QUINTESSENCE AS A MODIFIED MATTER MODEL AND F(R) GRAVITY AS A MODIFIED GRAVITY MODEL OF DARK ENERGY - Sahputra, Nadillia
From supernova observation (Riess, 1998), we know that the universe is in accelerated expansion. According to general relativity, dark energy is the cause of the acceleration. Dark energy is a matter with negative pressure that covers around 70% of the universe (Riess, 1998). To further understand dark energy, many physicists then construct mathematical models that describe dark energy. In general, models can be derived from two approaches, giving modified matter model and modified gravity model. This final project will then discuss one example from each model. Firstly, quintessence model as an example of a modified matter model and secondly f(R) gravity model as an example of a modified gravity model. Quintessence model can be well understood using dynamical system analysis. Using Einstein equations and the equation of motion, we can obtain the autonomous equation and system stability can be analysed. The evolution of cosmological parameter (density parameter and equation of state) can be obtained by system trajectory in phase space. This final project will discuss two scalar field potential models such as exponential potential and inverse power-law potential. Exponential potential can not thoroughly describe cosmological evolution. For that reason, inverse power-law potential then used to complete the cosmic evolution scenario. In inverse power-law potential, there is a tracking behaviour that attracts solutions into its trajectory. This behaviour will help answer the coincidence problem. Model's eligibility then being evaluated using cosmological evolution parameter and supernova (SN) Ia data. The model can not accurately fit the data. In other words, the model can not accurately describe cosmic evolution. F(R) gravity model has two approaches, such as metric formalism and Palatini formalism. In metric formalism, the Christoffel symbol depends on the metric while in Palatini formalism, the Christoffel symbol is independent form the metric. Even though there are two different approaches, both can still derive the Einstein field equation. Then, by using dynamical system analysis, the evolution of the density parameter and equation of state can be obtained. This final project will discuss specifically power-law model for both formalisms. Then, can be founded that metric formalism has a matter-dominated epoch that is cosmologically not viable. On the contrary, Palatini formalism can give rise to an appropriate cosmological evolution.