Testing modified gravity at cosmological distances with LISA standard sirens

Abstract

Modifications of General Relativity leave their imprint both on the cosmic ex-Contents A GW luminosity distance and the flux-luminosity relation 53 B Technical details on bigravity 55 B.1 Hassan-Rosen theory of bigravity 55 B.2 Details on the WKB approximation for bigravity 56References 58 5. In the presence of anisotropic stress, or in theories where tensors couple with additional fields already at linearised level (as in theories breaking spatial diffeomorphisms), the tensor evolution equation contains a "source term" Π A in the right hand side of eq. (1.2). In absence of anisotropic stress, and in cosmological scenarios where spatial diffeomorphisms are preserved, we have Π A = 0.The physical consequences of these parameters have been discussed at length in the literature (see [18] for a review on their implications for GW astronomy). In this paper we investigate how they affect a specific observable, the GW luminosity distance, which can be probed by LISA standard sirens. The space-based interferometer LISA can qualitatively and quantitatively improve our tests on the propagation of gravitational waves in theories of modified gravity. LISA can probe signals from standard sirens of supermassive black hole mergers (MBHs) at redshifts z ∼ O(1 − 10), much larger than the redshifts z ∼ O(10 −1 ) of typical sources detectable from second-generation ground-based interferometers. This implies that LISA can test the possible time dependence of the parameters controlling deviations from GR or the standard ΛCDM model, since GWs travel large cosmological distances before reaching the observer. Moreover, as we will review in section 4, LISA can measure the luminosity distance to MBHs with remarkable precision, thereby reaching an accuracy not possible for second-generation ground-based detectors.It is also interesting to observe that LISA can probe GWs in the frequency range in the milli-Hz regime (more precisely, in the interval 10 −4 − 10 0 Hz), much smaller than the typical frequency interval of ground-based detectors, 10 1 − 10 3 Hz. This is a theoretically interesting range to explore since several theories of modified gravity designed to explain dark energy, such as Horndeski, degenerate higher order scalar-tensor (DHOST) theories or massive gravity, have a low UV cutoff, typically of order Λ cutoff ∼ H 2 0 M Pl 1/3 ∼ 10 2 Hz.This cutoff is within the frequency regime probed by LIGO, making a comparison between modified gravity predictions and GW observations delicate [19]. The frequency range tested by LISA, instead, is well below this cutoff, hence it lies within the range of validity of the theories under consideration. The paper is organized as follows. In section 2 we recall the notion of modified GW propagation and GW luminosity distance, that emerges generically in modified theories of gravity. In section 3 we discuss the prediction on modified GW propagation of some of the best studied modified-gravity theories: scalar-tensor theories (with particular emphasis on Horndeski and DHOST theories), infrared non-l...

Science case for the Einstein telescope

“…This behavior turns out to be completely generic to modified gravity models (scalar-tensor theories, nonlocal modifications of gravity, bigravity, etc.) [203]. For most models, the deviations from GR can be parametrized in terms of two parameters (Ξ 0 , n) as [195] d gw…”

Gaussian processes reconstruction of modified gravitational wave propagation

“…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 some instances the effect is related to the time variation of the Newton constant (or, equivalently, of the Planck mass) that takes place in these models.…”

Prospects for improving cosmological parameter estimation with gravitational-wave standard sirens from Taiji

“…Similar issues concerning LISA and TianQin [39][40][41][42][43][44] have been investigated in Ref. [31,45,46]. Therefore, in this paper, we make a forecast for the prospect of Taiji in cosmological parameter estimation by using the simulated standard siren data.…”