What do gravitational wave detectors say about polymer quantum effects?

Abstract

We compute the expected response of detector arms of gravitational wave observatories to polymerized gravitational waves. The mathematical and theoretical features of these waves were discussed in our previous work. In the present manuscript, we find both perturbative analytical, and full nonperturbative numerical solutions to the equations of motion of the detector arms using the method of geodesic deviations. These results show the modifications to both frequency and amplitude of the signal measured by the detector. Furthermore, we study the detectability of these signals in LISA by analyzing the modes in the frequency space.

Constraining the quantum gravity polymer scale using LIGO data

“…The reality conditions on the fields indicates that not all the modes are independent. To have an independent expansion for each mode and write the Hamiltonian as a set of decoupled harmonic oscillators, we introduce new variables A λ,k and E λ,k and split the lattice L into positive and negative sectors; for more details see [11,12]. In terms of these new variables, the Hamiltonian of the perturbation field reads…”

“…Actually, in the standard representation one can recover the fundamental operators A and E due to the weak continuity condition of the Stone-von Neumann theorem is satisfied. However, polymer quantization violates such a condition and therefore, it is not unitarily equivalent to the standard quantum mechanics [11,12]. In this case, the Hilbert space is given by L 2 (R, dx Bohr ), where the configuration space, R, is the Bohr compactification of the real line and dx Bohr is the Haar measure.…”

“…The result yields a modification of the classical Hamiltonians in which the kinetic term is modified in the case of discrete A and in the case of discrete E the quadratic harmonic potential. We call these modified Hamiltonians effective Hamiltonians 12 .…”

“…This method can be applied to both matter, e.g. GRBs [10] and spacetime or its perturbations themselves [11,12].…”

“…In our previous work [11], we derived the equations of motion for polymer-quantized plane wave metric perturbations and provided numerical solutions, as well as approximate analytical solutions, to those equations of motion. Expanding on this work, we have also calculated the alterations to the response of a Michelson-Morley-like GW observatory under the influence of polymer effects [12,13]. The polymer quantization model has also been applied to the propagation of gamma-ray bursts [10].…”