Lightcone fluctuations and an estimation on the size of the extra dimension in a quasiperiodically compactified Kaluza-Klein model

Abstract

In this dissertation, we present a review of the formalism involved in the study of light cone fluctuations accompanied by new results and discussions conducted throughout this master’s program. We initially conducted a review of the Linearized Theory of Gravity in the classical regime. We began by considering the weak gravitational field limit while allowing it to vary with time we sought to determine the modification caused by this expansion on the elements of General Relativity (GR), derived the field equations for the perturbation and discussed the gauge freedom associated to the latter. Following this first contact with linearized gravity, we worked under the assumption that the perturbation is quantized and provided a review of lightcone fluctuation effects which leads to the removal of divergences associated with the classical lightcone and discussed the possibility of observing the effects of such fluctuations upon photon propagation. Continuing our analysis, we reviewed the procedure to express ⟨σ2 1⟩ in terms of the Hadamard function for the graviton in (d +1) dimensions. Finally, we presented the new results obtained during this research. Inspired by the work in Ref. [1], we sought to expand the description of a possible extra spatial dimension by making it compact through a quasiperiodic boundary condition. We discussed the transition to models with extra dimensions and calculated quantities associated with the deviation in the photon propagation time as a consequence of the compactified space’s topology. We also discussed the requirements for the size of the extra dimension in order to obtain detectable changes on a photon flight time using the Near Infrared Spectrograph (NIRSpec) aboard the James Webb Telescope as a model for detections. For this purpose, we divided our analysis into two parts: one for the periodic case and another for cases where the phase regulator of the quasiperiodic condition is nonzero. Consequently, we found that the resulting effects of each scenario upon photon propagation fundamentally differs from one another other.