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The effects of a running gravitational coupling and the entropic force on future singularities are considered. Although it is expected that the quantum corrections remove the future singularities or change the singularity type, treating the running gravitational coupling as a function of energy density is found to cause no change in the type of singularity but causes a delay in the time that a singularity occurs. The entropic force is found to replaces the singularity type $II$ by $bar{III}$ ($a=$const., $H=$const., $dot{H} to infty$, $p to infty$, $rho to infty$) which differs from previously known type $III$ and to remove the $w$-singularity. We also consider an effective cosmological model and show that the types $I$ and $II$ are replaced by the singularity type $III$.
Starting from the dipole representation of small-$x$ evolution we implement the running of the coupling in a self-consistent way. This results in an evolution equation for the dipole density in Borel $(b)$ space. We show that the Borel image of the d
We link observational parameters such as the deceleration parameter, the jerk, the kerk (snap) and higher-order derivatives of the scale factor, called statefinders, to the conditions which allow to develop sudden future singularities of pressure wit
Entropic force originates in the assumption that there is a horizon for the universe. This horizon gives rise to additional terms in the equations of motion. Using dynamical system calculations, our results show that in the presence of dark energy fo
Much of the success of gravitational-wave astronomy rests on perturbation theory. Historically, perturbative analysis of gravitational-wave sources has largely focused on post-Newtonian theory. However, strong-field perturbation theory is essential i
Possibilities emerging out of the dynamical evolutions of collapsing systems are addressed in this thesis through analytical investigations of the highly non-linear Einstein Field Equations. Studies of exact solutions and their properties, play a non