** Authors:**
KANGUJAM PRIYOKUMAR SINGH

** Abstract: **
This paper presents cosmological models in which the
gravitational and cosmological constants G and \Lambda are
time-dependent. We find a variety of solutions for the variation of
cosmological parameters. It is also found that, in the case of matter
dominated Robertson-Walker Universe, if the cosmological constant
\Lambda \ne 0, the Hubble's constant H is not constant at all but
inversely proportional to the cosmic time. The conservation law for
the energy momentum tensor is still valid with our law of variation:
\Lambda \propto R^{-2} and G\rho \propto \frac{\Lambda }{8\pi}.

** Keywords: **
Cosmology, cosmological model, homogeneous isotropic,
cosmic time, variable cosmological constant

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