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Abstract It is well known that Friedmann-Robertson-Walker (FRW) standard cosmology suffers from some problems. Several theories have been suggested to tackle such problems, in which energy-momentum distribution is described by a phenomenological second-order tensor. A pure geometric field theory has been used to construct a new cosmological model. The obtained model is free from two cosmological standard problems: the flatness problem and the particle horizons problem, and it is shown to be devoid of initial singularity under a certain condition. Due to the importance of studying the motion of the spinning fluids, which may contribute to describing the status of the accretion disc orbiting a compact gravitational field as in an active galactic nucleus (AGN). In Chapter II, we obtained the equation of motion for spinning fluids in three different geometries. Riemannian geometry, which is the standard platform of GR, Finsler geometry, and Parametrized Absolute Parallelism (PAP) geometry, which has non-vanishing curvature and torsion simultaneously. In Chapter III, we study spinning fluids motion in some classes of Bi-metric type theories of gravity. In Chapter IV, the concept of geodesic invariance under coordinate transformation has been revisited to include modified geodesics in PAP-space. Key words: Cosmology, Spinning fluids, Bi-metric type theories of gravity, Modified geodesic mapping. |