[Paper Review] Note on the speed of GW150914 in gravity's rainbow

Bogeun Gwak, Wontae Kim+1 more|arXiv (Cornell University)|Aug 15, 2016

Black Holes and Theoretical Physics2 references3 citations

TL;DR

This paper investigates the speed of gravitational waves from GW150914 using gravity's rainbow, a framework that modifies dispersion relations without breaking Lorentz invariance. By constraining the deviation between graviton and light speeds from LIGO observations, it derives an upper bound of η ≤ 4.6×10⁵⁹ for the rainbow parameter, indicating negligible quantum gravity effects at GW150914's energy scale.

ABSTRACT

Without breaking Lorentz invariance, we investigate the speed of graviton in event GW150914 by using the modified dispersion relation from gravity's rainbow. The proper range of the parameter in the modified dispersion relation is determined by taking into account the gap between the speed of the graviton and that obtained from event GW150914.

Motivation & Objective

• To investigate the speed of gravitons in GW150914 using gravity’s rainbow, a quantum gravity framework that preserves Lorentz invariance at low energies.
• To determine the range of the rainbow parameter η without introducing a graviton mass, using observational constraints from GW150914.
• To assess the magnitude of quantum gravity effects on gravitational wave propagation at the Planck scale.
• To test whether gravity’s rainbow can explain the observed speed of GW150914 while remaining consistent with LIGO’s upper bound on graviton mass.

Proposed method

• The study employs a modified dispersion relation (MDR) from gravity’s rainbow, parameterized by rainbow functions g₁ and g₂, with g₁ = 1 and g₂ = √(1 - η(ω/ωₚ)^n).
• The group velocity of the graviton is derived from the MDR to compute its propagation speed, which is compared to the speed of light.
• The energy of the gravitational wave is taken as 250 Hz, the peak frequency in GW150914, to evaluate the speed deviation.
• The upper bound on the speed difference (Δv_g < 2.0×10⁻¹² m/s) from LIGO’s graviton mass constraint (m_g < 1.2×10²² eV/c²) is used to constrain the parameter η.
• The analysis assumes n = 2 for the exponent in the rainbow function and solves for η using the inequality Δv = η(1 + n/2)(ω/ωₚ)^n c < 2.0×10⁻¹² m/s.
• The effective rainbow effect is estimated as η(ω/ωₚ)^n ≤ 3.3×10⁻²¹ to quantify the smallness of quantum gravity corrections.

Experimental results

Research questions

• RQ1 What is the range of the rainbow parameter η in gravity’s rainbow that is consistent with the observed speed of GW150914?
• RQ2 How do quantum gravity effects in gravity’s rainbow modify the dispersion relation of massless gravitons without breaking Lorentz invariance?
• RQ3 To what extent do the observed constraints on graviton speed from GW150914 limit the magnitude of rainbow effects at the Planck scale?
• RQ4 Can the speed difference between gravitational waves and light in GW150914 be explained by gravity’s rainbow without introducing a massive graviton?

Key findings

• The upper bound on the rainbow parameter is determined as η ≤ 4.6×10⁵⁹ at the 250 Hz frequency of GW150914.
• The effective rainbow correction is estimated to be η(ω/ωₚ)^n ≤ 3.3×10⁻²¹, indicating extremely small quantum gravity effects.
• The speed of the graviton in gravity’s rainbow is slightly slower than light, with the deviation governed by the parameter η and the energy-dependent rainbow functions.
• The analysis shows that gravity’s rainbow effects are negligible at the energy scale of GW150914, consistent with general relativity in the low-energy limit.
• The result supports the viability of gravity’s rainbow as a quantum gravity framework that remains consistent with current gravitational wave observations.