Non-Minimal Theories
We have recently been able to show that our software can handle non-minimal kinetic terms. Exotic models of gravity, such as that proposed by Dvali, Gabadadze and Porrati (DGP) (Dvali:2000hr) and its extensions (deRham:2007xp, deRham:2007rw), attempted to explain the observed acceleration of the Universe with a modification of the gravitational potential at large scales due to the inclusion of large extra spatial dimensions; these models describe how a higher (>4) dimensional description of spacetime modifies our description of gravity. Specifically, gravity on the embedded four-dimensional brane has a localized non-minimal (non-canonical) kinetic term; this kinetic term then interpolates between sub-Hubble scales where gravity is well described by a four-dimensional theory and super-Hubble scales where gravity resembles the higher order theory.
Moreover, the structure of stable non-canonical kinetic terms seem to be unique. This idea was nucleated by two of my collaborators, Claudia de-Rham (Case Western Reserve University) and Andrew Tolley (Case Western Reserve University), who realized that two compelling and ghost-free models (DGP, its extensions and DBI Inflation (Silverstein:2003hf, Alishahiha:2004eh)) contain the same (deRham:2010eu), Gallileon, symmetry. This early work (deRham:2010kj) speculated that there would be a unique action with a finite number of terms that would always be ghost-free, a fact later proven in (Hassan:2011hr), and produce second-order equations of motion.
We started our explorations of non-minimal models by examining one of the simplest scenarios--a DBI-type inflaton coupled to a canonical scalar, matter, field. Although DBI-type models were particularly popular before the recent constraints on primordial non-gaussianity from the Planck mission (Ade:2013uln,Ade:2013zuv); they are still extremely important from a model building standpoint as they are one of only a few stable effective four-dimensional inflationary models with a non-minimal kinetic term (deRham:2010eu).
We looked at whether or not a DBI-type field can (pre)reheat the Universe---a question that has been open since DBI-type fields were seen as a viable inflationary model. The first studies assumed that the matter field was non-minmal (Lachapelle:2008sy), although they quickly started to do real estimates of whether preheating is robust in the presence of a non-minimal inflationary field (Matsuda:2008hk, Bouatta:2010bp). These initial estimates were somewhat primative in that they required that the non-minimal nature of the fields were only a perturbation to the canonical case. We were able to extend this argument remarkably further to show that the non-canonical nature of the field allows for both traditional parametric resonance, but also a self-resonance effect in the inflaton (Child:2013ria).
