Generalized assisted inflation

Scalar field theory has become the generic playground for building cosmological models related to particle physics, in particular for obtaining inflationary cosmologies. One such class of models involves exponential potentials @exp(A16p/pmPl 2 f)# , which lead to power law inflation, a }t, with p.1, for sufficiently flat potentials @1–3#. A number of related features have also been discovered for such potentials: in a universe containing a perfect fluid and such a scalar field, then for a wide range of parameters the scalar field ‘‘mimics’’ the perfect fluid, adopting its equation of state @4–6# and leading to attractor scaling solutions at late time @7#. These solutions offer a plausible mechanism for stabilizing the dilaton field in models of gaugino condensation arising in supersymmetry breaking @8#. It is generally assumed that even if there are many scalar fields present, only one of them will dominate the dynamics and roll down the potential slowly. However, recently Liddle, Mazumdar, and Schunck ~LMS! @9# have demonstrated in a particular example that multiple scalar fields, each with an exponential potential, can lead to inflationary solutions, even if the individual field potentials are too steep for inflation. There exists a cumulative effect of all the fields that can give rise to inflationary behavior—a result they termed ‘‘assisted inflation.’’ Malik and Wands have demonstrated that the associated attractor solution could be identified through a rotation in field space, with a hybrid model where the vacuum energy had an exponential dependence upon the dilaton field @10#. Multiple exponential potentials do arise in modern Kaluza-Klein theories. Indeed, they are a natural outcome of the compactification of higher dimensional theories down to 311 dimensions. With this in mind it is worth investigating such potentials in a bit more detail. Indeed, Kanti and Olive have recently proposed a possible realization of assisted inflation based on the compactification of a five-dimensional Kaluza-Klein model @11#. It also raises the question, could inflation arise out of the 11-dimensional supergravity models compactified on squashed seven spheres for example? Such models have been investigated by a num-