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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 er physical parameters are derived. It is shown that in $H^3$ model accelerated expansion of the Universe takes place at negative energy density, but with a positive pressure. It has also been possible to obtain the change of sign of the deceleration parameter $q$ during cosmic evolution.
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