Cats, Mak (2026) Phase space analysis of cosmologies with an exponential and power-law potential. Bachelor's Thesis, Mathematics.
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Abstract
We present a phase space analysis of two scalar field cosmologies with different potentials. For an exponential potential, we derive the Copeland-Liddle-Wands system and identify up to five fixed points, whose existence and stability depends on the barotropic index $\gamma$ and the steepness lambda of the potential V = V_0 exp(-lambda*kappa*phi). The key result is a scaling solution which acts as the unique late-time attractor for lambda^2 > 3gamma, in which the scalar field energy density remains a fixed fraction of the total energy density independent of initial conditions. For lambda^2 < 3gamma, the scalar field dominated solution is instead the global attractor, with accelerated expansion occurring when lambda^2 < 2. Phase portraits are generated numerically using a fourth-order Runge-Kutta method and shown to agree with the analytical predictions. For the Ratra-Peebles power-law potential, the phase space becomes three-dimensional, and after compactification we identify two critical lines and three fixed points, with the scalar field dominated point acting like a cosmological constant, driving accelerated expansion.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Sterk, A.E. and Meerburg, P.D. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 16 Jul 2026 11:44 |
| Last Modified: | 16 Jul 2026 11:44 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37418 |
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