Standard Sirens Research Articles

Cosmological model-independent measurement of cosmic curvature using distance sum rule with the help of gravitational waves

ABSTRACT 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 ΔΩk ≃ 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 104 SGL data could provide the precise measurement of ΔΩk ≃ 10−2 with the help of GWs. In addition, our results confirm that this method of constraining Ωk 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.

Current and future constraints on cosmology and modified gravitational wave friction from binary black holes

Gravitational wave (GW) standard sirens are well-established probes with which one can measure cosmological parameters, and are complementary to other probes like the cosmic microwave background (CMB) or supernovae standard candles. Here we focus on dark GW sirens, specifically binary black holes (BBHs) for which there is only GW data. Our approach relies on the assumption of a source frame mass model for the BBH distribution, and we consider four models that are representative of the BBH population observed so far. In addition to inferring cosmological and mass model parameters, we use dark sirens to test modified gravity theories. These theories often predict different GW propagation equations on cosmological scales, leading to a different GW luminosity distance which in some cases can be parametrized by variables Ξ0 and n. General relativity (GR) corresponds to Ξ0 = 1. We perform a joint estimate of the population parameters governing mass, redshift, the variables characterizing the cosmology, and the modified GW luminosity distance. We use data from the third LIGO-Virgo-KAGRA observation run (O3) and find — for the four mass models and for three signal-to-noise ratio (SNR) cuts of 10, 11, 12 — that GR is consistently the preferred model to describe all observed BBH GW signals to date. Furthermore, all modified gravity parameters have posteriors that are compatible with the values predicted by GR at the 90% confidence interval (CI). We then focus on future observation runs O4 and O5, and for simplicity consider one specific mass model. We show that there are strong correlations between cosmological, astrophysical and modified gravity parameters. If GR is the correct theory of gravity, and assuming narrow priors on the cosmological parameters, we forecast an uncertainty of the modified gravity parameter Ξ0 of 51% with ∼ 90 detections at O4-like sensitivities, and Ξ0 of 20% with an additional ∼ 400 detections at O5-like sensitivity. We also consider how these forecasts depend on the current uncertainties of BBHs population distributions.

Does nonstationary noise in LIGO and Virgo affect the estimation of H0 ?

Gravitational-wave observations of binary neutron star mergers and their electromagnetic counterparts provide an independent measurement of the Hubble constant, $H_0$, through the standard-sirens approach. Current methods of determining $H_0$, such as measurements from the early universe and the local distance ladder, are in tension with one another. If gravitational waves are to break this tension a thorough understanding of systematic uncertainty for gravitational-wave observations is required. To accurately estimate the properties of gravitational-wave signals measured by LIGO and Virgo, we need to understand the characteristics of the detectors noise. Non-gaussian transients in the detector data and rapid changes in the instrument, known as non-stationary noise, can both add a systematic uncertainty to inferred results. We investigate how non-stationary noise affects the estimation of the luminosity distance of the source, and therefore of $H_0$. Using a population of 200 simulated binary neutron star signals, we show that non-stationary noise can bias the estimation of the luminosity distance by up to 2.4\%. However, only $\sim$15\% of binary neutron star signals would be affected around their merger time with non-stationary noise at a similar level to that seen in the first half of LIGO-Virgo's third observing run. Comparing the expected bias to other systematic uncertainties, we argue that non-stationary noise in the current generation of detectors will not be a limiting factor in resolving the tension on $H_0$ using standard sirens. Although, evaluating non-stationarity in gravitational-wave data will be crucial to obtain accurate estimates of $H_0$.

The redshift dependence of black hole mass distribution: is it reliable for standard sirens cosmology?

ABSTRACT An upper limit on the mass of a black hole set by the pair-instability supernovae (PISN) process can be useful in inferring the redshift of the gravitational wave (GW) sources by lifting the degeneracy between mass and redshift. However, for this technique to work, it is essential that the PISN mass scale is redshift independent or at least has a predictable redshift dependence. We show that the observed PISN mass scale can get smeared and the position of the PISN mass scale is likely to exhibit a strong redshift dependence due to a combined effect from the non-zero value of the delay time between the formation of a star and the merging of two black holes and the metallicity dependence of PISN mass scale. Due to the unknown form of the delay-time distribution, the redshift dependence of the PISN mass cutoff of the binary black holes (BBHs) cannot be well characterized and will exhibit a large variation with the change in redshift. As a result, the use of a fixed PISN mass scale to infer the redshift of the BBHs from the observed masses will be systematically biased. Though this uncertainty is not severe for the third observation run conducted by the LIGO–Virgo–KAGRA collaboration, in the future this uncertainty will cause a systematic error in the redshift inferred from the PISN mass scale. The corresponding systematic error will be a bottleneck in achieving a few per cent precision measurements of the cosmological parameters using this method in the future.

A New Way to Explore Cosmological Tensions Using Gravitational Waves and Strong Gravitational Lensing

In recent years, a crisis in the standard cosmology has been caused by inconsistencies in the measurements of some key cosmological parameters, the Hubble constant H 0 and cosmic curvature parameter Ω K , for example. It is necessary to remeasure them with the cosmological model-independent methods. In this paper, based on the distance sum rule, we present such a way to constrain H 0 and Ω K simultaneously in the late universe from strong gravitational lensing time-delay (SGLTD) data and gravitational wave (GW) standard siren data simulated from the future observation of the Einstein Telescope (ET). Based on the data for six currently observed SGLTDs, we find that the constraint precision of H 0 from the combined 100 GW events can be comparable with the measurement from the SH0ES collaboration. As the number of GW events increases to 700, the constraint precision of H 0 will exceed that of the Planck 2018 results. Considering 1000 GW events as the conservative estimation of ET in the 10 yr observation, we obtain H 0 = 73.69 ± 0.36 km s−1 Mpc−1 with a 0.5% uncertainty and . In addition, we simulate 55 strong gravitational lensing (SGL) systems with a 6.6% uncertainty for the measurement of time-delay distance. By combining with 1000 GWs, we infer that H 0 = 73.65 ± 0.35 km s−1 Mpc−1 and Ω K = 0.008 ± 0.048. Our results suggest that this approach can play an important role in exploring cosmological tensions.

High-precision Measurements of Cosmic Curvature from Gravitational Wave and Cosmic Chronometer Observations

Although the spatial curvature has been measured with very high precision, it still suffers from the well-known cosmic curvature tension. In this paper, we use an improved method to determine the cosmic curvature, by using the simulated data of binary neutron star mergers observed by the second generation space-based DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO). By applying the Hubble parameter observations of cosmic chronometers to the DECIGO standard sirens, we explore different possibilities of making measurements of the cosmic curvature referring to a distant past: one is to reconstruct the Hubble parameters through the Gaussian process without the influence of hypothetical models, and the other is deriving constraints on Ω K in the framework of the non-flat Λ cold dark matter model. It is shown that in the improved method DECIGO could provide a reliable and stringent constraint on the cosmic curvature (Ω K = −0.007 ± 0.016), while we could only expect the zero cosmic curvature to be established at the precision of ΔΩ K = 0.11 in the second model-dependent method. Therefore, our results indicate that in the framework of methodology proposed in this paper, the increasing number of well-measured standard sirens in DECIGO could significantly reduce the bias of estimations for cosmic curvature. Such a constraint is also comparable to the precision of Planck 2018 results with the newest cosmic microwave background (CMB) observations (ΔΩ K ≈ 0.018), based on the concordance ΛCDM model.

Multiple Measurements of Gravitational Waves Acting as Standard Probes: Model-independent Constraints on the Cosmic Curvature with DECIGO

Although the spatial curvature has been precisely determined via observations of the cosmic microwave background by the Planck satellite, it still suffers from the well-known cosmic curvature tension. As a standard siren, gravitational waves (GWs) from binary neutron star mergers provide a direct way to measure the luminosity distance. In addition, the accelerating expansion of the universe may cause an additional phase shift in the gravitational waveform, which will allow us to measure the acceleration parameter. This measurement provides an important opportunity to determine the curvature parameter Ω k in the GW domain based on the combination of two different observables for the same objects at high redshifts. In this study, we investigate how such an idea could be implemented with the future generation of the space-based Decihertz Interferometer Gravitational-wave Observatory (DECIGO) in the framework of two model-independent methods. Our results show that DECIGO could provide a reliable and stringent constraint on the cosmic curvature at a precision of ΔΩ k = 0.12, which is comparable to existing results based on different electromagnetic data. Our constraints are more stringent than the traditional electromagnetic method from the Pantheon sample of Type Ia supernovae, which shows no evidence for a deviation from a flat universe at z ∼ 2.3. More importantly, with our model-independent method, such a second-generation space-based GW detector would also be able to explore the possible evolution of Ω k with redshift, through direct measurements of cosmic curvature at different redshifts (z ∼ 5). Such a model-independent Ω k reconstruction to the distant past could become a milestone in gravitational-wave cosmology.

Multi-Messenger Constraints on the Hubble Constant through Combination of Gravitational Waves, Gamma-Ray Bursts and Kilonovae from Neutron Star Mergers

The simultaneous detection of gravitational waves and light from the binary neutron star merger GW170817 led to independent measurements of distance and redshift, providing a direct estimate of the Hubble constant H0 that does not rely on a cosmic distance ladder, nor assumes a specific cosmological model. By using gravitational waves as “standard sirens”, this approach holds promise to arbitrate the existing tension between the H0 value inferred from the cosmic microwave background and those obtained from local measurements. However, the known degeneracy in the gravitational-wave analysis between distance and inclination of the source led to a H0 value from GW170817 that was not precise enough to resolve the existing tension. In this review, we summarize recent works exploiting the viewing-angle dependence of the electromagnetic signal, namely the associated short gamma-ray burst and kilonova, to constrain the system inclination and improve on H0. We outline the key ingredients of the different methods, summarize the results obtained in the aftermath of GW170817 and discuss the possible systematics introduced by each of these methods.

A standard siren cosmological measurement from the potential GW190521 electromagnetic counterpart ZTF19abanrhr

ABSTRACT The identification of the electromagnetic (EM) counterpart candidate ZTF19abanrhr to the binary black hole merger GW190521 opens the possibility to infer cosmological parameters from this standard siren with a uniquely identified host galaxy. The distant merger allows for cosmological inference beyond the Hubble constant. Here, we show that the three-dimensional spatial location of ZTF19abanrhr calculated from the EM data remains consistent with the latest sky localization of GW190521 provided by the LIGO-Virgo Collaboration. If ZTF19abanrhr is associated with the GW190521 merger, and assuming a flat wCDM model, we find that $H_0=48^{+23}_{-10}\, \mathrm{km} \, \mathrm{s}^{-1}\, \mathrm{Mpc}^{-1}$, $\Omega _m=0.35^{+0.41}_{-0.26}$, and $w_0=-1.31^{+0.61}_{-0.48}$ (median and $68{{\ \rm per\ cent}}$ credible interval). If we use the Hubble constant value inferred from another gravitational-wave event, GW170817, as a prior for our analysis, together with assumption of a flat ΛCDM and the model-independent constraint on the physical matter density ωm from Planck, we find $H_0=68.9^{+8.7}_{-6.0}\, \mathrm{km} \, \mathrm{s}^{-1}\, \mathrm{Mpc}^{-1}$.

Investigating the dynamical models of cosmology with recent observations and upcoming gravitational-wave data

We explore and compare the capabilities of the recent observations of standard cosmological probes and the future observations of gravitational-wave (GW) standard sirens on constraining cosmological parameters. It is carried out in the frameworks of two typical dynamical models of cosmology, i.e., the $$\omega _0\omega _a$$ CDM model with $$\omega (z) = \omega _0 +\omega _a*z/(1+z)$$ , and the $$\xi $$ -index model with $$\rho _X\propto \rho _ma^{\xi }$$ , where $$\omega (z)$$ is the dark energy equation of state, and $$\rho _X$$ and $$\rho _m$$ are the energy densities of dark energy and matter, respectively. In the cosmological analysis, the employed data sets include the recent observations of the standard cosmological probes, i.e., Type Ia supernovae (SNe Ia), baryon acoustic oscillation (BAO) and cosmic microwave background (CMB), and also the mock GW standard siren sample with 1000 merging neutron star events anticipated from the third-generation detectors. In the scenarios of both $$\omega _0\omega _a$$ CDM and $$\xi $$ -index models, it turns out that the mock GW sample can reduce the uncertainty of the Hubble constant $$H_0$$ by about 50% relative to that from the joint SNe+BAO+CMB sample; nevertheless, the SNe+BAO+CMB sample demonstrates better performance on limiting other parameters. Furthermore, the Bayesian evidence is applied to compare the dynamical models with the $$\Lambda $$ CDM model. The Bayesian evidences computed from the SNe+BAO+CMB sample reveal that the $$\Lambda $$ CDM model is the most supported one; moreover, the $$\omega _0\omega _a$$ CDM model is more competitive than the $$\xi $$ -index model.

Anisotropy of the gravitational-wave standard sirens and its cosmological applications

We analyze the anisotropic factors present in the gravitational wave signal, such as the peculiar velocity of the observer and the inhomogeneous distribution of matter in the universe. We model the gravitational wave source as a standard siren, extract the anisotropic part of its luminosity distance d_L, and obtain the Hubble parameter H(z) by direct calculation instead of integration. Finally, we derive the equation of state w_mathrm{DE}(z) for the dark energy by both model-dependent and model-independent methods, and further investigate the cosmological significance of the simulated H(z) measurements. The advantage of this approach is that it makes full use of the anisotropic part of the d_L data, which directly gives the value of H(z) at certain redshifts. This approach is sensitive to the local features of H(z) and does not depend on the cosmological model.

Constraining cosmological extra dimensions with gravitational wave standard sirens: From theory to current and future multimessenger observations

The propagation of gravitational waves (GWs) at cosmological distances offers a new way to test the gravitational interaction at the largest scales. Many modified theories of gravity, usually introduced to explain the observed acceleration of the universe, can be probed in an alternative and complementary manner with respect to standard electromagnetic (EM) observations. In this paper we consider a homogeneous and isotropic cosmology with extra spatial dimensions at large scales, which represents a simple phenomenological prototype for extra-dimensional modified gravity cosmological models. By assuming that gravity propagates through the higher-dimensional spacetime, while photons are constrained to the usual four dimensions of general relativity, we derive from first principles the relation between the luminosity distance measured by GW detectors and the one inferred by EM observations. We then use this relation to constrain the number of cosmological extra dimensions with the binary neutron star event GW170817 and the binary black hole merger GW190521. We further provide forecasts for the Laser Interferometer Space Antenna (LISA) by simulating multi-messenger observations of massive black hole binary (MBHB) mergers. This paper extends and updates previous analyses which crucially neglected an additional redshift dependency in the GW-EM luminosity distance relation which affects results obtained from multi-messenger GW events at high redshift, in particular constraints expected from LISA MBHBs.

Reconstruction of the dark sectors’ interaction: A model-independent inference and forecast from GW standard sirens

ABSTRACT Interacting dark matter (DM) – dark energy (DE) models have been intensively investigated in the literature for their ability to fit various data sets as well as to explain some observational tensions persisting within the ΛCDM cosmology. In this work, we employ the Gaussian processes (GP) algorithm to perform a joint analysis by using the geometrical cosmological probes such as Cosmic chronometers, Supernova Type Ia, Baryon Acoustic Oscillations, and the H0LiCOW lenses sample to infer a reconstruction of the coupling function between the dark components in a general framework, where the DE can assume a dynamical character via its equation of state. In addition to the joint analysis with these data, we simulate a catalogue with standard siren events from binary neutron star mergers, within the sensitivity predicted by the Einstein Telescope, to reconstruct the dark sector coupling with more accuracy in a robust way. We find that the particular case, where w = −1 is fixed on the DE nature, has a statistical preference for an interaction in the dark sector at late times. In the general case, where w(z) is analysed, we find no evidence for such dark coupling, and the predictions are compatible with the ΛCDM paradigm. When the mock events of the standard sirens are considered to improve the kernel in GP predictions, we find a preference for an interaction in the dark sector at late times.

Dynamical dark energy models in the light of gravitational-wave transient catalogues

The study of current gravitational waves (GW) catalogues provide an interesting model independent way to understand further the nature of dark energy. In this work, we present an update of the constrains related to dynamical dark energy parametrisations using recent Gravitational-Wave Transient catalogues (GWTC-1 and GWTC-2) along with Type Ia supernova (SNeIa) and Cosmic Chronometers (CC) catalogues. According to our Bayesian results using the full SNeIa+CC+GW database, the ΛCDM model shows a strong preference against two dark energy parameterisation known as Barboza-Alcaniz (BA) and the Low Correlation (LC) models. Also, we obtain a very strong preference against the Chevallier-Polarski-Linder (CPL) model. Furthermore, we generated a mock GW catalogue and estimate that we require approximately 1000 standard sirens to have a constrain of H 0 within 1% relative error, quantity that is out of reach of current standard sirens candidates in GWTC-1 and GWTC-2 catalogues.

Cosmography with standard sirens from the Einstein Telescope

We discuss the power of third-generation gravitational wave detectors to constrain cosmographic parameters in the case of electromagnetically bright standard sirens focusing on the specific case of the Einstein Telescope. We analyze the impact that the redshift source distribution, the number of detections and the observational error in the luminosity distance have on the inference of the first cosmographic parameters, and show that with a few hundreds detections the Hubble constant can be recovered at sub-percent level whereas the deceleration parameter at a few percent level, both with negligible bias.

Cosmological perturbation theory in f(Q,T) gravity

We developed the cosmological linear theory of perturbations for f(Q,T) gravity, which is an extension of symmetric teleparallel gravity, with Q the non-metricity and T the trace of the stress-energy tensor. By considering an ansatz of f(Q,T) = f 1(Q)+f 2(T), which has been broadly studied in the literature and the coincident gauge where the connection vanishes, we got equations consistent with f(Q) gravity when fT = 0. In the case of the tensor perturbations, the propagation of gravitational waves was found to be identical to f(Q), as expected. For scalar perturbations, outside the limit fT = 0, we got that the coupling between Q and T in the Lagrangian produces a coupling between the perturbation of the density and the pressure. This coupling is preserved when considering the weak coupling limit between Q and T. On the other hand, in the strong coupling limit with a generic function of the form f 2(T) = αT + β T 2, the perturbative equations are heavily driven by the f 2(T) derivatives when β ≠ 0. However, when β = 0, the perturbative equations are identical to the weak coupling limit even though this case is a non-minimally coupling one. The presence of T in the Lagrangian breaks the equation of the conservation of energy, which in turn breaks the standard ρ' + 3\U0001d4d7 (ρ+p) = 0 relation. We also derived a coupled system of differential equations between δ, the density contrast and v in the \U0001d4d7 ≪ k limit and with negligible time derivative of the scalar perturbation potentials, which will be useful in future studies to see whether this class of theories constitute a good alternative to dark matter. These results might also enable to test f(Q,T) gravity with CMB and standard siren data that will help to determine if these models can reduce the Hubble constant tension and if they can constitute an alternative to the ΛCDM model.

Constraining the Hubble constant to a precision of about 1% using multi-band dark standard siren detections

Gravitational wave signal from the inspirai of stellar-mass binary black hole can be used as standard sirens to perform cosmological inference. This inspirai covers a wide range of frequency bands, from the millihertz band to the audio-band, allowing for detections by both space-borne and ground-based gravitational wave detectors. In this work, we conduct a comprehensive study on the ability to constrain the Hubble constant using the dark standard sirens, or gravitational wave events that lack electromagnetic counterparts. To acquire the redshift information, we weight the galaxies within the localization error box with photometric information from several bands and use them as a proxy for the binary black hole redshift. We discover that TianQin is expected to constrain the Hubble constant to a precision of roughly 30% through detections of 10 gravitational wave events; in the most optimistic case, the Hubble constant can be constrained to a precision of <10%, assuming TianQin I+II. In the optimistic case, the multi-detector network of TianQin and LISA is capable of constraining the Hubble constant to within 5% precision. It is worth highlighting that the multi-band network of TianQin and Einstein Telescope is capable of constraining the Hubble constant to a precision of about 1%. We conclude that inferring the Hubble constant without bias from photo-z galaxy catalog is achievable, and we also demonstrate self-consistency using the P-P plot. On the other hand, high-quality spectroscopic redshift information is crucial for improving the estimation precision of Hubble constant.

A pixelated approach to galaxy catalogue incompleteness: improving the dark siren measurement of the Hubble constant

ABSTRACT The use of gravitational wave standard sirens for cosmological analyses is becoming well known, with particular interest in measuring the Hubble constant, H0, and in shedding light on the current tension between early- and late-time measurements. The current tension is over 4σ and standard sirens will be able to provide a completely independent measurement. Dark sirens (binary black hole or neutron star mergers with no electromagnetic counterparts) can be informative if the missing redshift information is provided through the use of galaxy catalogues to identify potential host galaxies of the merger. However, galaxy catalogue incompleteness affects this analysis, and accurate modelling of it is essential for obtaining an unbiased measurement of H0. Previously most methods have assumed uniform completeness within the sky area of a gravitational wave event. This paper presents an updated methodology in which the completeness of the galaxy catalogue is estimated in a directionally dependent matter, by pixelating the sky and computing the completeness of the galaxy catalogue along each line of sight. The H0 inference for a single event is carried out on a pixel-by-pixel basis, and the pixels are combined for the final result. A reanalysis of the events in the first gravitational wave transient catalogue leads to an improvement on the measured value of H0 of approximately 5 per cent compared to the 68.3 per cent highest density interval of the equivalent LIGO and Virgo result, with H0 = $68.8^{+15.9}_{-7.8}$ km s−1 Mpc−1.

Multiband gravitational wave cosmology with stellar origin black hole binaries

Massive stellar origin black hole binaries (SBHBs), originating from stars above the pair-instability mass gap, are primary candidates for multiband gravitational wave (GW) observations. Here we study the possibility to use them as effective dark standard sirens to constrain cosmological parameters. The long lasting inspiral signal emitted by these systems is accessible by the future $Laser \; Interferometer \; Space \; Antenna$ (LISA), while the late inspiral and merger are eventually detected by third generation ground-based telescopes such as the $Einstein \; Telescope$ (ET). The direct measurement of the luminosity distance and the sky position to the source, together with the inhomogeneous redshift distribution of possible host galaxies, allow us to infer cosmological parameters by probabilistic means. The efficiency of this statistical method relies in high parameter estimation performances. We show that this multiband approach allows a precise determination of the Hubble constant H$_0$ with just ${\cal O}(10)$ detected sources. For selected SBHB population models, assuming $4$ ($10$) years of LISA observations, we find that H$_0$ is typically determined at $\sim 2\%$ ($\sim 1.5\%$), whereas $\Omega_m$ is only mildly constrained with a typical precision of $30\%$ ($20\%$). We discuss the origin of some outliers in our final estimates and we comment on ways to reduce their presence.

A forecast of using fast radio burst observations to constrain holographic dark energy

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.