Gravitational Wave Standard Sirens Research Articles

Exploring bulk viscous unified scenarios with gravitational waves standard sirens

ABSTRACT We consider the unified bulk viscous scenarios and constrain them using the Cosmic Microwave Background observations from Planck 2018 and the Pantheon sample from Type Ia supernovae. Then we generate the luminosity distance measurements from ${\cal O}(10^3)$ mock Gravitational Wave Standard Sirens (GWSS) events for the proposed Einstein Telescope. We then combine these mock luminosity distance measurements from the GWSS with the current cosmological probes in order to forecast how the mock GWSS data could be effective in constraining these bulk viscous scenarios. Our results show that a non-zero time dependent bulk viscosity in the universe sector is strongly preferred by the current cosmological probes and will possibly be confirmed at many standard deviations by the future GWSS measurements. We further mention that the addition of GWSS data can significantly reduce the uncertainties of the key cosmological parameters obtained from the usual cosmological probes employed in this work.

Impacts of gravitational-wave standard siren observations from Einstein Telescope and Cosmic Explorer on weighing neutrinos in interacting dark energy models

Multi-messenger gravitational wave (GW) observation for binary neutron star merger events could provide a rather useful tool to explore the evolution of the Universe. In particular, for the third-generation GW detectors, i.e. the Einstein Telescope (ET) and the Cosmic Explorer (CE), proposed to be built in Europe and the U.S., respectively, lots of GW standard sirens with known redshifts could be obtained, which would exert great impacts on the cosmological parameter estimation. The total neutrino mass could be measured by cosmological observations, but such a measurement is model-dependent and currently only gives an upper limit. In this work, we wish to investigate whether the GW standard sirens observed by ET and CE could help improve the constraint on the neutrino mass, in particular in the interacting dark energy (IDE) models. We find that the GW standard siren observations from ET and CE can only slightly improve the constraint on the neutrino mass in the IDE models, compared to the current limit. The improvements in the IDE models are weaker than those in the standard cosmological model. Although the limit on neutrino mass can only be slightly updated, the constraints on other cosmological parameters can be significantly improved by using the GW observations.

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.

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.

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.

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.

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.

On Dark Gravitational Wave Standard Sirens as Cosmological Inference and Forecasting the Constraint on Hubble Constant using Binary Black Holes Detected by Deci-hertz Observatory

Gravitational wave (GW) signals from compact binary coalescences can be used as standard sirens to constrain cosmological parameters if their redshift can be measured independently by electromagnetic signals. However, mergers of stellar binary black holes (BBHs) may not have electromagnetic counterparts and thus have no direct redshift measurements. These dark sirens may be still used to statistically constrain cosmological parameters by combining their GW measured luminosity distances and localization with deep redshift surveys of galaxies around it. We investigate this dark siren method to constrain cosmological parameters in detail by using mock BBH and galaxy samples. We find that the Hubble constant can be constrained well with an accuracy ≲1% with a few tens or more of BBH mergers at redshift up to 1 if GW observations can provide accurate estimates of their luminosity distance (with relative error of ≲0.01) and localization (≲0.1 deg2), though the constraint may be significantly biased if the luminosity distance and localization errors are larger. We also introduce a simple method to correct this bias and find it is valid when the luminosity distance and localization errors are modestly large. We further generate mock BBH samples, according to current constraints on BBH merger rate and the distributions of BBH properties, and find that the Deci-hertz Observatory (DO) in a half year observation period may detect about one hundred BBHs with signal-to-noise ratio ϱ ≳ 30, relative luminosity distance error ≲0.02 and localization error ≲0.01 deg2. By applying the dark standard siren method, we find that the Hubble constant can be constrained to the ∼0.1%–1% level using these DO BBHs, an accuracy comparable to the constraints obtained by using electromagnetic observations in the near future, thus it may provide insight into the Hubble tension. We also demonstrate that the constraint on the Hubble constant applying this dark siren method is robust and does not depend on the choice of the prior for the properties of BBH host galaxies.

Using a multi-messenger and multi-wavelength observational strategy to probe the nature of dark energy through direct measurements of cosmic expansion history

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<z<5 and 0<z<0.3. In addition, gravitational wave (GW) standard siren observations could make measurements on the dipole anisotropy of luminosity distance, which will also provide the H(z) measurements in the redshift range of 0<z<3. In this work, we propose a multi-messenger and multi-wavelength observational strategy to measure H(z) based on the three next-generation projects, E-ELT, SKA, and DECIGO, and we wish to see whether the future H(z) measurements could provide tight constraints on dark-energy parameters. The dark energy models we consider include ΛCDM, wCDM, CPL, HDE, and IΛCDM models. It is found that E-ELT, SKA1, and DECIGO are highly complementary in constraining dark energy models. Although any one of these three data sets can only give rather weak constraints on each model we consider, the combination of them could significantly break the parameter degeneracies and give much tighter constraints on almost all the cosmological parameters. Moreover, we find that the combination of E-ELT, SKA1, DECIGO, and CMB could further improve the constraints on dark energy parameters, e.g., σ(w 0)=0.024 and σ(w a)=0.17 in the CPL model, which means that these three promising probes will play a key role in helping reveal the nature of dark energy.

Space-borne atom interferometric gravitational wave detections. Part I. The forecast of bright sirens on cosmology

Atom interferometers (AIs) as gravitational-wave (GW) detectors have been proposed a decade ago. Both ground and space-based projects will be in construction and preparation in the near future. In this paper, for the first time, we investigate the potential of the space-borne AIs on detecting GW standard sirens and hence the applications on cosmology. We consider AEDGE as our fiducial AI GW detector and estimate the number of bright sirens that would be obtained within a 5-years data-taking period of GW and with the follow-up observation of electromagnetic (EM) counterparts. We then construct the mock catalogue of bright sirens and predict their ability on constraining cosmological parameters such as the Hubble constant, dynamics of dark energy, and modified gravity theory. Our preliminary results show around order \U0001d4aa (30) bright sirens can be obtained from a 5-years operation time of AEDGE and the follow-up observation of EM counterparts. The bright sirens alone can measure H 0 with a precision 2.1%, which is sufficient to arbitrate the Hubble tension. Combining current most precise electromagnetic experiments, the inclusion of AEDGE bright sirens can improve the measurement of the equation of state of dark energy, though marginally. Moreover, by modifying GW propagation on cosmological scales, the deviations from general relativity (modified gravity theory effects) can be constrained at 5.7% precision level.

How will our knowledge of short gamma-ray bursts affect the distance measurement of binary neutron stars?

Gravitational waves from binary neutron stars associated with short gamma-ray bursts have drawn considerable attention due to their prospect in cosmology. For such events, the sky locations of sources can be pinpointed with techniques such as identifying the host galaxies. However, the cosmological applications of these events still suffer from the problem of degeneracy between luminosity distance and inclination angle. To address this issue, a technique was proposed in previous study, i.e., using the collimation property of short gamma-ray bursts. Based on the observations, we assume that the cosine of inclination follows a Gaussian distribution, which may act as a prior in the Bayes analysis to break the degeneracy. This paper investigates the effects of different Gaussian priors and detector configurations on distance measurement and cosmological research. We first derive a simplified Fisher information matrix for demonstration, and then conduct quantitative analyses via simulation. By varying the number of third-generation detectors and the scale of prior, we generate four catalogs of 1000 events. It is shown that, in the same detecting period, a network of detectors can recognize more and farther events than a single detector. Besides, adopting tighter prior and employing multiple detectors both decrease the error of luminosity distance. Also considered is the performance of a widely adopted formula in the error budget, which turns out to be a conservative choice in each case. As for cosmological applications, for the ΛCDM model, 500, 200, 600, and 300 events are required for the four configurations to achieve 1% H0 accuracy. With all 1000 events in each catalog, H0 and Ωm can be constrained to (0.66%, 0.37%, 0.76%, 0.49%), and (0.010, 0.006, 0.013, 0.010), respectively. The results of the Gaussian process also show that the gravitational wave standard siren can serve as a probe of cosmology at high redshifts.

How can gravitational-wave standard sirens and 21-cm intensity mapping jointly provide a precise late-universe cosmological probe?

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 $\mathrm{ET}+\mathrm{Taiji}+\mathrm{SKA}$ data give $\ensuremath{\sigma}({H}_{0})=0.28\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ in the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, $\ensuremath{\sigma}(w)=0.028$ in the $w\mathrm{CDM}$ model, which are better than the results of $Planck+\mathrm{BAO}+\mathrm{SNe}$, and $\ensuremath{\sigma}({w}_{0})=0.077$ and $\ensuremath{\sigma}({w}_{a})=0.295$ in the CPL model, which are comparable with the results of $Planck+\mathrm{BAO}+\mathrm{SNe}$. In the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, the constraint precision of ${H}_{0}$ and ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{m}}$ 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.

Forecast for cosmological parameter estimation with gravitational-wave standard sirens from the LISA-Taiji network

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° 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 H0 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.

Calibrating systematic errors in the distance determination with the luminosity–distance space large-scale structure of dark sirens and its potential applications

ABSTRACT The cosmological luminosity–distance can be measured from gravitational wave (GW) standard sirens, free of astronomical distance ladders, and the associated systematics. However, it may still contain systematics arising from various astrophysical, cosmological, and experimental sources. With the large amount of dark standard sirens of upcoming third generation GW experiments, such potential systematic bias, can be diagnosed and corrected by statistical tools of the large-scale structure of the universe. We estimate that, by cross-correlating the dark siren luminosity–distance space distribution and galaxy redshift space distribution, multiplicative error m in the luminosity distance measurement can be constrained with 1σ uncertainty σm ∼ 0.1. This is already able to distinguish some binary black hole origin scenarios unambiguously. Significantly better constraints and therefore more applications may be achieved by more advanced GW experiments.

Gravitational-wave detector networks: standard sirens on cosmology and modified gravity theory

We construct the catalogues of standard sirens (StS) based on the future gravitational wave (GW) detector networks, i.e., the second-generation ground-based advanced LIGO+advanced Virgo+KAGRA+LIGO-India (HLVKI), the third-generation ground-based Einstein Telescope+two Cosmic Explorer (ET+2CE), and the space-based LISA+Taiji. From the corresponding electromagnetic (EM) counterpart detectors for each networks, we sample the joint GW+EM detections from the probability to construct the Hubble diagram of standard sirens for 10 years detections of HLVKI, 5 years detections of ET+2CE, and 5 years of detections of LISA+Taiji, which we estimate would be available and released in the 2030s. Thus we construct a combined Hubble diagram from these ground and spaced-based detector networks to explore the expansion history of our Universe from redshift 0 to 7. We give a conservative and realistic estimation of the catalogue and Hubble diagram of GW standard sirens and their potential on studying cosmology and modified gravity theory in the 2030s. We adopt two strategies for the forecasts. One is the traditional model-fitting Markov-Chain Monte-Carlo method (MCMC). The results show that the combined StS alone can constrain the Hubble constant at the precision level of 0.34%, 1.76 times more tightly than the current most precise measurement from Planck+BAO+Pantheon. The joint StS with current EM experiments will improve the constraints of cosmological parameters significantly. The modified gravity theory can be constrained with 0.46% error from the GW propagation. In the second strategy, we use the machine-learning nonparametric reconstruction techniques, i.e., the Gaussian process (GP) with the Artificial Neural Networks (ANN) as a comparison. GP reconstructions can give comparable results with MCMC. We anticipate more works and research on these topics.

Machine Learning the Cosmic Curvature in a Model-independent Way

Abstract In this work, we achieve the determination of the cosmic curvature ΩK in a cosmological model-independent way, by using the Hubble parameter measurements H(z) and type Ia supernovae (SNe Ia). In our analysis, two nonlinear interpolating tools are used to reconstruct the Hubble parameter, one is the Artificial Neural Network (ANN) method, and the other is the Gaussian process (GP) method. We find that ΩK based on the GP method can be greatly influenced by the prior of H0, while the ANN method can overcome this. Therefore, the ANN method may have more advantages than GP in the measurement of the cosmic curvature. Based on the ANN method, we find a spatially open universe is preferred by the current H(z) and SNe Ia data, and the difference between our result and the value inferred from Planck CMB is 1.6σ. In order to test the reliability of the ANN method, and the potentiality of the future gravitational waves (GW) standard sirens in the measurement of the cosmic curvature, we constrain ΩK using the simulated Hubble parameter and GW standard sirens in a model-independent way. We find that the ANN method is reliable and unbiased, and the error of ΩK is ∼0.186 when 100 GW events with electromagnetic counterparts are detected, which is $\sim 56\%$ smaller than that constrained from the Pantheon SNe Ia. Therefore, the data-driven method based on ANN has potential in the measurement of the cosmic curvature.

Constraining scalar-tensor modified gravity with gravitational waves and large scale structure surveys

The first multi-messenger gravitational wave event has had a transformative effect on the space of modified gravity models. In this paper we study the enhanced tests of gravity that are possible with a future set of gravitational wave standard siren events. We perform MCMC constraint forecasts for parameters in Horndeski scalar-tensor theories. In particular, we focus on the complementarity of gravitational waves with electromagnetic large-scale structure data from galaxy surveys. We find that the addition of fifty low redshift (z ≲ 0.2) standard sirens from the advanced LIGO network offers only a modest improvement (a factor 1.1–1.3, where 1.0 is no improvement) over existing constraints from electromagnetic observations of large-scale structures. In contrast, high redshift (up to z ∼ 10) standard sirens from the future LISA satellite will improve constraints on the time evolution of the Planck mass in Horndeski theories by a factor ∼ 5. By simulating different scenarios, we find this improvement to be robust to marginalisation over unknown merger inclination angles and to variation between three plausible models for the merger source population.

Constraints on the distance duality relation with standard sirens

We use gravitational wave (GW) standard sirens, in addition to Type Ia supernovae (SNIa) and baryon acoustic oscillation (BAO) mock data, to forecast constraints on the electromagnetic and gravitational distance duality relations (DDR) . We make use of a parameterised approach based on a specific DDR violation model, along with a machine learning reconstruction method based on the Genetic Algorithms. We find that GW provide an alternative to the use of BAO data to constrain violations of the DDR, reaching 3% constraints on the violation parameter we consider when combined with SNIa, which is only improved by a factor of ≈1.4 if one instead considers the combination of BAO and SNIa. We also investigate the possibility that a neglected modification of gravity might lead to a false detection of DDR violations, even when screening mechanisms are active. We find that such a false detection can be extremely significant, up to ≈10σ for very extreme modified gravity scenarios, while this reduces to ≈4σ in a more realistic case. False detections can also provide a smoking gun for the modified gravity mechanism at play, as a result of the tension introduced between the SNIa+GW and SNIa+BAO combinations.