Evolution Of The Universe And Dark Energy Mystery

We study the evolving universe in the presence of dark energy via di�erent well-known cosmological parameters.Firstly, we consider interacting new holographic dark energy model with cold dark matter in non-�at FRW universe.We obtain the equation of state parameter which represents the evolution of the universe from vacuum dark energy region towards quintessence region for particular values of the constant parameters.It is found that this model always remains unstable against small perturbations.The correspon- dence of this model with quintessence, tachyon, k-essence and dilaton scalareld models is also established.The dynamics of scalar elds and potentials provide consistent behavior with the accelerated expansion of the universe.We also consider interacting generalized holographic dark energy with cold dark matter in non-�at universe.We find that the deceleration parameter lies in the accelerated expansion phase of the universe and the equation of state parameter provides quintom like nature.This dark energy model is stable against small perturbations for specific range of constant parameters. It is found that the quintessence and tachyon potentials correspond to scaling solutions.Secondly, the pilgrim dark energy phenomenon is explored by choosing three cuto�s such as Hubble as well as event horizon and conformal age of the universe in �at universe. We study the pilgrim dark energy which plays an e�ective role on the equation of state parameter for exploring phantom region of the universe.The freezing region is found in the !� � !0� plane and the �CDM is achieved in the state finders plane for all three models of pilgrim dark energy.The conjecture of pilgrim dark energy is also studied by assuming the apparent and event horizons in non-�at universe and develop !� � !0� as well as r � s plane.It is interesting to mention here that the pilgrim dark energy with event horizon yields phantom region for all cases of d2 with u < 0. For these models, !� � !0� plane provides the thawing as well as freezing region and �CDM limit.The r � s plane shows the correspondence with di�erent models such as quintessence and phantom dark energy, �CDM and chaplygin gas.Also, we investigate the validity of the generalized second law of thermodynamics with event horizon in �at as well as non-�at universe. Finally, we consider the modi�ed holographic dark energy interacting with cold dark matter with varying G in �at and non-�at Kaluza-Klein universes.For this dark energy model, we assume event horizon as an infrared cuto� scale. We discuss the equation of state parameter and check the validity of the generalized second law of thermodynamics.In non-�at Kaluza-Klein case, we investigate the s�r plane in which the corresponding curves meet the limit of �CDM model