Limits on the number of spacetime dimensions from GW170817 (1801.08160v3)

Abstract: The observation of GW170817 in both gravitational and electromagnetic waves provides a number of unique tests of general relativity. One question we can answer with this event is: Do large-wavelength gravitational waves and short-frequency photons experience the same number of spacetime dimensions? In models that include additional non-compact spacetime dimensions, as the gravitational waves propagate, they "leak" into the extra dimensions, leading to a reduction in the amplitude of the observed gravitational waves, and a commensurate systematic error in the inferred distance to the gravitational wave source. Electromagnetic waves would remain unaffected. We compare the inferred distance to GW170817 from the observation of gravitational waves, $d_L^\mathrm{GW}$, with the inferred distance to the electromagnetic counterpart NGC 4993, $d_L^\mathrm{EM}$. We constrain $d_L^\mathrm{GW} = (d_L^\mathrm{EM}/\mathrm{Mpc})^\mathrm{\gamma}$ with $\gamma = 1.01^{+0.04}_{-0.05}$ (for the SHoES value of $H_0$) or $\gamma = 0.99^{+0.03}_{-0.05}$ (for the Planck value of $H_0$), where all values are MAP and minimal 68% credible intervals. These constraints imply that gravitational waves propagate in $D=3+1$ spacetime dimensions, as expected in general relativity. In particular, we find that $D = 4.02^{+0.07}_{-0.10}$ (SHoES) and $D = 3.98^{+0.07}_{-0.09}$ (Planck). Furthermore, we place limits on the screening scale for theories with $D>4$ spacetime dimensions, finding that the screening scale must be greater than $\sim 20$ Mpc. We also place a lower limit on the lifetime of the graviton of $t > 4.50 \times 10^8$ yr.

• The paper demonstrates that gravitational and electromagnetic observations yield consistent luminosity distances, affirming a (3+1)-dimensional spacetime structure.
• Using Bayesian inference on the GW170817 event, the study finds no evidence of gravitational leakage into extra non-compact dimensions.
• By contrasting inferred distances, the analysis sets a strong lower bound on the screening scale for potential extra dimensions and constraints on graviton lifetime.

Constraints on Spacetime Dimensions from GW170817

The observation of the gravitational wave event GW170817, accompanied by electromagnetic signals, provides a unique opportunity to test the predictions of general relativity (GR) and to explore the implications of modified gravity theories. The paper "Limits on the number of spacetime dimensions from GW170817" by Kris Pardo et al. investigates whether gravitational waves (GW) and electromagnetic waves (EM) traverse the same number of spacetime dimensions when propagated through the cosmos. It particularly examines if GW might demonstrate leakage into additional, non-compact spacetime dimensions as described by certain higher-dimensional gravity theories.

Objective and Methods

The paper's aim is to compare the distances inferred from the gravitational wave signals ($d_L^\mathrm{GW}$) with those inferred from electromagnetic observations of the source, specifically the host galaxy NGC 4993 ($d_L^\mathrm{EM}$). Under GR, both should propagate through four spacetime dimensions (3 spatial + 1 temporal), hence no discrepancy should be observed. Modifications to GR that suggest extra spacetime dimensions predict gravitational waves to dissipate energy as they "leak" into the extra dimensions, possibly resulting in a measurable reduction of the GW amplitude—and thereby infer a mismatched distance compared to EM observations.

This paper capitalizes on the dual nature of GW170817 as both a GW and EM observable event. Using Bayesian inference, the researchers statistically correlate the differences in the inferred luminosity distances from GW and EM observations with the possibility of extra spacetime dimensions.

Results

The constraints derived from the joint GW-EM observations of GW170817 strongly suggest that gravitational waves propagate through the expected $(3+1)$-dimensional spacetime. The dimension count is pinned at $D = 4.02^{+0.07}_{-0.10}$ with the SHoES value of the Hubble constant ($H_0$) or $D = 3.98^{+0.07}_{-0.09}$ using the Planck value. These results are consistent with the prediction of GR. Notably, the paper places a lower bound on any screening scale for dimensions $D > 4$ to be greater than approximately 20 Mpc.

Furthermore, minimum constraints are placed on the graviton's lifetime, postulating a lower limit of greater than $4.50 \times 10^8$ years. This assumes that any discrepancy would partially arise from graviton behavior modifications, which these results do not suggest.

Implications

The implications of these findings are notable for theories positing additional non-compact spacetime dimensions. If certain extra-dimensional models predict gravity’s propagation into unseen dimensions, the GW and EM observations of GW170817 effectively constrain the magnitude and scale of such phenomena. The screening scale must be substantial enough to remain undetected by current observational proxies.

Discussion and Future Work

While the results of Pardo et al. substantiate GR's robustness amid multi-messenger astronomical phenomena, they also indicate pathways for refining modified gravity theory models. Future GW detections across varied distances may further elucidate the propagation characteristics through even minor assumed discrepancies in gravity’s apparent travel distance. No significant evidence for extra-dimensional spacetime structures supports continued reliance on GR’s established model for cosmological comprehension. However, as detection techniques and theoretical models evolve, the continued observation of multi-messenger events remains essential in seeking out fundamental insights into the nature of spacetime and field interactions at cosmological scales.