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Register a new userTesting the general theory of relativity using gravitational wave propagation from dark standard sirens
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Alternative theories of gravity predict modifications in the propagation of gravitational waves (GW) through space-time. One of the smoking-gun predictions of such theories is the change in the GW luminosity distance to GW sources as a function of redshift relative to the electromagnetic (EM) luminosity distance expected from EM probes. We propose a multi-messenger test of the theory of general relativity from the propagation of gravitational waves by combining EM and GW observations to resolve these issues from GW sources without EM counterparts (which are also referred to as dark standard sirens). By using the relation between the geometric distances accessible from baryon acoustic oscillation measurements, and luminosity distance measurements from the GW sources, we can measure any deviation from the general theory of relativity via the GW sources of unknown redshift that will be detectable by networks of GW detectors such as LIGO, Virgo, and KAGRA. Using this technique, the fiducial value of the frictional term can be measured to a precision $Xi_0=0.98^{+0.04}_{-0.23}$ after marginalizing over redshift dependence, cosmological parameters, and GW bias parameters with $sim 3500$ dark standard sirens of masses $30,rm M_odot$ each distributed up to redshift $z=0.5$. For a fixed redshift dependence, a value of $Xi_0=0.99^{+0.02}_{-0.02}$ can be measured with a similar number of dark sirens. Application of our methodology to the far more numerous dark standard sirens detectable with next generation GW detectors, such as LISA, Einstein Telescope and Cosmic Explorer, will allow achievement of higher accuracy than possible from use of bright standard sirens.
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Studies of dark energy at advanced gravitational-wave (GW) interferometers normally focus on the dark energy equation of state $w_{rm DE}(z)$. However, modified gravity theories that predict a non-trivial dark energy equation of state generically also predict deviations from general relativity in the propagation of GWs across cosmological distances, even in theories where the speed of gravity is equal to $c$. We find that, in generic modified gravity models, the effect of modified GW propagation dominates over that of $w_{rm DE}(z)$, making modified GW propagation a crucial observable for dark energy studies with standard sirens. We present a convenient parametrization of the effect in terms of two parameters $(Xi_0,n)$, analogue to the $(w_0,w_a)$ parametrization of the dark energy equation of state, and we give a limit from the LIGO/Virgo measurement of $H_0$ with the neutron star binary GW170817. We then perform a Markov Chain Monte Carlo analysis to estimate the sensitivity of the Einstein Telescope (ET) to the cosmological parameters, including $(Xi_0,n)$, both using only standard sirens, and combining them with other cosmological datasets. In particular, the Hubble parameter can be measured with an accuracy better than $1%$ already using only standard sirens while, when combining ET with current CMB+BAO+SNe data, $Xi_0$ can be measured to $0.8%$ . We discuss the predictions for modified GW propagation of a specific nonlocal modification of gravity, recently developed by our group, and we show that they are within the reach of ET. Modified GW propagation also affects the GW transfer function, and therefore the tensor contribution to the ISW effect.
In general relativity, the angular radius of the shadow of a black hole is primarily determined by its mass-to-distance ratio and depends only weakly on its spin and inclination. If general relativity is violated, however, the shadow size may also depend strongly on parametric deviations from the Kerr metric. Based on a reconstructed image of Sagittarius A* (Sgr A*) from a simulated one-day observing run of a seven-station Event Horizon Telescope (EHT) array, we employ a Markov chain Monte Carlo algorithm to demonstrate that such an observation can measure the angular radius of the shadow of Sgr A* with an uncertainty of ~1.5 uas (6%). We show that existing mass and distance measurements can be improved significantly when combined with upcoming EHT measurements of the shadow size and that tight constraints on potential deviations from the Kerr metric can be obtained.
We study the cosmological propagation of gravitational waves (GWs) beyond general relativity (GR) across homogeneous and isotropic backgrounds. We consider scenarios in which GWs interact with an additional tensor field and use a parametrized phenomenological approach that generically describes their coupled equations of motion. We analyze four distinct classes of derivative and non-derivative interactions: mass, friction, velocity, and chiral. We apply the WKB formalism to account for the cosmological evolution and obtain analytical solutions to these equations. We corroborate these results by analyzing numerically the propagation of a toy GW signal. We then proceed to use the analytical results to study the modified propagation of realistic GWs from merging compact binaries, assuming that the GW signal emitted is the same as in GR. We generically find that tensor interactions lead to copies of the originally emitted GW signal, each one with its own possibly modified dispersion relation. These copies can travel coherently and interfere with each other leading to a scrambled GW signal, or propagate decoherently and lead to echoes arriving at different times at the observer that could be misidentified as independent GW events. Depending on the type of tensor interaction, the detected GW signal may exhibit amplitude and phase distortions with respect to a GW waveform in GR, as well as birefringence effects. We discuss observational probes of these tensor interactions with both individual GW events, as well as population studies for both ground- and space-based detectors.
We study the holographic dark energy (HDE) model by using the future gravitational wave (GW) standard siren data observed from the Einstein Telescope (ET) in this work. We simulate 1000 GW standard siren data based on a 10-year observation of the ET to make this analysis. We find that all the cosmological parameters in the HDE model can be tremendously improved by including the GW standard siren data in the cosmological fit. The GW data combined with the current cosmic microwave background anisotropies, baryon acoustic oscillations, and type Ia supernovae data will measure the cosmological parameters $Omega_{rm m}$, $H_0$, and $c$ in the HDE model to be at the accuracies of 1.28%, 0.59%, and 3.69%, respectively. A comparison with the cosmological constant model and the constant-$w$ dark energy model shows that, compared to the standard model, the parameter degeneracies will be broken more thoroughly in a dynamical dark energy model. We find that the GW data alone can provide a fairly good measurement for $H_0$, but for other cosmological parameters the GW data alone can only provide rather weak measurements. However, due to the fact that the parameter degeneracies can be broken by the GW data, the standard sirens can play an essential role in improving the parameter estimation.
Gravitational-wave sources offer us unique testbeds for probing strong-field, dynamical and nonlinear aspects of gravity. In this chapter, we give a brief overview of the current status and future prospects of testing General Relativity with gravitational waves. In particular, we focus on three theory-agnostic tests (parameterized tests, inspiral-merger-ringdown consistency tests, and gravitational-wave propagation tests) and explain how one can apply such tests to example modified theories of gravity. We conclude by giving some open questions that need to be resolved to carry out more accurate tests of gravity with gravitational waves.
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