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Register a new userStandard Sirens as a novel probe of dark energy
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Cosmological models with a dynamical dark energy field typically lead to a modified propagation of gravitational waves via an effectively time-varying gravitational coupling $G(t)$. The local variation of this coupling between the time of emission and detection can be probed with standard sirens. Here we discuss the role that Lunar Laser Ranging (LLR) and binary pulsar constraints play in the prospects of constraining $G(t)$ with standard sirens. In particular, we argue that LLR constrains the matter-matter gravitational coupling $G_N(t)$, whereas binary pulsars and standard sirens constrain the quadratic kinetic gravity self-interaction $G_{gw}(t)$. Generically, these two couplings could be different in alternative cosmological models, in which case LLR constraints are irrelevant for standard sirens. We use the Hulse-Taylor pulsar data and show that observations are highly insensitive to time variations of $G_{gw}(t)$ yet highly sensitive to $G_N(t)$. We thus conclude that future gravitational waves data will become the best probe to test $G_{gw}(t)$, and will hence provide novel constraints on dynamical dark energy models.
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Under the assumption that a dynamical scalar field is responsible for the current acceleration of the Universe, we explore the possibility of probing its physics in black hole merger processes with gravitational wave interferometers. Remaining agnostic about the microscopic physics, we use an effective field theory approach to describe the scalar dynamics. We investigate the case in which some of the higher derivative operators, that are highly suppressed on cosmological scales, instead become important on typical distances for black holes. If a coupling to the Gauss-Bonnet operator is one of them, a non-trivial background profile for the scalar field can be sourced in the surroundings of the black hole, resulting in a potentially large amount of hair. In turn, this can induce sizeable modifications to the spacetime geometry or a mixing between the scalar and the gravitational perturbations. Both effects will ultimately translate into a modification of the quasi-normal mode spectrum in a way that is also sensitive to other operators besides the one sourcing the scalar background. The presence of deviations from the predictions of general relativity in the observed spectrum can therefore serve as a window onto dark energy physics.
In dark energy models where a scalar field $phi$ is coupled to the Ricci scalar $R$ of the form $e^{-2Q (phi-phi_0)/M_{rm pl}}R$, where $Q$ is a coupling constant, $phi_0$ is todays value of $phi$, and $M_{rm pl}$ is the reduced Planck mass, we study how the recent Lunar Laser Ranging (LLR) experiment places constraints on the nonminimal coupling from the time variation of gravitational coupling. Besides a potential of the light scalar responsible for cosmic acceleration, we take a cubic Galileon term into account to suppress fifth forces in over-density regions of the Universe. Even if the scalar-matter interaction is screened by the Vainshtein mechanism, the time variation of gravitational coupling induced by the cosmological background field $phi$ survives in the solar system. For a small Galileon coupling constant $beta_3$, there exists a kinetically driven $phi$-matter-dominated-epoch ($phi$MDE) prior to cosmic acceleration. In this case, we obtain the stringent upper limit $Q le 3.4 times 10^{-3}$ from the LLR constraint. For a large $beta_3$ without the $phi$MDE, the coupling $Q$ is not particularly bounded from above, but the cosmological Vainshtein screening strongly suppresses the time variation of $phi$ such that the dark energy equation of state $w_{rm DE}$ reaches the value close to $-1$ at high redshifts. We study the modified gravitational wave propagation induced by the nonminimal coupling to gravity and show that, under the LLR bound, the difference between the gravitational wave and luminosity distances does not exceed the order $10^{-5}$ over the redshift range $0<z<100$. In dark energy models where the Vainshtein mechanism is at work through scalar derivative self-interactions, it is difficult to probe the signature of nonminimal couplings from the observations of standard sirens.
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.
Recently it was shown that the inclusion of higher signal harmonics in the inspiral signals of binary supermassive black holes (SMBH) leads to dramatic improvements in parameter estimation with the Laser Interferometer Space Antenna (LISA). In particular, the angular resolution becomes good enough to identify the host galaxy or galaxy cluster, in which case the redshift can be determined by electromagnetic means. The gravitational wave signal also provides the luminosity distance with high accuracy, and the relationship between this and the redshift depends sensitively on the cosmological parameters, such as the equation-of-state parameter $w=p_{rm DE}/rho_{rm DE}$ of dark energy. With a single binary SMBH event at $z < 1$ having appropriate masses and orientation, one would be able to constrain $w$ to within a few percent. We show that, if the measured sky location is folded into the error analysis, the uncertainty on $w$ goes down by an additional factor of 2-3, leaving weak lensing as the only limiting factor in using LISA as a dark energy probe.
Standard sirens are the gravitational wave (GW) analog of the astronomical standard candles, and can provide powerful information about the dynamics of the Universe. In this work, we simulate a catalog with 1000 standard siren events from binary neutron star mergers, within the sensitivity predicted for the third generation of the ground GW detector called Einstein telescope. After correctly modifying the propagation of GWs as input to generate the catalog, we apply our mock data set on scalar-tensor theories where the speed of GW propagation is equal to the speed of light. As a first application, we find new observational bounds on the running of the Planck mass, when considering appropriate values within the stability condition of the theory, and we discuss some consequences on the amplitude of the running of the Planck mass. In the second part, we combine our simulated standard sirens catalog with other geometric cosmological tests (Supernovae Ia and cosmic chronometers measurements) to constrain the Hu-Sawicki $f(R)$ gravity model. We thus find new and non-null deviations from the standard $Lambda$CDM model, showing that in the future the $f(R)$ gravity can be tested up to 95% confidence level. The results obtained here show that the statistical accuracy achievable by future ground based GW observations, mainly with the ET detector (and planed detectors with a similar sensitivity), can provide strong observational bounds on modified gravity theories.
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