predictions are the Higgs mass m$_{h}$ as it enters the tree level potential, and then the top mass, the highest mass that enters in loops of SM particle. Independently of inflation, current accelerator experiments allow these masses to range in [319] m$_{h}$ ∈ [114 . 4 − 182] GeV and m$_{t}$ ∈ [169 − 173] GeV. The evolution of the CMB predictions with respect to these masses is given in details in [589]. We will here only mention that compared to the classical values (equivalent to large m$_{h}$ ), n$_{s}$ r and | α$_{s}$ | increases when m$_{h}$ decreases or when m$_{t}$ increases. In particular, for the spectral index to be within the 1 σ contour of WMAP ( n$_{s}$ < 0 . 99), the mass of the Higgs is found [589] to be larger than m$_{h}$ > ∼ 125 . 7 + 3 . 8 ( m$_{t}$ − 171 GeV 2 GeV ) − 1 . 4 ( α$_{SU(3)}$ ( M$_{Z}$ ) − 0 . 1176 0 . 0020 ) ± 2GeV , (218) where α$_{SU(3)}$ is the strong coupling and the ± 2 GeV is due to theoretical uncertainties from higher order corrections. Testing this model in the future will therefore require the discovery of the Higgs particle at the LHC, which is expected if its mass is within the above range, together with an improvement of the error bar on n$_{s}$ as given by the PLANCK and some improvement on the top quark mass measurement at the LHC and the ILC. From phenomenological point of view SM Higgs inflation is a welcoming news, the Higgs can directly produce the SM degrees of freedom as shown in Refs. [124, 608]. Historically, SUSY inflation was first introduced to cure the flatness problem and asso- ciated fine tuning of new inflation [609, 610], but since then utilizing SUSY as a tool for inflation has gained in popularity. The fundamental reason is similar to the resolution of the hierarchy problem for which SUSY was introduced, i.e. to protect the flatness of the potential. The scalar sector is now described by a superpotential W and a K¨ ahler potential K , instead of just a scalar potential (see Sec. III C). Another difference with non-SUSY effective field theory concerns the range of VEVs allowed, which is now below the Planck scale. Close to the Planckian VEVs SUGRA corrections become important. One of course recovers the global SUSY in the limit when M$_{P}$ → ∞ . E. SUSY models of inflation In four dimensions, the N = 1 SUSY potential receives two contributions; one from the 98