Constraints on TeV-scale hybrid inflation and comments on non-hybrid alternatives

During hybrid inflation, the slowly-rolling inflaton field has a significant coupling to the trigger field which is responsible for most of the potential. Barring a fine-tuned accidental cancellation, this coupling induces a minimal one-loop contribution to the inflaton potential. The requirement that this contribution be not too large constrains a wide class of hybrid inflation models. Assuming that the inflaton perturbation generates structure in the Universe, the inflaton field and/or the trigger field after inflation have to be bigger than 10 GeV. This and other results make hybrid inflation at or below the TeV scale problematical. (There is no problem with hybrid inflation at the high energy scales normally considered.) ‘New’ and thermal inflation seem to be viable alternatives for inflation at or below the TeV scale, including the case that quantum gravity is at the TeV scale. In any case, supersymmetry is needed required during inflation, in order to protect a scalar mass. Introduction Hybrid inflation, where some ‘trigger’ field χ responsible for the bulk of the potential is different from the slowly-rolling inflaton field φ, has proved a very useful paradigm which may in the end turn out to be the one chosen by Nature. The original model [1] worked with a tree-level potential, the slope of the inflaton potential being given by the mass term 1 2 mφ. The potential was soon shown to be derivable from spontaneously broken global supersymmetry (susy), with either the F term [2, 3] or the D term [3] dominating. For each type of model, the one-loop correction to the inflaton potential coming from the trigger field and its superpartners (trigger supermultiplet) was evaluated [4, 5]. Later, realizations of the tree-level model in the context of softly broken supersymmetry were given [6, 7], leading to a one-loop correction A subset of the hybrid inflation constraints appeared in the unpublished note hep-ph/9904371 In these models the inflaton mass vanishes at the level of global supersymmetry, but supergravity corrections can give a suitable mass which indeed tends to be somewhat too large in the F term model.