The detection of gravitational waves (GW) has been a remarkable breakthrough for many reasons, among them, the possibility of discarding or testing different theories describing gravity. Some of these new theories require the existence of additional dimensions to the standard 3D+1 of general relativity (GR). These extra dimensions are mainly required to give an alternative route to the dark matter and energy hypothesis, since gravity would leak into these additional dimensions, diminishing the amplitude of the GW signal observed. This would give an error in the inferred distance to the gravitational wave source predicted by GR. If true, it could account for the yet undetectable dark matter and energy, at the cost of challenging GR theory, since the existence of dark matter and dark energy results from assuming that GR is valid at all scales and distances.
The collision of two neutron stars detected last year gives an additional insight, due to the electromagnetic waves accompanying the gravitational signal. Such was the case of the GW170817 event detected in LIGO on Aug. 17, 2017, where gravitational waves, gamma-rays, X-rays, radio waves, optical and infrared light were produced. Such an event prompted the following question: “do large-wavelength gravitational waves and short frequency photons experience the same number of spacetime dimensions?” Kris Pardo et al JCAP07(2018)048
Researchers from the University of Chicago tested modified gravity theories in this way for the first time, by comparing the differences in time delay between the propagation of GW and EM waves through spacetime. According to GR, the GW amplitude decreases inversely with luminosity distance. Deviations from this relationship could result from the existence of compact extra-dimensions. If gravity leaks into these other dimensions along the way, the signal measured would have been weaker than expected, while the electromagnetic waves would remain unaffected. Comparing the luminosity distance of GW170817 extracted under the assumption of GR to the EM-measured distance to its host galaxy, NGC 4993, authors found strong deviations on theories with gravitational leakage. In other words, the researchers involved in this study found no evidence for extra spatial dimensions. GW170817 is fully consistent with GR.
“It appears for now that the universe has the same familiar dimensions—three in space and one of time—even on scales of a hundred million light-years.”
– Louise Lerner