimation in different dark energy models should be detailedly investigated. Different from the usually considered $w(z)$-parameterized models in the literature, in this work we investigate the holographic dark energy (HDE) model and the Ricci dark energy (RDE) model, which originate from the holographic principle of quantum gravity, using the simulated localized FRB data as a cosmological probe for the first time. We show that the Hubble constant $H_0$ can be constrained to about 2% precision in the HDE model with the Macquart relation of FRB by using 10000 accurately-localized FRBs combined with the current CMB data, which is similar to the precision of the SH0ES value. Using 10000 localized FRBs combined with the CMB data can achieve about 6% constraint on the dark-energy parameter $c$ in the HDE model, which is tighter than the current BAO data combined with CMB. We also study the combination of the FRB data and another low-redshift cosmological probe, i.e. gravitational wave (GW) standard siren data, with the purpose of measuring cosmological parameters independent of CMB. Although the parameter degeneracies inherent in FRB and in GW are rather different, we find that more than 10000 FRBs are demanded to effectively improve the constraints in the holographic dark energy models., Comment: 24 pages, 6 figures; published in JCAP

In the next decades, the gravitational-wave (GW) standard siren observations and the neutral hydrogen 21-cm intensity mapping (IM) surveys, as two promising cosmological probes, will play an important role in precisely measuring cosmological parameters. In this work, we make a forecast for cosmological parameter estimation with the synergy between the GW standard siren observations and the 21-cm IM surveys. We choose the Einstein Telescope (ET) and the Taiji observatory as the representatives of the GW detection projects and choose the Square Kilometre Array (SKA) phase I mid-frequency array as the representative of the 21-cm IM experiments. In the simulation of the 21-cm IM data, we assume perfect foreground removal and calibration. We find that the synergy of the GW standard siren observations and the 21-cm IM survey could break the cosmological parameter degeneracies. The joint ET+Taiji+SKA data give $\sigma(H_0)=0.28\ {\rm km\ s^{-1}\ Mpc^{-1}}$ in the $\Lambda$CDM model, $\sigma(w)=0.028$ in the $w$CDM model, which are better than the results of $Planck$+BAO+SNe, and $\sigma(w_0)=0.077$ and $\sigma(w_a)=0.295$ in the CPL model, which are comparable with the results of $Planck$+BAO+SNe. In the $\Lambda$CDM model, the constraint precision of $H_0$ and $\Omega_{\rm m}$ is less than or rather close to 1%, indicating that the magnificent prospects for precision cosmology with these two promising cosmological probes are worth expecting., Comment: 12 pages, 7 figures

Measurements of time-delay cosmography of lensed quasars can provide an independent probe to explore the expansion history of the late-time Universe. In this paper, we employ the time-delay cosmography measurements from seven lenses (here abbreviated as the TD data) to constrain interacting dark energy (IDE) models. We mainly focus on the scenario of vacuum energy (with $w=-1$) interacting with cold dark matter, and consider four typical cases of the interaction form $Q$. When the TD data alone are employed, we find that the IDE models with $Q\propto \rho_{\rm de}$ seem to have an advantage in relieving the $H_{0}$ tension between the cosmic microwave background (CMB) and TD data. When the TD data are added to the CMB$+$BAO$+$SN$+H_0$ data, we find that: (i) the coupling parameter $\beta$ in all the considered IDE models is positive within 1$\sigma$ range, implying a mild preference for the case of cold dark matter decaying into dark energy; (ii) the IDE model with $Q = \beta H_{0} \rho_{\rm c}$ slightly relieves the $S_8$ tension, but the other considered IDE models further aggravate this tension; (iii) the Akaike information criteria of the IDE models with $Q \propto \rho_{\rm c}$ are lower than that of the $\Lambda$CDM model, indicating that these IDE models are more preferred by the current mainstream data. We conclude that the considered IDE models have their own different advantages when the TD data are employed, and none of them can achieve good scores in all aspects., Comment: 8 pages, 3 figures

We forecast constraints on cosmological parameters in the interacting dark energy models using the mock data generated for neutral hydrogen intensity mapping (IM) experiments. In this work, we only consider the interacting dark energy models with energy transfer rate $Q=\beta H\rho_{\rm c}$, and take BINGO, FAST, SKA1-MID, and Tianlai as typical examples of the 21 cm IM experiments. We find that the Tianlai cylinder array will play an important role in constraining the interacting dark energy model. Assuming perfect foreground removal and calibration, and using the Tianlai-alone data, we obtain $\sigma(H_0)=0.19$ km s$^{-1}$ Mpc$^{-1}$, $\sigma(\Omega_{\rm m})=0.0033$ and $\sigma(\sigma_8)=0.0033$ in the I$\Lambda$CDM model, which are much better than the results of Planck+optical BAO (i.e. optical galaxy surveys). However, the Tianlai-alone data cannot provide a very tight constraint on the coupling parameter $\beta$ compared with Planck+optical BAO, while the Planck+Tianlai data can give a rather tight constraint of $\sigma(\beta)=0.00023$ due to the parameter degeneracies being well broken by the data combination. In the I$w$CDM model, we obtain $\sigma(\beta)=0.00079$ and $\sigma(w)=0.013$ from Planck+Tianlai. In addition, we also make a detailed comparison among BINGO, FAST, SKA1-MID, and Tianlai in constraining the interacting dark energy models. We show that future 21 cm IM experiments will provide a useful tool for exploring the nature of dark energy and play a significant role in measuring the coupling between dark energy and dark matter., Comment: 13 pages, 5 figures

In the near future, the redshift drift observations in optical and radio bands will provide precise measurements on $H(z)$ covering the redshift ranges of $2

LISA and Taiji are expected to form a space-based gravitational-wave (GW) detection network in the future. In this work, we make a forecast for the cosmological parameter estimation with the standard siren observation from the LISA-Taiji network. We simulate the standard siren data based on a scenario with configuration angle of $40^{\circ}$ between LISA and Taiji. Three models for the population of massive black hole binary (MBHB), i.e., pop III, Q3d, and Q3nod, are considered to predict the events of MBHB mergers. We find that, based on the LISA-Taiji network, the number of electromagnetic (EM) counterparts detected is almost doubled compared with the case of single Taiji mission. Therefore, the LISA-Taiji network's standard siren observation could provide much tighter constraints on cosmological parameters. For example, solely using the standard sirens from the LISA-Taiji network, the constraint precision of $H_0$ could reach $1.3\%$. Moreover, combined with the CMB data, the GW-EM observation based on the LISA-Taiji network could also tightly constrain the equation of state of dark energy, e.g., the constraint precision of $w$ reaches about $4\%$, which is comparable with the result of CMB+BAO+SN. It is concluded that the GW standard sirens from the LISA-Taiji network will become a useful cosmological probe in understanding the nature of dark energy in the future., Comment: 13 pages, 4 figures; accepted for publication in Science China - Physics, Mechanics & Astronomy

Fast radio bursts (FRBs) are a mysterious astrophysical phenomenon of bright pulses emitted at radio frequencies, and they are expected to be frequently detected in the future. The dispersion measures of FRBs are related to cosmological parameters, thus FRBs have the potential to be developed into a new cosmological probe if their data can be largely accumulated in the future. In this work, we study the capability of future FRB data to improve cosmological parameter estimation in two dynamical dark energy models. We find that the simulated FRB data can break the parameter degeneracies inherent in the current cosmic microwave background (CMB) data. Therefore, the combination of the CMB and FRB data can significantly improve the constraints on the Hubble constant and dark energy parameters, compared to those using CMB or FRB alone. If 10,000 FRB events with known redshifts are detected in the future, they would perform better than the baryon acoustic oscillation (BAO) data in breaking the parameter degeneracies inherent in the CMB data. We also find that the combination of FRB and gravitational-wave (GW) standard siren data provides an independent low-redshift probe to verify the results from the CMB and BAO data. For the data combination of CMB, GW, and FRB, it is found that the main contribution to the constraints comes from the CMB and GW data, but the inclusion of the FRB data still can evidently improve the constraint on the baryon density., Comment: 11 pages, 6 figures

In this work, we investigate the constraints on the total neutrino mass in the scenario of vacuum energy interacting with cold dark matter (abbreviated as I$\Lambda$CDM) by using the latest cosmological observations. We consider four typical interaction forms, i.e., $Q=\beta H \rho_{\rm de}$, $Q=\beta H \rho_{\rm c}$, $Q=\beta H_{0} \rho_{\rm de}$, and $Q=\beta H_{0} \rho_{\rm c}$, in the I$\Lambda$CDM scenario. To avoid the large-scale instability problem in interacting dark energy models, we employ the extended parameterized post-Friedmann method for interacting dark energy to calculate the perturbation evolution of dark energy in these models. The observational data used in this work include the cosmic microwave background (CMB) measurements from the Planck 2018 data release, the baryon acoustic oscillation (BAO) data, the type Ia supernovae (SN) observation (Pantheon compilation), and the 2019 local distance ladder measurement of the Hubble constant $H_{0}$ from the Hubble Space Telescope. We find that, compared with those in the $\Lambda$CDM+$\sum m_{\nu}$ model, the constrains on $\sum m_{\nu}$ are looser in the four I$\Lambda$CDM+$\sum m_{\nu}$ models. When considering the three mass hierarchies of neutrinos, the constraints on $\sum m_{\nu}$ are tightest in the degenerate hierarchy case and loosest in the inverted hierarchy case. In addition, in the four I$\Lambda$CDM+$\sum m_{\nu}$ models, the values of coupling parameter $\beta$ are larger using the CMB+BAO+SN+$H_{0}$ data combination than that using the CMB+BAO+SN data combination, and $\beta>0$ is favored at more than 1$\sigma$ level when using CMB+BAO+SN+$H_{0}$ data combination. The issue of the $H_{0}$ tension is also discussed in this paper. We find that, compared with the $\Lambda$CDM+$\sum m_{\nu}$ model, the $H_{0}$ tension can be alleviated in the I$\Lambda$CDM+$\sum m_{\nu}$ model to some extent., Comment: 13 pages, 7 figures

Considering the mass splittings of three active neutrinos, we investigate how the nature of dark energy affects the cosmological constraints on the total neutrino mass $\sum m_\nu$ using the latest cosmological observations. In this paper, some typical dark energy models, including $\Lambda$CDM, $w$CDM, CPL, and HDE models, are discussed. In the analysis, we also consider the effects from the neutrino mass hierarchies, i.e., the degenerate hierarchy (DH), the normal hierarchy (NH), and the inverted hierarchy (IH). We employ the current cosmological observations to do the analysis, including the Planck 2018 temperature and polarization power spectra, the baryon acoustic oscillations (BAO), the type Ia supernovae (SNe), and the Hubble constant $H_0$ measurement. In the $\Lambda$CDM+$\sum m_\nu$ model, we obtain the upper limits of the neutrino mass $\sum m_\nu < 0.123$ eV (DH), $\sum m_\nu < 0.156$ eV (NH), and $\sum m_\nu < 0.185$ eV (IH) at the $95\%$ C.L., using the Planck+BAO+SNe data combination. For the $w$CDM+$\sum m_\nu$ model and the CPL+$\sum m_\nu$ model, larger upper limits of $\sum m_\nu$ are obtained compared to those of the $\Lambda$CDM+$\sum m_\nu$ model. The most stringent constraint on the neutrino mass, $\sum m_\nu<0.080$ eV (DH), is derived in the HDE+$\sum m_\nu$ model. In addition, we find that the inclusion of the local measurement of the Hubble constant in the data combination leads to tighter constraints on the total neutrino mass in all these dark energy models., Comment: 9 pages, 4 figures

The third-generation ground-based gravitational-wave (GW) detector, Cosmic Explorer (CE), is scheduled to start its observation in the 2030s. In this paper, we make a forecast for cosmological parameter estimation with gravitational-wave standard siren observation from the CE. We use the simulated GW standard siren data of CE to constrain the $\Lambda$CDM, $w$CDM and CPL models. We combine the simulated GW data with the current cosmological electromagnetic observations including the latest cosmic microwave background anisotropies data from Planck, the optical baryon acoustic oscillation measurements, and the type Ia supernovae observation (Pantheon compilation) to do the analysis. We find that the future standard siren observation from CE will improve the cosmological parameter estimation to a great extent, since the future GW standard siren data can well break the degeneracies generated by the optical observations between various cosmological parameters. We also find that the CE's constraining capability on the cosmological parameters is slightly better than that of the same-type GW detector, the Einstein Telescope. In addition, the synergy between the GW standard siren observation from CE and the 21 cm emission observation from SKA is also discussed., Comment: 17 pages, 4 figures

Taiji, a space-based gravitational-wave observatory, consists of three satellites forming an equilateral triangle with arm length of $3\times 10^6$ km, orbiting around the Sun. Taiji is able to observe the gravitational-wave standard siren events of massive black hole binary (MBHB) merger, which is helpful in probing the expansion of the universe. In this paper, we preliminarily forecast the capability of Taiji for improving cosmological parameter estimation with the gravitational-wave standard siren data. We simulate five-year standard siren data based on three fiducial cosmological models and three models of MBHB's formation and growth. It is found that the standard siren data from Taiji can effectively break the cosmological parameter degeneracies generated by the cosmic microwave background (CMB) anisotropies data, especially for dynamical dark energy models. The constraints on cosmological parameters are significantly improved by the data combination CMB+Taiji, compared to the CMB data alone. Compared to the current optical cosmological observations, Taiji can still provide help in improving the cosmological parameter estimation to some extent. In addition, we consider an ideal scenario to investigate the potential of Taiji on constraining cosmological parameters. We conclude that the standard sirens of MBHB from Taiji will become a powerful cosmological probe in the future., Comment: 12 pages, 8 figures; published online in Science Bulletin

The recent local measurement of the Hubble constant based on the distance-ladder method has reached a $1.91\%$ precision, but this result is in tension with the early-universe measurements at the more than 4$\sigma$ level, bringing a crisis to the contemporary cosmology. In addition to the end-to-end test of the $\Lambda$CDM model in the late universe, it is also of great interest to see how the local $H_0$ measurement affects the determination of the primordial power spectra, and further to test the influences for the inflation model selection. Here, we constrain the primordial power spectra of scalar and tensor perturbations by using a series of observational data, including the Planck 2015 cosmic microwave background (CMB) temperature and polarization power spectra data, the Planck 2018 lensing power spectrum data, the BICEP2/Keck Array CMB B-mode data, and also the prior of optical depth $\tau=0.054\pm0.007$, as well as the late-universe measurements (baryon acoustic oscillations and type Ia supernovae). In particular, we use the latest $1.91\%$ measurement of the Hubble constant, $H_{0}=74.03\pm1.42$ km s$^{-1}$ Mpc$^{-1}$, in this cosmological test. We find that considering the latest local $H_{0}$ measurement in the data combination will lead to a larger fit value of $n_{\rm s}$. With the addition of the latest local measurement of $H_{0}$, it is found that the natural inflation model is totally excluded at the $2\sigma$ level, the Starobinsky $R^{2}$ inflation model is marginally favored at around the $2\sigma$ level, and the spontaneously broken SUSY inflation model is the most favored model., Comment: 2 pages, 1 figure

Applying the distance sum rule in strong gravitational lensing (SGL) and type Ia supernova (SN Ia) observations, one can provide an interesting cosmological model-independent method to determine the cosmic curvature parameter $\Omega_k$. In this paper, with the newly compiled data sets including 161 galactic-scale SGL systems and 1048 SN Ia data, we place constraints on $\Omega_k$ within the framework of three types of lens models extensively used in SGL studies. Moreover, to investigate the effect of different mass lens samples on the results, we divide the SGL sample into three sub-samples based on the center velocity dispersion of intervening galaxies. In the singular isothermal sphere (SIS) and extended power-law lens models, a flat universe is supported with the uncertainty about 0.2, while a closed universe is preferred in the power-law lens model. We find that the choice of lens models and the classification of SGL data actually can influence the constraints on $\Omega_k$ significantly., Comment: 10 pages, 4 figures; accepted for publication in The Astrophysical Journal

We investigate the impacts of dark energy on constraining massive (active/sterile) neutrinos in interacting dark energy (IDE) models by using the current observations. We employ two typical IDE models, the interacting $w$ cold dark matter (I$w$CDM) model and the interacting holographic dark energy (IHDE) model, to make an analysis. To avoid large-scale instability, we use the parameterized post-Friedmann approach to calculate the cosmological perturbations in the IDE models. The cosmological observational data used in this work include the Planck cosmic microwave background (CMB) anisotropies data, the baryon acoustic oscillation data, the type Ia supernovae data, the direct measurement of the Hubble constant, the weak lensing data, the redshift-space distortion data, and the CMB lensing data. We find that the dark energy properties could influence the constraint limits of active neutrino mass and sterile neutrino parameters in the IDE models. We also find that the dark energy properties could influence the constraints on the coupling strength parameter $\beta$, and a positive coupling constant, $\beta>0$, can be detected at the $2.5\sigma$ statistical significance for the IHDE+$\nu_s$ model by using the all-data combination. In addition, we also discuss the "Hubble tension" issue in these scenarios. We find that the $H_0$ tension can be effectively relieved by considering massive sterile neutrinos, and in particular in the IHDE+$\nu_s$ model the $H_0$ tension can be reduced to be at the $1.28\sigma$ level., Comment: 14 pages, 9 figures

Future observations of 21 cm emission from neutral hydrogen survey will become a promising approach to probe the large scale structure of Universe. In this paper, we investigate the impacts of Square Kilometer Array (SKA) 21 cm observation on the estimation of cosmological parameters. We use the simulated data of the baryonic acoustic oscillation (BAO) measurements based on the future SKA experiment with the intensity mapping (IM) technique to do the analysis. For the current observations, we use the latest cosmic microwave background (CMB) observation from {\it Planck} 2018, the optical BAO measurements, and the Type Ia supernovae (SN) observation (Pantheon compilation). We find that the SKA mock data could break the degeneracy between the matter density and the Hubble constant, further improving the cosmological constraints to a great extent. We also find that the constraint on the equation of state parameters of dark energy could be significantly improved by including the SKA mock data into the cosmological global fit., Comment: 8 pages, 3 figures, accepted for publication in PLB

In this work, we investigate the impacts of the future gravitational-wave (GW) standard siren observation by the Einstein Telescope (ET) on constraining the interacting dark energy (IDE) models. We simulate 1000 GW events in the redshift range of $0\lesssim z \lesssim 5$ based on the 10-year observation of the ET. We combine the simulated GW data with the current mainstream cosmological electromagnetic observations including the cosmic microwave background anisotropies, the baryon acoustic oscillations, and the type Ia supernovae to constrain the IDE models. We consider typical IDE models in the context of a perturbed universe. To avoid the large-scale instability problem for IDE models, we apply the extended parameterized post-Friedmann approach to calculate the cosmological perturbations. We find that the addition of the GW standard siren data could significantly improve the constraint accuracies for most of the cosmological parameters (e.g., $H_{0}$, $w$, and $\Omega_{\rm m}$). For the coupling parameter $\beta$, the constraint errors could also be slightly improved when adding the GW data in the cosmological fit., Comment: 22 pages, 5 figures; accepted for publication in JCAP

In this work, we investigate what role the redshift drift data of Square Kilometre Array (SKA) will play in the cosmological parameter estimation in the future. To test the constraint capability of the redshift drift data of SKA-only, the $\Lambda$CDM model is chosen as a reference model. We find that using the SKA1 mock data, the $\Lambda$CDM model can be loosely constrained, while the model can be well constrained when the SKA2 mock data are used. When the mock data of SKA are combined with the data of the European Extremely Large Telescope (E-ELT), the constraints can be significantly improved almost as good as the data combination of the type Ia supernovae observation (SN), the cosmic microwave background observation (CMB), and the baryon acoustic oscillations observation (BAO). Furthermore, we explore the impact of the redshift drift data of SKA on the basis of SN+CMB+BAO+E-ELT in the $\Lambda$CDM model, the $w$CDM model, the CPL model, and the HDE model. We find that the redshift drift measurement of SKA could help to significantly improve the constraints on dark energy and could break the degeneracy between the cosmological parameters. Therefore, we conclude that redshift-drift observation of SKA would provide a good improvement in the cosmological parameter estimation in the future and has the enormous potential to be one of the most competitive cosmological probes in constraining dark energy., Comment: 12 pages, 5 figures; accepted for publication in the European Physical Journal C