Bound on quantum fluctuations in gravitational waves from LIGO-Virgo

We derive some of the central equations governing quantum fluctuations in grav-itational waves, making use of general relativity as a sensible effective quantum theory at large distances. We begin with a review of classical gravitational waves in general relativity, including the energy in each mode. We then form the quantum ground state and coherent state, before then obtaining an explicit class of squeezed states. Since existing gravitational wave detections arise from merging black holes, and since the quantum nature of black holes remains puzzling, one can be open-minded to the possibility that the wave is in an interesting quantum mechanical state, such as a highly squeezed state. We compute the time and space two-point correlation functions for the quantized metric perturbations. We then constrain its amplitude with LIGO-Virgo observations. Using existing LIGO-Virgo data, we place a bound on the (exponential) squeezing parameter of the quantum gravitational wave state ofC<41.

Automated summary

We derive the central equations governing quantum fluctuations in gravitational waves using general relativity as an effective quantum theory at large distances. After reviewing classical gravitational waves in general relativity and constructing the quantum ground state and coherent state, we obtain a specific class of squeezed states. We then compute two-point correlation functions for the quantized metric perturbations and use LIGO-Virgo observations to constrain the amplitude of the quantum gravitational wave state with an exponential squeezing parameter of C<41.