In the presence of fields without superpotential but with large vevs through D-terms the mass-squared of the inflaton in the context of supergravity hybrid inflation receives positive contributions which could cancel the possibly negative Kähler potential ones. The mechanism is demonstrated using Kähler potentials associated with products of SU (1, 1)/U (1) Kähler manifolds. In a particularly simple model of this type all supergravity corrections to the Fterm potential turn out to be proportional to the inflaton mass allowing even for an essentially completely flat inflationary potential. The model also allows for a detectable gravitational wave contribution to the microwave background anisotropy. Its initial conditions are quite natural largely due to a built in mechanism for a first stage of "chaotic" D-term inflation.
1The hybrid inflationary scenario [1] has many advantages compared to most other inflationary models [2]. It does not involve tiny inflaton self-couplings and succeeds in reconnecting inflation with phase transitions in grand unified theories (GUTs). In its simplest realization it involves a gauge singlet inflaton and a possibly gauge non-singlet non-inflaton field. During inflation the non-inflaton field finds itself trapped in a false vacuum state and the universe expands quasi-exponentially dominated by the almost constant false vacuum energy density. Inflation ends with (or just before) a very rapid phase transition when the non-inflaton field rolls to its true vacuum state ("waterfall").The simplest supersymmetric (SUSY) particle physics model implementing the above scenario in the context of a "unifying" gauge group G (of rank ≥ 5) which breaks sponta-16 GeV is described by a superpotential which includes the terms [3]Here Φ,Φ is a conjugate pair of left-handed SM singlet superfields which belong to N ddimensional representations of G and reduce its rank by their vacuum expectation values (vevs), S is a gauge singlet left-handed superfield, µ is a superheavy mass scale related to M X and λ a real and positive coupling constant. The superpotential terms in Eq. (1) are the dominant couplings involving the superfields S, Φ,Φ which are consistent with a continuous R-symmetry under which W → e iγ W , S → e iγ S, Φ → Φ andΦ →Φ. The potential obtained from W has, in the supersymmetric limit, a SUSY vacuum atwhere the scalar components of the superfields are denoted by the same symbols as the corresponding superfields, M X is the mass acquired by the gauge bosons and g the G gauge coupling constant. By an appropriate R-trasformation we can bring the complex field S on the real axis, i.e. S ≡ 1 √ 2 σ, where σ is a real scalar field. For any fixed value of σ 2 > σ 2 c , whereλ, the potential of the globally supersymmetric model has a minimum at Φ 2 =Φ = 0 with a σ-independent value V gl = µ 4 and the universe expands quasi-exponentially.When σ 2 falls below σ 2 c the false vacuum state at Φ =Φ = 0 becomes unstable and Φ,Φ roll rapidly to their true vacuum.If global supersymmetry is promoted ...