Modified gravitational-wave propagation and standard sirens

Abstract

Studies of dark energy at advanced gravitational-wave (GW) interferometers normally focus on the dark energy equation of state wDE(z). However, modified gravity theories that predict a nontrivial 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 wDE(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 (Ξ0, n), analogue to the (w0, wa) parametrization of the dark energy equation of state, and we give a limit from the LIGO/Virgo measurement of H0 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 (Ξ0, 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, Ξ0 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.arXiv:1805.08731v3 [gr-qc]

Gravity in the infrared and effective nonlocal models

“…The numerical integration then gives again a result very well fitted by eq. (3.61), with Ξ 0 0.97 and n 2.5 [165]. However, contrary to the RT model, here the deviation from GR is only about 3%.…”

“…First, by the different mean values of H 0 and Ω M between the RT model with the given ∆N and ΛCDM; second, by the different redshift dependence of the DE density, or, equivalently, the different DE equation of state w DE (z). However, we have seen in Table 2 that Bayesian parameter estimation gives for the RT model values of H 0 and Ω M very close to those of ΛCDM, particularly at large ∆N ; furthermore, as discussed in [165], the change in the value of these parameters goes precisely in the direction to cancel the effect in the change of the DE equation of state. This is due to the fact that Bayesian parameter estimation in practice requires the model to fit some fixed distance scales at large redshifts, such as the scales given by the CMB peaks or by the BAO oscillations; thus, if, compared to ΛCDM, one changes w DE (z) in the direction of giving, say, a larger (electromagnetic) luminosity distance at large redshift, H 0 and Ω M change in the direction such that they partially compensate for this change.…”

“…Let us then study first the general consequences of eq. (3.50) (we closely follow the discussion in [164,165]). We proceed as in the GR case, except that now, to eliminate the friction term, we must introduceχ A (η, k) from Then we getχ…”

“…This can lead to delays between the arrival time of a GW and the associated electromagnetic signal [200][201][202]. 34 See [165] for a discussion of how modified GW propagation affects the ISW effect. 35 Note that eq.…”

Cosmic acceleration in the nonlocal approach to the cosmological constant problem

“…For instance, in the papers [37][38][39] 9 , analytic infinite derivative gravity theories are proposed to resolve unsolved problems such as black hole and big bang singularities at a classical level as well as quantum level. Moreover, more recently, a detailed discussion of conceptual aspects related to nonlocal gravity and its cosmological consequences has been presented in the paper [41]. It is true that our present work is closely related to these works in that we rely on nonlocal operation and make use of the higher derivative terms, but a big difference is that in our work taking the space-time average of operators plays a critical role to understand the cosmological constant problem.…”