In this thesis we make a contribution in the area of Extended Theories of Gravity (ETG) by studying the dynamics of the R ln R model. We draw attention to the importance of introducing complete alternative theories of gravity and studying the possible geometrical origin of Dark Energy (unknown form of energy), which is commonly thought to be responsible for the present epoch of accelerated expansion that our universe undergoes. The first chapter of the thesis is an introduction to one of the most successful models in the realm of cosmology i.e. the CDM model. At the end of the first chapter we give a brief discussion on the ground breaking news from the BICEP2 experiment. However, part of the community argues that the BICEP2 results cannot be ascribed to a primordial gravitational waves. In fact, the recent dust map was released by Planck's team lowered the chances that the signal detected by BICEP2 team can be due to primordial gravitational waves. The second chapter introduces a review of the motivations that stimulated researchers to pursue new theories of gravity. Moreover, we revisit the mathematical basis of the f (R) theory of gravity and explain how a viable model of f (R) can account for the most bizarre phenomenon in the universe, namely Dark Energy. The third chapter is dedicated to the basis and the techniques of the theory of dynamical systems. The fifth chapter includes some original work on the R ln R model dynamics in two different versions (compact and non-compact phase space). In this thesis, we show that the R ln R model cannot be considered as a viable model since it has serious flaws. These flaws will be addressed, in detail, in chapter 5.
Reference:
Aboelhassan, S. 2015. Probing the cosmological dynamics of a logarithmic f (R) theory of gravity. University of Cape Town.
Aboelhassan, S. N. (2015). Probing the cosmological dynamics of a logarithmic f (R) theory of gravity. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/15727
Aboelhassan, Sheref Nasereldin. "Probing the cosmological dynamics of a logarithmic f (R) theory of gravity." Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2015. http://hdl.handle.net/11427/15727
Aboelhassan SN. Probing the cosmological dynamics of a logarithmic f (R) theory of gravity. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2015 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/15727