Gravitational wave interference via gravitational lensing: Measurements of luminosity distance, lens mass, and cosmological parameters

Abstract Gravitational wave (GW) signals from compact binary coalescences can be used as standard sirens to constrain cosmological parameters if its 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 details by using mock BBH and galaxy samples. We find that the Hubble constant can be well constrained with an accuracy $\lesssim 1\%$ with a few tens or more BBH mergers at redshift up to $1$ if GW observations can provide accurate estimates of its luminosity distance (with relative error of $\lesssim 0.01$) and localization ($\lesssim 0.1\mathrm{deg}^2$), though the constraint may be significantly biased if the luminosity distance and localization errors are larger. We further generate mock BBH samples, according to current constraints on BBH merger rate and the distributions of BBH properties, and find that Deci-Hertz Observatory (DO) in a half year observation period may detect about one hundred BBHs with signal-to-noise ratio $\varrho \gtrsim 30$, relative luminosity distance error $\lesssim 0.02$, and localization error $\lesssim 0.01\mathrm{deg}^2$. By applying the dark standard siren method, we find that the Hubble constant can be constrained to $\sim 0.1-1\%$ 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 using this dark siren method are robust and do not depend on the choice of the prior for the properties of BBH host galaxies.

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Lensing Magnification Seen by Gravitational Wave Detectors

Universe ◽

10.3390/universe8010019 ◽

2021 ◽

Vol 8 (1) ◽

pp. 19

Author(s):

Giulia Cusin ◽

Ruth Durrer ◽

Irina Dvorkin

Keyword(s):

Gravitational Wave ◽

Gravitational Lensing ◽

Analytic Approach ◽

Source Population ◽

Luminosity Distance ◽

Wave Source ◽

Underlying Distribution ◽

Detector Sensitivity ◽

Strong Lensing

In this paper, we studied the gravitational lensing of gravitational wave events. The probability that an observed gravitational wave source has been (de-)amplified by a given amount is a detector-dependent quantity which depends on different ingredients: the lens distribution, the underlying distribution of sources and the detector sensitivity. The main objective of the present work was to introduce a semi-analytic approach to study the distribution of the magnification of a given source population observed with a given detector. The advantage of this approach is that each ingredient can be individually varied and tested. We computed the expected magnification as both a function of redshift and of the observedsource luminosity distance, which is the only quantity one can access via observation in the absence of an electromagnetic counterpart. As a case study, we then focus on the LIGO/Virgo network and on strong lensing (μ>1).

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Anisotropy of the galaxy cluster X-ray luminosity–temperature relation

Astronomy and Astrophysics ◽

10.1051/0004-6361/201731222 ◽

2018 ◽

Vol 611 ◽

pp. A50 ◽

Cited By ~ 5

Author(s):

Konstantinos Migkas ◽

Thomas H. Reiprich

Keyword(s):

Galaxy Clusters ◽

Statistical Significance ◽

Cosmological Parameters ◽

Galaxy Cluster ◽

Luminosity Distance ◽

Temperature Relation ◽

X Ray ◽

Two Samples ◽

The Galaxy ◽

Group A

We introduce a new test to study the cosmological principle with galaxy clusters. Galaxy clusters exhibit a tight correlation between the luminosity and temperature of the X-ray-emitting intracluster medium. While the luminosity measurement depends on cosmological parameters through the luminosity distance, the temperature determination is cosmology-independent. We exploit this property to test the isotropy of the luminosity distance over the full extragalactic sky, through the normalization a of the LX–T scaling relation and the cosmological parameters Ωm and H0. To this end, we use two almost independent galaxy cluster samples: the ASCA Cluster Catalog (ACC) and the XMM Cluster Survey (XCS-DR1). Interestingly enough, these two samples appear to have the same pattern for a with respect to the Galactic longitude. More specifically, we identify one sky region within l ~ (−15°, 90°) (Group A) that shares very different best-fit values for the normalization of the LX–T relation for both ACC and XCS-DR1 samples. We use the Bootstrap and Jackknife methods to assess the statistical significance of these results. We find the deviation of Group A, compared to the rest of the sky in terms of a, to be ~2.7σ for ACC and ~3.1σ for XCS-DR1. This tension is not significantly relieved after excluding possible outliers and is not attributed to different redshift (z), temperature (T), or distributions of observable uncertainties. Moreover, a redshift conversion to the cosmic microwave background (CMB) frame does not have an important impact on our results. Using also the HIFLUGCS sample, we show that a possible excess of cool-core clusters in this region, is not able to explain the obtained deviations. Furthermore, we tested for a dependence of the results on supercluster environment, where the fraction of disturbed clusters might be enhanced, possibly affecting the LX–T relation. We indeed find a trend in the XCS-DR1 sample for supercluster members to be underluminous compared to field clusters. However, the fraction of supercluster members is similar in the different sky regions, so this cannot explain the observed differences, either. Constraining Ωm and H0 via the redshift evolution of LX–T and the luminosity distance via the flux–luminosity conversion, we obtain approximately the same deviation amplitudes as for a. It is interesting that the general observed behavior of Ωm for the sky regions that coincide with the CMB dipole is similar to what was found with other cosmological probes such as supernovae Ia. The reason for this behavior remains to be identified.

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Cosmological Parameters and Gravitational Lensing Statistics

Annals of the New York Academy of Sciences ◽

10.1111/j.1749-6632.1995.tb17617.x ◽

1995 ◽

Vol 759 (1) ◽

pp. 600-603

Author(s):

PHILLIP HELBIG

Keyword(s):

Gravitational Lensing ◽

Cosmological Parameters

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Constraints in the Δ0-Ω0 plane from gravitational lensing

Symposium - International Astronomical Union ◽

10.1017/s0074180900216318 ◽

2005 ◽

Vol 201 ◽

pp. 245-254

Author(s):

Phillip. Helbig

Keyword(s):

Gravitational Lensing ◽

Cosmological Parameters ◽

Gravitational Lenses ◽

Extragalactic Surveys

I review simultaneous constraints on the cosmological parameters Δ0 and Ω0 from gravitational lensing. The emphasis is on systematic extragalactic surveys for strong gravitational lenses, mainly the largest and best-defined such survey, JVAS/CLASS.

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Assessing the effect of lens mass model in cosmological application with updated galaxy-scale strong gravitational lensing sample

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1902 ◽

2019 ◽

Vol 488 (3) ◽

pp. 3745-3758 ◽

Cited By ~ 8

Author(s):

Yun Chen ◽

Ran Li ◽

Yiping Shu ◽

Xiaoyue Cao

Keyword(s):

Density Profile ◽

Gravitational Lensing ◽

Mass Density ◽

Cosmological Parameters ◽

Mass Model ◽

Surface Mass ◽

Cosmological Application ◽

Surface Mass Density ◽

Resolution Imaging ◽

Lens Galaxies

ABSTRACT By comparing the dynamical and lensing masses of early-type lens galaxies, one can constrain both the cosmological parameters and the density profiles of galaxies. We explore the constraining power on cosmological parameters and the effect of the lens mass model in this method with 161 galaxy-scale strong lensing systems, which is currently the largest sample with both high-resolution imaging and stellar dynamical data. We assume a power-law mass model for the lenses, and consider three different parametrizations for γ (i.e. the slope of the total mass density profile) to include the effect of the dependence of γ on redshift and surface mass density. When treating δ (i.e. the slope of the luminosity density profile) as a universal parameter for all lens galaxies, we find the limits on the cosmological parameter Ωm are quite weak and biased, and also heavily dependent on the lens mass model in the scenarios of parametrizing γ with three different forms. When treating δ as an observable for each lens, the unbiased estimate of Ωm can be obtained only in the scenario of including the dependence of γ on both the redshift and the surface mass density, that is $\Omega _\mathrm{ m} = 0.381^{+0.185}_{-0.154}$ at 68 per cent confidence level in the framework of a flat ΛCDM model. We conclude that the significant dependencies of γ on both the redshift and the surface mass density, as well as the intrinsic scatter of δ among the lenses, need to be properly taken into account in this method.

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Cross-correlation of the thermal Sunyaev–Zel’dovich effect and weak gravitational lensing: Planck and Subaru Hyper Suprime-Cam first-year data

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa117 ◽

2020 ◽

Vol 492 (4) ◽

pp. 4780-4804 ◽

Cited By ~ 5

Author(s):

Ken Osato ◽

Masato Shirasaki ◽

Hironao Miyatake ◽

Daisuke Nagai ◽

Naoki Yoshida ◽

...

Keyword(s):

Gravitational Lensing ◽

Cross Correlation ◽

High Redshift ◽

Cosmological Parameters ◽

First Year ◽

Weak Gravitational Lensing ◽

Mass Bias ◽

Cross Correlation Analysis ◽

Sunyaev Zel'dovich Effect ◽

Calibration Techniques

ABSTRACT Cross-correlation analysis of the thermal Sunyaev–Zel’dovich (tSZ) effect and weak gravitational lensing (WL) provides a powerful probe of cosmology and astrophysics of the intracluster medium. We present the measurement of the cross-correlation of tSZ and WL from Planck and Subaru Hyper-Suprime Cam. The combination enables us to study cluster astrophysics at high redshift. We use the tSZ-WL cross-correlation and the tSZ autopower spectrum measurements to place a tight constraint on the hydrostatic mass bias, which is a measure of the degree of non-thermal pressure support in galaxy clusters. With the prior on cosmological parameters derived from the analysis of the cosmic microwave background anisotropies by Planck and taking into account foreground contributions both in the tSZ autopower spectrum and the tSZ-WL cross-correlation, the hydrostatic mass bias is estimated to be $26.9^{+8.9}_{-4.4} {{\ \rm per\ cent}}$ ($68{{\ \rm per\ cent}}$ CL), which is consistent with recent measurements by mass calibration techniques.

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Gravitational-wave luminosity distance in quantum gravity

Physics Letters B ◽

10.1016/j.physletb.2019.135000 ◽

2019 ◽

Vol 798 ◽

pp. 135000 ◽

Cited By ~ 4

Author(s):

Gianluca Calcagni ◽

Sachiko Kuroyanagi ◽

Sylvain Marsat ◽

Mairi Sakellariadou ◽

Nicola Tamanini ◽

...

Keyword(s):

Quantum Gravity ◽

Gravitational Wave ◽

Luminosity Distance

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GRAVITATIONAL LENSING BOUND ON THE AVERAGE REDSHIFT OF GAMMA RAY BURSTS IN MODELS WITH EVOLVING LENSES

International Journal of Modern Physics D ◽

10.1142/s0218271899000353 ◽

1999 ◽

Vol 08 (04) ◽

pp. 507-517 ◽

Cited By ~ 2

Author(s):

DEEPAK JAIN ◽

N. PANCHAPAKESAN ◽

S. MAHAJAN ◽

V. B. BHATIA

Keyword(s):

Gravitational Lensing ◽

Gamma Ray ◽

Cosmological Parameters ◽

Evolutionary Model ◽

Gamma Ray Bursts ◽

The Other ◽

Upper Limit ◽

Evolving Model ◽

Evolving Models ◽

The Universe

Identification of gravitationally lensed Gamma Ray Bursts (GRBs) in the BATSE 4B catalog can be used to constrain the average redshift <z> of the GRBs. In this paper we investigate the effect of evolving lenses on the <z> of GRBs in different cosmological models of the universe. The cosmological parameters Ω and Λ have an effect on the <z> of GRBs. The other factor which can change the <z> is the evolution of galaxies. We consider three evolutionary model of galaxies. In particular, we find that the upper limit on <z> of GRBs is higher in evolving model of galaxies as compared to non-evolving models of galaxies.

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GRAVITATIONAL LENS AMPLIFICATION OF GRAVITATIONAL RADIATION

International Journal of Modern Physics D ◽

10.1142/s0218271802002578 ◽

2002 ◽

Vol 11 (07) ◽

pp. 1067-1074 ◽

Cited By ~ 7

Author(s):

ALEXANDER F. ZAKHAROV ◽

YURI V. BARYSHEV

Keyword(s):

Gravitational Wave ◽

Gravitational Lensing ◽

Gravitational Radiation ◽

Gravitational Lens ◽

Wave Form ◽

Gravitational Lenses ◽

Approximation Model ◽

Radiation Sources ◽

Wave Space ◽

Stellar Masses

In a recent paper by Wang, Turner and Stebbins (1996) an influence of gravitational lensing on increasing an estimated rate of gravitational radiation sources was considered. We show that the authors used the geometrical optics approximation model for gravitational lensing and thus they gave overestimated rate of possible events for possible sources of gravitational radiation for the advanced LIGO detector. We show also that if we would use a more correct model of gravitational lensing, one could conclude that more strong influence on increasing rate of estimated events of gravitational radiation for advanced LIGO detector could give gravitational lenses of galactic masses but not gravitational lenses of stellar masses as Wang et al. concluced. Moreover, binary gravitational lenses could give essential distortion of gravitational wave form template, especially gravitational wave template of periodic sources and the effect could be significant for templates of quasi-periodic sources which could be detected by a future gravitational wave space detector like LISA.

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