Lensing Magnification Seen by Gravitational Wave Detectors

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).

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.

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

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.

BiGONLight: light propagation with bi-local operators in Numerical Relativity

BiGONLight, Bilocal Geodesic Operators framework for Numerical Light propagation, is a new tool for light propagation in Numerical Relativity. The package implements the Bi-local Geodesic Operators formalism, a new framework for light propagation in General Relativity. With BiGONLight it is possible to extract observables such as angular diameter distance, luminosity distance, magnification as well as new real-time observables like parallax and redshift drift within the same computation. As a test-bed for our code we consider two exact cosmological models, the ΛCDM and the inhomogeneous Szekeres model, and a simulated dust universe. All our tests show an excellent agreement with known results.

Lensing magnification: gravitational waves from coalescing stellar-mass binary black holes

ABSTRACT Gravitational waves (GWs) may be magnified or de-magnified due to lensing. This phenomenon will bias the distance estimation based on the matched filtering technique. Via the multi-sphere ray-tracing technique, we study the GW magnification effect and selection effect with particular attention to the stellar-mass binary black holes. We find that, for the observed luminosity distance $\lesssim 3\, \mathrm{Gpc}$, which is the aLIGO/Virgo observational horizon limit, the average magnification keeps as unity, namely unbiased estimation, with the relative distance uncertainty $\sigma (\hat{d})/\hat{d}\simeq 0.5{{\ \rm per\ cent}}\sim 1{{\ \rm per\ cent}}$. Beyond this observational horizon, the estimation bias can not be ignored, and with the scatters $\sigma (\hat{d})/\hat{d} = 1{{\ \rm per\ cent}}\sim 15{{\ \rm per\ cent}}$. Furthermore, we forecast these numbers for Einstein Telescope (ET). We find that the average magnification keeps closely as unity for the observed luminosity distance $\lesssim 90\, \mathrm{Gpc}$. The luminosity distance estimation error due to lensing for ET is about $\sigma (\hat{d})/\hat{d} \simeq 10{{\ \rm per\ cent}}$ for the luminosity distance $\gtrsim 25\, \mathrm{Gpc}$. Unlike the aLIGO/Virgo case, this sizable error is not due to the selection effect. It purely comes from the unavoidably accumulated lensing magnification. Moreover, we investigated the effects of the orientation angle and the BH mass distribution models. We found that the results are strongly dependent on these two components.

Measuring the Hubble function with standard candle clustering

Supernova Ia magnitude surveys measure the dimensionless luminosity distance H0DL. However, from the distances alone one cannot obtain quantities like H(z) or the dark energy equation of state, unless further cosmological assumptions are imposed. Here we show that by measuring the power spectrum of density contrast and of peculiar velocities of supernovae one can estimate also H(z)/H0 regardless of background or linearly perturbed cosmology and of galaxy-matter bias. This method, dubbed Clustering of Standard Candles (CSC) also yields the redshift distortion parameter β(k, z) and the biased matter power spectrum in a model-independent way. We forecast that an optimistic (pessimistic) LSST may be able to constrain H(z)/H0 to 5–13% (9–40%) in redshift bins of Δz = 0.1 up to at least z = 0.6.

FRW cosmological models with cosmological constant in f (R,T) theory of gravity

In the present paper, we have generalized the behaviors of {\color{blue}transit-decelerating to accelerating} FRW cosmological model in f (R, T) gravity theory, where R, T are Ricci scalar and trace of energy-momentum tensor respectively. The solution of the corresponding field equations is obtained by assuming a linear function of the Hubble parameter H, i.e., q = c₁ + c₂H which gives a time-dependent DP (deceleration parameter) q(t)=-1+\frac{c_2}{\sqrt{2c_2 t +c_3}}, where c₃ and c₂ are arbitrary integrating constants [Tiwari et al., Eur. Phys. J. Plus: 131, 447 (2016); 132, 126 (2017)]. There are two scenarios in which we explain the particular form of scale factor thus obtained (i) By using the recent constraints from OHD and JLA data which shows a cosmic deceleration to acceleration and (ii) By using new constraints from supernovae type la union data which shows accelerating expansion universe (q<0) throughout the evolution. We have observed that the EoS parameter, energy density parameters, and important cosmological planes yield the results compatible with the modern observational data. For the derived models, we have calculated various physical parameters as Luminosity distance, Distance modulus, and Apparent magnitude versus redshift for both supporting current observations.

Intrinsically symmetric cosmological model in the presence of dissipative fluids

Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact solution to Einstein’s field equations where the spatial sections are flat and the source is a nonperfect fluid such that the dissipative terms can be written in terms of spatial gradients of the energy density under a suitable choice of the coordinate system. It is shown through the calculation of the luminosity distance as a function of the redshift that the presence of such inhomogeneities may lead to an effective deceleration parameter compatible with either the standard [Formula: see text]CDM model or LTB models depending on the choice of boundary conditions with no exotic matter. This fact is another evidence that different inhomogeneous models should be carefully investigated in order to verify which model may be compatible with observations and still be as close as possible to the standard model regarding the underlying assumptions, without resorting necessarily to exotic matter components.