fluctuations are the most important ones to judge the merits of the models, especially the spectral index, tensor to scalar ratio, and running of the spectral tilt with the help of slow- roll parameters ϵ , η , and ξ $^{2}$, as defined in Sec. II A $^{46}$. We will also discuss generation of non-Gaussianities and cosmic strings (see Sec. II E for more details about the current status of the cosmological data), in order to visualize how well a given model matches the obser- vations. Although we might not be able to pin down the model(s) of inflation, but certainly we would be able to rule them out from observations. From particle physics point of view, there exists an important criteria for a successful inflation; which is to end inflation in the right vacuum where the SM baryons can be excited naturally after the end of inflation in order to have a successful baryogenesis and BBN. B. Non-SUSY one-field models The most general form for the potential of a gauge singlet scalar field φ contains an infinite number of terms, V = V$_{0}$ + ∞ ∑ α =2 λ$_{α}$ M α − 4 P φ α . (161) In 4 d , restricting to renormalizable terms allows to prevent all terms with α ≥ 4. Further- more, assuming extra symmetries can ensure that certain neglected terms in this series are not generated at the loop level. Note that this is the case for the constant term V$_{0}$ also. The usual example of such a symmetry is the parity Z$_{2}$ , under which φ → − φ , which al- lows to prevent all terms with α odd. Most phenomenological models of inflation proposed initially assume that one or two terms in Eq. (161) dominate over the others, though some do contain an infinite number of terms. In Refs. [500, 501], terms proportional to φ $^{2}$, φ 3 and φ 4 with adjustable coefficients were included in studying the inflationary dynamics and the perturbations, and in Ref. [502] non-renormalizable terms up to the 6th order were also taken into account in order to put bound on tensor to scalar ratio. 46 Review of some of these models using the Hubble-flow parameters of Eq. (41) has been performed in [207, 499]. 77