THE PARAMETERIZED POST-FRIEDMANNIAN FRAMEWORK FOR THE INTERACTING DARK ENERGY IN COSMOLOGICAL MODEL WITH NONMINIMAL DERIVATIVE COUPLING - Widiyani, Agustina
In almost the last two decades, cosmological observations from measurements of the cosmic microwave background (CMB), Supernovae Ia (SN Ia), and baryon acoustic oscillations (BAO) indicate that the universe is currently in an accelerated expansion phase. The development of this observational evidence shows that the components that fill the universe in the form of cold dark matter (CDM) about 25% and dark energy (DE) about 70%. These two dark sectors are the main components of the universe today which are considered to have an influence on the acceleration of the universe's expansion. The existence of the two dark sectors is only detected indirectly through gravitational effects so that they have the possibility of interacting non-gravitationally. The interacting dark energy (IDE) scenario in which dark energy interacts directly with dark matter (having non-zero coupling with each other) is one way to reduce or solve the problems that arise in the ?CDM model, namely namely the fine-tunning and coincidence problems. The ?CDM model is a cosmological standard model that can describe the universe in accordance with cosmological observations where dark energy in the form of the cosmological constant (?) as the dominant filling component of the universe interacts with dark matter in the form of cold dark matter (CDM). The true nature of the two dark sectors is not yet known, so one of the main goals of modern cosmology is to discover the nature of dark energy, which is the dominant component of the universe in its accelerated expansion phase. To gain a better understanding of the dark energy nature and its role in the evolution of the universe, the equation of state and the speed of sound parameters are needed. These two parameters are important to study in the IDE model because they provide important information about the behavior and properties of dark energy. The equation of state explains the correlation between the pressure and the energy density of dark energy to understand how it affects the evolution of the background universe. At the perturbation level, the speed of sound is a parameter like the equation of state and relates pressure disturbances and energy density so that they affect the growth of structure in the universe. Physicists are still developing the theory of gravity by modifying the cosmological parameters of Einstein's field equations or called the theory of modified gravity (MG). The theory of modified gravity must pass the test on the solar system scale. There are two approaches to performing cosmological tests the theory of modified gravity. The first approach, a theory of gravity is determined through its Lagrangian which produces the equations of motion for homogeneous expansion and cosmological perturbation. The second approach is inspired by the Parameterized Post-Newtonian (PPN) framework for testing the solar system. However, at the gigaparsec (Gpc) scale where dark energy appears to be driving accelerated expansion, there are no more bound test particle orbits to measure. So based on the cosmological perturbation theory, a different approach is needed to examine the cosmology of the very common modified gravity. Therefore, a new formalism is introduced which parameterizes the cosmological perturbation theory of various modified gravity models. This formalism is known as a Parameterized Post-Friedmannian (PPF) framework. The formalism of PPF is similar to PPN in that the cosmological parameters have assumed that some of Einstein's field equations remain valid under the theory of modified gravity. This PPF formalism tests the modified gravity model independently to pave the way for independent models to classify and test IDE theory. In this dissertation research, a dark energy model with non-minimum coupling between the curvature and the scalar field derivative or called the non-minimal derivative coupling (NMDC) of the scalar field has been studied. Modeling dark energy with NMDC will provide an accelerated expansion of the universe. Here, the dark energy model with NMDC is modified into a dark energy model that interacts with dark matter (Interacting Dark Energy, IDE) and is examined whether its interaction affects the evolution of the equation of state and the speed of sound. The impact of this interaction implies that the interaction effect on the dark energy equation of state is much stronger than the effect of varying the speed of sound. The PPF framework has been applied to various the theory of modified gravity including the IDE model. In previous research, the IDE model within the PPF framework has been carried out using a quintessence scenario in which the scalar field is non-minimum coupling with gravity. Here, the scenario is developed considering the actions of NMDC. This research begins by studying the cosmological perturbation of the general perturbation metric with the NMDC action of the scalar field. Then, the PPF formalism is applied in the Type 1 IDE model where this model is classified through the field independent function. Thus, classification of the model can be revealed by looking at the PPF coefficient resulting from the scalar mode linear perturbation in metric and fluid variables. Based on the classification of the PPF coefficient results obtained, the parameterization of the Type 1 IDE model with NMDC corresponds to the type 1 IDE model class without NMDC. Therefore, the IDE model with NMDC is a subcase of the type 1 IDE model without NMDC.