Scenario of inflationary cosmology from the phenomenological \(\Lambda\) models

Choosing the three phenomenological models of the dynamical cosmological term \(\Lambda\), viz., \(\Lambda \sim (\dot a/a)^2\), \(\Lambda \sim {\ddot a/a}\) and \(\Lambda \sim \rho\) where \(a\) is the cosmic scale factor, it has been shown by the method of numerical analysis that the three models are equivalent for the flat Universe \(k=0\). The evolution plots for dynamical cosmological term \(\Lambda\) vs. time \(t\) and also the cosmic scale factor \(a\) vs. \(t\) are drawn here for \(k=0, +1\). A qualitative analysis has been made from the plots which supports the idea of inflation and hence expanding Universe.