Constraining cosmological extra dimensions with gravitational wave standard sirens: from theory to current and future multi-messenger observations

TL;DR

This paper investigates how gravitational wave observations, combined with electromagnetic signals, can constrain the existence of extra spatial dimensions in the universe, using current events and future space-based detectors.

Contribution

It derives a new relation between GW and EM luminosity distances in models with extra dimensions and applies it to current data and future forecasts, extending previous analyses.

Findings

Constraints on the number of extra dimensions from GW170817 and GW190521.

Forecasts for LISA's ability to detect extra dimensions using MBHB mergers.

Identification of redshift-dependent effects in GW-EM luminosity distance relations.

Abstract

The propagation of gravitational waves (GWs) at cosmological distances offers a new way to test the gravitational interaction at the largest scales. Many modified theories of gravity, usually introduced to explain the observed acceleration of the universe, can be probed in an alternative and complementary manner with respect to standard electromagnetic (EM) observations. In this paper we consider a homogeneous and isotropic cosmology with extra spatial dimensions at large scales, which represents a simple phenomenological prototype for extra-dimensional modified gravity cosmological models. By assuming that gravity propagates through the higher-dimensional spacetime, while photons are constrained to the usual four dimensions of general relativity, we derive from first principles the relation between the luminosity distance measured by GW detectors and the one inferred by EM observations. We then use this relation to constrain the number of cosmological extra dimensions with the binary neutron star event GW170817 and the binary black hole merger GW190521. We further provide forecasts for the Laser Interferometer Space Antenna (LISA) by simulating multi-messenger observations of massive black hole binary (MBHB) mergers. This paper extends and updates previous analyses which crucially neglected an additional redshift dependency in the GW-EM luminosity distance relation which affects results obtained from multi-messenger GW events at high redshift, in particular constraints expected from LISA MBHBs.