Modified theory of gravity with a scalar density field

Pioneering attempts to modify the General Theory of Relativity were initiated in the 1920s, just after Einstein introduced the theory in 1915. However, such initiatives have increased significantly (especially since the 1990s), after realizing that the Universe has entered in an accelerated expansion phase. Because it is not possible to explain this mysterious speedy expansion with the original form of the General Theory of Relativity, we need to modify it or introduce new alternative theories. In this context, extensive investigations have been performed in literature on the modification of General Theory of Relativity. For instance, the MOND, TeVeS, scalar-tensor, metric f(R)-gravity, Palatini f(R)-gravity and the metric-affine f(R)-gravity theories have been taken into account intensively. In this thesis, we mainly intorduce a new modified gravitational theory including a weight 2 scalar density. We derive equations of motion for a scalar field and the aforementioned scalar density, respectively, and compare them. Finally, the results are discussed comparatively from a different perspective within the framework of FRW cosmology.