Abstract
In 1998, it was discovered[1, 2] that we live in a universe that is expanding at an accelerating rate. While an expanding universe was supported by earlier models of the universe containing matter and radiation, all these models predict a decelerating expansion. To explain this acceleration, a new component with negative pressure had to be included in the total energy budget of the universe. This mysterious negative pressure component has been named dark energy, and is characterized by an equation of state parameter w_de < −1/3. The most popular model today to describe the universe is the ΛCDM-model, where Λ corresponds to a cosmological constant type dark energy with equation of state w_de = −1. In the Planck 2018 survey [3, 4], they constrain the dark energy equation of state parameter to w_de = −1.03±0.03, which is consistent with a cosmological constant. It is however also consistent with w_de < −1. Furthermore, in their analysis of a time-varying equation of state, they find that most of the best fit parameter space lies within the regime w_de < −1. This subset of dark energy types was first discussed by R.R Caldwell in 1999[5], where he coined the term Phantom energy. Phantom energy predicts a far more spectacular and violent future of our universe than simply accelerated expansion. In the paper ”Phantom energy and cosmic doomsday [6], Caldwell et. al find that a phantom energy universe will end in a Big Rip. In a finite time in the future, the expansion of the universe will reach a point where spacetime itself is ripped apart! They present a timeline over when different structures might be ripped apart leading up to the big rip in a universe with w_de = −3/2. Their work serves as the motivation of this thesis, where the goal is to explore more in- depth how different structures are affected by the increasing expansion rate. We set up three models of an earth-like planet, a hydrogen atom, and a meson in an expanding background. We find that a non-relativistic approach is sufficient to describe both the motion of the planet and the hydrogen atom. For the meson, however, we find that a more extensive model is needed to give sufficient results. We calculate two timelines, one corresponding to a universe with w_de = −3/2 (the doomsday universe from now), and one with w_de = −1.03(the Planck universe). In the doomsday universe, the big rip happens 18.8 Gyr in the future, the planet is ripped from its orbit only 4.2 months before this. The hydrogen is ripped apart at 10^(−17) seconds before the big rip and the meson only 10^(−24)s before. In the Planck universe, that the big rip happens in 19.4 Gyr, with the planet, atom, and meson being ripped apart 9.6 years, 10^(-15) s and 10^(−23) s respectively.
Veiledere: Professor Øystein Elgarøy, Institutt for teoretisk astrofysikk, UiO
Intern sensor: Professor David Fonseca Mota, Institutt for teoretisk astrofysikk, UiO
Ekstern sensor: Professor Sigbjørn Hervik, Institutt for matematikk og fysikk, UiS