Probing the size of extra dimension with gravitational wave astronomy

TL;DR

This paper investigates how gravitational wave observations can constrain the size of extra dimensions in the Randall-Sundrum II model by analyzing waveform phase corrections caused by quantum effects on black hole binaries.

Contribution

It introduces a method to estimate upper bounds on the AdS curvature scale using gravitational wave data, improving previous constraints significantly.

Findings

DECIGO/BBO can constrain the extra dimension size to about 0.33 micrometers.

Detection of 10^5 BH/NS binaries per year enhances measurement sensitivity.

Constraints weaken to 1.5 micrometers when binary eccentricities are considered.

Abstract

In Randall-Sundrum II (RS-II) braneworld model, it has been conjectured according to the AdS/CFT correspondence that brane-localized black hole (BH) larger than the bulk AdS curvature scale $\ell$ cannot be static, and it is dual to a four dimensional BH emitting the Hawking radiation through some quantum fields. In this scenario, the number of the quantum field species is so large that this radiation changes the orbital evolution of a BH binary. We derived the correction to the gravitational waveform phase due to this effect and estimated the upper bounds on $\ell$ by performing Fisher analyses. We found that DECIGO/BBO can put a stronger constraint than the current table-top result by detecting gravitational waves from small mass BH/BH and BH/neutron star (NS) binaries. Furthermore, DECIGO/BBO is expected to detect 10$^5$ BH/NS binaries per year. Taking this advantage, we found that DECIGO/BBO can actually measure $\ell$ down to $\ell=0.33 \mu$m for 5 year observation if we know that binaries are circular a priori. This is about 40 times smaller than the upper bound obtained from the table-top experiment. On the other hand, when we take eccentricities into binary parameters, the detection limit weakens to $\ell=1.5 \mu$m due to strong degeneracies between $\ell$ and eccentricities. We also derived the upper bound on $\ell$ from the expected detection number of extreme mass ratio inspirals (EMRIs) with LISA and BH/NS binaries with DECIGO/BBO, extending the discussion made recently by McWilliams. We found that these less robust constraints are weaker than the ones from phase differences.