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We perform a deductive study of accelerating Universe and focus on the importance of variable time-dependent $Lambda$ in the Einsteins field equations under the phenomenological assumption, $Lambda =alpha H^2$ for the full physical range of $alpha$. The relevance of variable $Lambda$ with regard to various key issues like dark matter, dark energy, geometry of the field, age of the Universe, deceleration parameter and barotropic equation of state has been trivially addressed. The deceleration parameter and the barotropic equation of state parameter obey a straight line relationship for a flat Universe described by Friedmann and Raychaudhuri equations. Both the parameters are found identical for $alpha = 1$.
The origin of negative pressure fluid (the dark energy) is investigated in the quantum model of the homogeneous, isotropic and closed universe filled with a uniform scalar field and a perfect fluid which defines a reference frame. The equations of th
The description of the cosmological expansion and its possible local manifestations via treating the proper conformal transformations as a coordinate transformation from a comoving Lorentz reference frame (RF) to an uniformly accelerated RF is given.
Among various phenomenological $Lambda$ models, a time-dependent model $dot Lambdasim H^3$ is selected here to investigate the $Lambda$-CDM cosmology. Using this model the expressions for the time-dependent equation of state parameter $omega$ and oth
The description of the cosmological expansion and its possible local manifestations via treating the proper conformal transformations as a coordinate transformation from a comoving Lorentz reference frame to an uniformly accelerated one is given. The
In this paper, we have investigated a bulk viscous anisotropic Universe and constrained its model parameters with recent $H(z)$ and Pantheon compilation data. Using cosmic chronometric technique, we estimate the present value of Hubbles constant as $