Quantum Noise of Gravitons and Stochastic Force on Geodesic Separation

Abstract

In this work we consider the effects of gravitons and their fluctuations on the dynamics of two masses using the Feynman-Vernon influence functional formalism, applied to nonequilibrium quantum field theory and semiclassical stochastic gravity earlier by Calzetta, Hu and Verdaguer [1-3], and most recently, to this problem by Parikh, Wilczek and Zahariade [4-6]. The Hadamard function of the gravitons yields the noise kernel acting as a stochastic tensorial force in a Langevin equation governing the motion of the separation of the two masses. The fluctuations of the separation due to the graviton noise are then solved for various quantum states including the Minkowski vacuum, thermal, coherent and squeezed states. The previous considerations of Parikh et al. are only for some selected modes of the graviton, while in this work we have included all graviton modes and polarizations. We comment on the possibility of detecting these fluctuations in primordial gravitons using interferometors with long baselines in deep space experiments.

Graviton noise:the Heisenberg picture

“…In refs. [18][19] [20] [23] [24] the evolution of the particle density matrix and the scattering probability in an environment of gravitons have been calculated. In the semiclassical limit by means of the Feynman-Vernon method [25] a non-linear stochastic differential equation with a noise from gravitons has been derived (it is a stochastic perturbation of the the equation of geodesic deviation by the gravitational radiation reaction [26][27]).…”

Bound on Quantum Fluctuations in Gravitational Waves from LIGO

“…Important earlier work on the topic of quantum fluctuations in gravitation includes Refs. [24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”