Effects of expanding universe in the Schrödinger-Newton approach
Date of Issue2019
School of Physical and Mathematical Sciences
The cosmological constant is by far the simplest and most consistent way to model the accelerating expansion of our universe. In this project, we investigate the mass and length scale in which a particle should be superposed so that the effects induced by the cosmological constant dominate the dynamics of the particle in the Schrodinger-Newton approach. Within this framework, we extend the existing Schrodinger-Newton equation by replacing the Newtonian gravitational potential with a potential that includes the effects of self-gravitating interaction and dark energy in the form of the cosmological constant. A spherically symmetric Gaussian wave function is used as our initial condition and its evolution under the Schrodinger-Newton-Lambda equation" is solved numerically. First, we were able to recover most of the Schrodinger-Newton solutions found previously. The investigation on the mass and length scale showed terrestrial required values of approximately 10-20 kg superposed over the distance above 50 m. Unfortunately, the time required to observe the effects of cosmological constant for terrestrial particles turns out to be truly astronomical.
Final Year Project (FYP)