content_image/328668.jpg content_image/328669.jpg
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. 

## F. Other examples of gauge invariant inflatons 

## Within MSSM : 

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], 

<img src='content_image/328668.jpg'>

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], 

<img src='content_image/328669.jpg'>

