Abstract:
The scale at which supersymmetry is broken and the mechanism by which supersymmetry breaking is fed down to the observable sector has rich implications on the way Nature may have chosen to accomplish inflation. We discuss a simple model for slow rollover inflation which is minimal in the sense that the inflaton may be identified with the field responsible for the generation of the $\mu$-term. Inflation takes place at very late times and is characterized by a very low reheating temperature. This property is crucial to solve the gravitino problem and may help to ameliorate the cosmological moduli problem. The COBE normalized value of the vacuum energy driving inflation is naturally of the order of $10^{11}$ GeV. This favors the N=1 supergravity scenario where supersymmetry breaking is mediated by gravitational interactions. Nonetheless, smaller values of the vacuum energy are not excluded by present data on the temperature anisotropy and the inflationary scenario may be implemented in the context of new recent ideas about gauge mediation where the standard model gauge interactions can serve as the messangers of supersymmetry breaking. In this class of models supersymmetry breaking masses are usually prop ortional to the F-term of a gauge singlet superfield. The same F-term may provide the vacuum energy density necessary to drive inflation. The spectrum of density perturbations is characterized by a spectral index which is significantly displaced from one. The measurements of the temperature anisotropies in the cosmic microwave background radiation at the accuracy expected to result from the planned missions will be able to confirm or disprove this prediction and to help in getting some deeper insight into the nature of supersymmetry breaking.

Abstract:
We study the connection between inflation and supersymmetry breaking in the context of an O'Raifeartaigh model which can account for both hybrid inflation and a true vacuum where supersymmetry is spontaneously broken. For a weakly coupled inflaton field, the dynamics during the inflationary phase can be determined by the supersymmetry breaking scale $M_S\sim 10^{10}$ GeV, even if $H_I >> m_{3/2}$. The spectrum of density fluctuations is then almost scale invariant, with a spectral index $n-1={\cal O}(M_G^2/M_P^2)$. The mass parameter $M_G$ of the O'Raifeartaigh model is determined by the COBE normalization for the cosmic microwave background to be the grand unification scale, $M_G \sim 10^{16}$ GeV.

Abstract:
We consider dynamical models of supersymmetry breaking which naturally incorporate cosmological inflation. The inflaton plays an inevitable role in dynamical SUSY breaking and the hierarchical scales of inflation and SUSY breaking are simultaneously realized through a single dynamics.

Abstract:
We investigate the recently proposed class of chaotic inflation models in supergravity with an arbitrary inflaton potential. These models are extended to include matter fields in the visible sector and we employ a mechanism of SUSY breaking based on a particular phenomenological version of the KKLT mechanism (the KL model). We describe specific features of reheating in this class of models and show how one can solve the cosmological moduli and gravitino problems in this context.

Abstract:
We investigate the possibility of obtaining a low scale of supersymmetry breaking within the ISS framework using a metastable vacuum. This is achieved by introducing an R-symmetry preserving gravitational coupling of the ISS sector to a relatively low scale inflationary sector. We find the allowed range for the supersymmetry breaking scale, 10^4 GeV < \mu < 10^8 GeV, which is low enough to be amenable to gauge supersymmetry breaking mediation. This scenario is based upon a so-called hilltop inflation phase whose initial condition problem is also addressed.

Abstract:
In models of cosmological inflation motivated by dynamical supersymmetry breaking, the potential driving inflation may be characterized by inverse powers of a scalar field. These models produce observables similar to those typical of the hybrid inflation scenario: negligible production of tensor (gravitational wave) modes, and a blue scalar spectral index. In this short note, we show that, unlike standard hybrid inflation models, dynamical supersymmetric inflation (DSI) predicts a measurable deviation from a power-law spectrum of fluctuations, with a variation in the scalar spectral index $|dn / d(\ln k)|$ may be as large as 0.05. DSI can be observationally distinguished from other hybrid models with cosmic microwave background measurements of the planned sensitivity of the ESA's Planck Surveyor.

Abstract:
We argue that fields responsible for inflation and supersymmetry breaking are connected by gravitational couplings. In view of the recent progress in studying supersymmetry breaking in a metastable vacuum, we have shown that in models of supersymmetric hybrid inflation, where R-symmetry plays an important role, the scale of supersymmetry breaking is generated dynamically at the end of inflation and turns out to be consistent with gravity mediation.

Abstract:
We study the supergravity hybrid inflation model of Ref.[1] in the presence of a modulus field. The eta-problem is solved by a shift symmetry for the inflaton, which protects the inflaton mass even in the presence of the modulus field. Inflation is (nearly) unaffected by moduli stabilization, provided the scale of supersymmetry breaking in the post-inflation vacuum is small. Therefore the model has the nice phenomenology that it combines low scale supersymmetry breaking with high scale (grand unification scale) inflation.

Abstract:
We investigate cosmological moduli problem in the gauge-mediated supersymmetry breaking (GMSB). A mini-inflation (oscillating inflation) takes place when a scalar field corresponding to the flat direction in GMSB oscillates along the logarithmic potential induced by the gauge-mediation mechanism. It is shown that this oscillating inflation can sufficiently dilute the relic abundance of the string moduli for some ranges of parameters in the GMSB models.

Abstract:
In the context of colliding brane worlds I discuss a toy cosmological model, developed in collaboration with E. Gravanis, which arguably produces inflation and a relaxing to zero cosmological ``constant'' hierarchically small as compared to the supersymmetry breaking (TeV) scale. Supersymmetry breaking is induced by compactification of the brane worlds on magnetized tori. The crucial ingredient is the non-criticality (non conformality) of string theory on the observable brane world induced at the collision, which is thus viewed as a cause for departure from equilibrium in this system. The hierarchical smallness of the present-era vacuum energy, as compared to the SUSY breaking scale, is thus attributed to relaxation.