Probing the size of extra dimensions with gravitational wave astronomy

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 ℓ 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 ℓ 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 ℓ down to ℓ = 0.33µm 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 ℓ = 1.5µm due to strong degeneracies between ℓ and eccentricities. We also derived the upper bound on ℓ 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 [1]. We found that these less robust constraints are weaker than the ones from phase differences.

Implications of the gravitational wave event GW150914

“…For example, without prior knowledge of the spin magnitudes and component masses, they find that Einsteindilaton Gauss-Bonnet [67], dynamical Chern-Simons [68,69,70], and scalar-tensor theories (e.g., [71]) cannot be constrained meaningfully because of degeneracies with the masses and spins, and Einstein-AEther theory [72,73] and ideas involving extra dimensions ( [74]; see [75] for a limit based on the lack of Hawking evaporation of black holes in globular clusters) or time variation of Newton's constant G [76] are better constrained by other measurements, particularly those of binary pulsars.…”

Graviton mass bounds from space-based gravitational-wave observations of massive black hole populations

“…Del Pozzo et al [25] recently revisited graviton mass bounds using Bayesian inference (see also [26][27][28][29] for similar work including other possible alternatives to general relativity). They focused on ground-based observations of sources within 150 Mpc and found results consistent with Will's original analysis [10]: for example, their Fig.…”

“…It is natural to expect that one can obtain better constraints on these parameters, as well as other universal constants, by combining multiple observations (see e.g. [25,28,29,[36][37][38][39]). Assuming that estimates for individual sources are independent and Gaussian posteriors for each source, consistent with the Fisher matrix approximation, the width σ 2 of the combined posterior on 1/λ g is given by σ than the average bound obtained from typical observations.…”

Scientific Potential of Decigo Pathfinder and Testing Gr With Space-Borne Gravitational Wave Interferometers

“…Quasi-normal modes in this theory for non-spinning BHs have been calculated by Molina et al 309 and the corrections might be detected by future GW observations. For other theories, gravitational waves from compact binaries allow us to probe the size of the extra dimension 310,311 and the time variation of the gravitational constantĠ 312 . GWs from NS oscillations can be used to constrain not only scalartensor theories as mentioned above, but also other theories such as tensor-vectorscalar theory [313][314][315] .…”