Probing Noncommutative Gravity with Gravitational Wave and Binary Pulsar Observations

TL;DR

This paper investigates how noncommutative gravity, a quantum gravity approach, can be constrained using gravitational wave data and binary pulsar observations, improving previous bounds on spacetime noncommutativity.

Contribution

It extends previous analyses by relaxing assumptions, incorporating additional gravitational wave events, and using binary pulsar data to set bounds on noncommutative spacetime parameters.

Findings

Gravitational wave data provides stronger bounds than binary pulsar observations.

The noncommutative tensor is constrained to be of order unity when normalized by Planck scales.

The analysis derives corrections to gravitational wave phase and pericenter precession due to noncommutativity.

Abstract

Noncommutative gravity is a natural method of quantizing spacetime by promoting the spacetime coordinates themselves to operators which do not commute. This approach is motivated, for example, from a quantum gravity perspective, among others. Noncommutative gravity has been tested against the binary black hole merger event GW150914. Here, we extend and improve upon such a previous analysis by (i) relaxing an assumption made on the preferred direction due to noncommutativity, (ii) using posterior samples produced by the LIGO/Virgo Collaborations, (iii) consider other gravitational wave events, namely GW151226, GW170608, GW170814 and GW170817, and (iv) consider binary pulsar observations. Using Kepler's law that contains the noncommutative effect at second post-Newtonian order, we derive corrections to the gravitational waveform phase and the pericenter precession. Using the gravitational wave and double pulsar binary observations, we find bounds on a space-time noncommutative tensor $\theta^{0i}$ in terms of the preferred frame direction with respect to the orientation of each binary. We find that the gravitational wave bounds are stronger than the binary pulsar one by an order of magnitude and the noncommutative tensor normalized by the Planck length and time is constrained to be of order unity.