Gravitational-wave luminosity distance in modified gravity theories

Abstract

In modified gravity the propagation of gravitational waves (GWs) is in general different from that in general relativity. As a result, the luminosity distance for GWs can differ from that for electromagnetic signals, and is affected both by the dark energy equation of state wDE(z) and by a function δ(z) describing modified propagation. We show that the effect of modified propagation in general dominates over the effect of the dark energy equation of state, making it easier to distinguish a modified gravity model from ΛCDM. We illustrate this using a nonlocal modification of gravity that has been shown to fit remarkably well CMB, SNe, BAO and structure formation data, and we discuss the prospects for distinguishing nonlocal gravity from ΛCDM with the Einstein Telescope. We find that, depending on the exact sensitivity, a few tens of standard sirens with measured redshift at z ∼ 0.4, or a few hundreds at 1 < ∼ z < ∼ 2, could suffice.

Gaussian processes reconstruction of modified gravitational wave propagation

“…for some function δ(η). This behavior has been first found explicitly in scalar-tensor theories of the Horndeski class [31,33,[35][36][37] and in nonlocal infrared modifications of gravity [19,20]. The analysis in [41] showed that also scalar-tensor theories of the DHOST type, as well as bigravity, display this phenomenon, so an equation of propagation of the form (5) is completely generic and appears in all the best studied models of modified gravity.…”

“…In the context of standard General Relativity (GR), the coalescence of compact binaries provides another way of measuring d L , as was realized long ago [3] (see e.g. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] for a sample of the many developments of the idea), so these sources are referred to as "standard sirens", the GW analogue of standard candles. Together with a determination of the redshift (which is not provided by the gravitational signal and must be obtained from an electromagnetic counterpart or with statistical techniques), this allows us to use GW observations as probes of cosmology.…”

“…Depending on the network of telescopes and GRB satellites that will be operating at that time, in a few years ET could collect hundreds of NS-NS coalescences with observed electromagnetic counterpart [29,30]. sirens do not measure the same luminosity distance as electromagnetic probes [19,20,[31][32][33][34][35][36][37][38][39]. One must then distinguish between an 'electromagnetic luminosity distance' d em L , given by the standard expression (1,2), and a 'GW luminosity distance' d gw L .…”

Gravity in the infrared and effective nonlocal models

“…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…”

“…where d L (z) is the usual notion of luminosity distance (note that, since only the ratios a(z)/ã(0) and a(z)/a(0) enter, without loss of generality we can choose the normalizations a(0) = a(0) = 1). Equation (3.55) motivates the introduction of a 'GW luminosity distance' d gw L (z) [164], related to the standard luminosity distance appropriate for electromagnetic signals, that we henceforth denote by d em L (z), by d gw L (z) = [a(z)/ã(z)] d em L (z). Rewriting eq.…”