content_image/354244.jpg content_image/354246.jpg content_image/354247.jpg content_image/354249.jpg
this leads to the scalar potential [720] 

<img src='content_image/354244.jpg'>

where M$_{F}$ ∼ ( m$_{SUSY}$ × M$_{S}$ ) 1 / 2 and m$_{SUSY}$ ∼ 1 TeV is the soft SUSY breaking mass at the weak scale. For φ > M 2 $_{F}$/m$_{3}$$_{/}$$_{2}$ , usually the gravity mediated contribution, m 2 3 / $_{2}$φ$^{2}$, dominates the potential where m$_{3}$$_{/}$$_{2}$ is the gravitino mass. Here we will concentrate on the VEVs such that M$_{s}$ ≪ φ ≤ M 2 $_{F}$/m$_{3}$$_{/}$$_{2}$ . A successful inflation can be obtained near the point of inflection; 

<img src='content_image/354246.jpg'>

<img src='content_image/354247.jpg'>

In the vicinity of the inlection point, the total energy density is given by 

<img src='content_image/354249.jpg'>

There are couple of interesting points, first of all note that the scale of inflation is extremely low, the Hubble scale during inflation is given by: H$_{inf}$ ∼ M 2 $_{F}$/M$_{P}$ ∼ 10 − 3 − 10 − 1 eV for M$_{F}$ ∼ 1 − 10 TeV. The relevant number of e-foldings is N$_{Q}$ ∼ 40 [720]. For M$_{F}$ ∼ 10 TeV, and φ$_{0}$ ∼ 10 11 GeV it is possible to match the CMB temperature anisotropy and the required tilt in the spectrum [720]. 

The validity of Eq. (338) for such a large VEV requires that M 2 F > (10 11 GeV) × m$_{3}$$_{/}$$_{2}$ . For M$_{F}$ ∼ 10 TeV this yields a bound on the gravitino mass, m$_{3}$$_{/}$$_{2}$ < 1 − 10 MeV, which is compatible with the warm dark matter constraints. 

## B. Quantum stability 

## 1. Radiative correction 

Since the MSSM inflaton candidates are represented by gauge invariant combinations of squarks and sleptons, the inflaton parameters receive corrections from gauge interactions which can be computed in a straightforward way. Quantum corrections result in a logarith- mic running of the soft SUSY breaking parameters m$_{φ}$ and A . The effective potential at 

