Gravitational-wave luminosity distance in quantum gravity

Abstract

Dimensional flow, the scale dependence of the dimensionality of spacetime, is a feature shared by many theories of quantum gravity (QG). We present the first study of the consequences of QG dimensional flow for the luminosity distance scaling of gravitational waves in the frequency ranges of LIGO and LISA. We find generic modifications with respect to the standard general-relativistic scaling, largely independent of specific QG proposals. We constrain these effects using two examples of multimessenger standard sirens, the binary neutron-star merger GW170817 and a simulated supermassive black-hole merger event detectable with LISA. We apply these constraints to various QG candidates, finding that the quantum geometries of group field theory, spin foams and loop quantum gravity can give rise to observable signals in the gravitational-wave spin-2 sector. Our results complement and improve GW propagation-speed bounds on modified dispersion relations. Under more model-dependent assumptions, we also show that bounds on quantum geometry can be strengthened by solar-system tests.

Quantum gravity and gravitational-wave astronomy

“…Conclusions, where we also comment on future bounds from pulsars, are in section 9. These results were in part anticipated in a short article [59].…”

Testing modified gravity at cosmological distances with LISA standard sirens

“…In turn, these features are encoded into the topological dimension D of spacetime (D = 4 in physical models) and three effective, scale-dependent "dimensions," namely the Hausdorff (called also fractal) dimension d H of position space, the Hausdorff dimension d k H of momentum space and the spectral dimension d S . In a classical spacetime, d H = d k H = d S = D. A general argument based on the scaling of fields and their kinetic terms indicates that correlation functions and distances depend on these dimensions through a geometric parameter Γ := d H /2 − d k H /d S that combines them together [164]. The relation between Γ and the parameter δ that expresses the modification of GW propagation (and that, as we have seen in section 2.2.2, in some theories is related to the time variation of the effective Planck mass) is…”

“…This is indeed the case. The model-independent analysis of [164] shows that theories with * = O( Pl ) and γ − 1 0.02 (3.56) can fall into the detectability range of interferometers. Such small non-zero values of γ − 1 can be obtained only in a near-IR regime.…”

“…For group field theory though, this is less obvious. However, for theories where particle and atomic physics are also affected, corrections are still of a power-law type ( / * ) α but, typically, with a power α different from the special combination of dimensions (3.54) [164]. Therefore, GW and particle-physics bounds are (at least partially) independent, leading to complementary constraints to the fundamental theories.…”

“…Therefore, GW and particle-physics bounds are (at least partially) independent, leading to complementary constraints to the fundamental theories. On the other hand, solar-system tests can yield stronger bounds on γ in QG scenarios where also the scalar sector is affected [164]. However, in many QGs models the correction to the Newton potential is not known, while the spin-2 sector is under better control and GWs can be a robust and, for the time being, unique way to constrain such models [164].…”