# A Naturally Short Low Scale Inflation

I'll discuss a model of short inflation which arises in a
non-minimal gravity theory with a derivatively coupled scalar field
without any potential terms. This field drives inflation solely by its
derivatives, which couple to the metric and matter only through
the combination $\bar g_{\mu\nu} = g_{\mu\nu} - \frac{1}{m^4}
\partial_\mu \phi \partial_\nu \phi$. This theory is free of
instabilities around the usual Minkowski vacuum. The force
which is mediated by $\phi$ exchange is weak since the leading
order coupling is given by a dimension-8 operator $\frac{1}{m^4}
\partial_\mu \phi \partial_\nu \phi ~ T^{\mu\nu}$. Inflation lasts
as long as $\dot \phi^2 > m^4$, and terminates gracefully once the
scalar field kinetic energy drops below $m^4$. The total number of
e-folds is given by the initial inflaton energy $\dot \phi_0^2$ as
${\cal N} \simeq \frac13 \ln(\frac{\dot \phi_0}{m^2})$. If
inflation starts when $\dot \phi^2_0 \sim M^4_P$, and $m \sim
m_{EW} \sim TeV$, the number of e-folds that results is ${\cal N}
\sim 25$. Because the scale of inflation is low, this is
sufficient to solve the horizon problem if the reheating
temperature is $T_{RH} \ga MeV$. In this instance, the inflaton
would lead to fermion-antifermion annihilation channels $f\bar f
\rightarrow \phi \phi$ accessible to the LHC, and it would give
very small corrections to the Newtonian potential, and to
supernova cooling rates, that are completely within experimental
limits.

hep group
Last modified: Wed Sep 17 21:35:31 EDT 2003