FRW Universe with Variable $G$ and $\mathrm{\Lambda }$-Terms

A new class of exact solutions of Einstein’s field equations with a perfect fluid source, variable gravitational coupling $G$ and cosmological term $\mathrm{\Lambda }$ for FRW spacetime is obtained by considering variable deceleration parameter models for the universe. The nature of the variables $G(t)$, $\mathrm{\Lambda }(t)$ and the energy density $\rho (t)$ have been examined for three cases : (i) exponential (ii) polynomial and (iii) sinusoidal form. The special types of models for dust, Zel’dovich and radiating universe are also mentioned in all these cases. The behaviour of these models of the universe are also discussed in the light of recent supernovae Ia observations.