State-dependent graviton noise in the equation of geodesic deviation

Abstract

We consider an equation of the geodesic deviation appearing in the problem of gravitational wave detection in an environment of gravitons. We investigate a state-dependent graviton noise (as discussed in a recent paper by Parikh,Wilczek and Zahariade) from the point of view of the Feynman integral and stochastic differential equations. The evolution of the density matrix and the transition probability in an environment of gravitons is obtained. We express the time evolution by a solution of a stochastic geodesic deviation equation with a noise dependent on the quantum state of the gravitational field.

Quantum State Evolution in an Environment of Cosmological Perturbations

“…We argued after [17] (see also [31]) that the noise from the gravitons can be observed in the wave detector owing to the strong squeezing during inflation. In this paper we extend our results of [20] to quantum scalar and tensor perturbations in an expanding Universe. We suggest that the quantized scalar and tensor perturbations have an effect upon detectors of cosmological perturbations as well as upon formation of inhomogeneities during the radiation domination epoch.…”

“…κτ 1 is large in the baryonic era. As shown in Section 13 (see also [20]), large R ensures big noise. To have a large noise in the radiation era (and subsequently in the baryonic era), we need big R i in the inflation era.…”

“…It would not make much difference whether we derived the density matrix considering, e.g., classical background of gravitational waves or coherent states of quantized gravitational waves. In the Appendix of [20], we showed that the assumption that gravitational waves have classical thermal distribution leads to the same friction and noise as the high temperature limit in the average (88) over the quantum Gibbs distribution. Nevertheless, for lower temperature, the noise and friction areh-dependent.…”

“…In a non-relativistic approximation, we derive the time evolution of the density matrix. We show that this time evolution is determined by a stochastic equation which is a generalization of the equation derived in [17][18][19][20][21] for tensor perturbations (gravitational waves) in the Minkowski metric. There was earlier work on the particle motion in an environment of a quantized metric [22][23][24][25][26][27] based on the geodesic equation.…”

“…The effect of gravitational waves can be studied by means of a stochastic geodesic deviation equation in a weak gravitational field on a flat background. In [20], we studied the interaction of non-relativistic particles with quantum tensor perturbations. We argued after [17] (see also [31]) that the noise from the gravitons can be observed in the wave detector owing to the strong squeezing during inflation.…”