where a is the scale factor of the universe and V$_{ϕ}$ is the energy density in the ϕ field. Note that ϕ is the field responsible for forming the false vacuum, which could either arise within MSSM or from some other sector.There are examples of ϕ field as an MSSM flat direction. Since φ is inside the plateau of its potential, its dynamics is frozen, hence V ( φ ) ∼ V ( φ$_{0}$ ) as long as H > H$_{MSSM}$ . Right after tunneling, H ≡ ˙ a/a = $_{r}$− 1 0 > H$_{false}$ . This implies that the last term on the right-hand side of Eq. (365) dominates over the first two terms, and hence the universe is curvature dominated. The ϕ field oscillates around the true vacuum of its potential at the origin, and quickly decays to radiation whose energy density is redshifted ∝ a − $^{4}$. On the other hand the curvature term is redshifted ∝ a − $^{2}$, while V ( φ ) remains essentially constant (due to extreme flatness of the inflaton potential) for H > H$_{MSSM}$ . As a result, the universe inside the bubble will remain curvature dominated until H ≃ H$_{MSSM}$ . At this point the inflaton field φ dominates the energy density and a phase of MSSM inflation begins. This blows the open universe inside the bubble and inflates away the curvature term. As long as the total number of e-foldings is N$_{Q}$ plus few, the observable part of the universe looks like flat today (within the limits of 5 year WMAP data) [13]. Perturbations of the correct size with acceptable spectral index will be generated during the slow-roll phase, and the SM degrees of freedom will be created from the decay of φ field in the post-inflationary phase. So far we have studied the flat direction inflaton represented by a monomial superfield, Φ, instead one can also imagine a polynomial I spanned by the Higgses and the sleptons as an example [710], where ν$_{i}$ are complex coefficients, H$_{u}$ is the up-type Higgs and L$_{i}$ are the sleptons. For a following field configuration, the polynomial I has a vanishing matter current and vanishing gauge fields [710], F. Other examples of gauge invariant inflatons Within MSSM : I = ν$_{1}$H$_{u}$L$_{1}$ + ν$_{2}$H$_{u}$L$_{2}$ + ν$_{3}$H$_{u}$L$_{3}$ (366) L$_{i}$ = $_{e}$− iχ/ $^{2}$φ$_{i}$   0 1   , H$_{u}$ = e iχ/ 2 √ ∑ i | φ$_{i}$ | 2   1 0   , (367) 170