Singular Inflation
  We prove that a homogeneous and isotropic universe containing a scalar field
with a power-law potential, $V(\phi )=A\phi ^{n}$, with $0<n<1$ and $A>0$
always develops a finite-time singularity at which the Hubble rate and its
first derivative are finite, but its second derivative diverges. These are the
first examples of cosmological models with realistic matter sources that
possess weak singularities of 'sudden' type. We also show that a large class of
models with even weaker singularities exist for non-integer $n>1$. More
precisely, if $k<n<k+1$ where $k$ is a positive integer then the first
divergence of the Hubble rate occurs with its ($k+2)$th derivative. At early
times these models behave like standard large-field inflation models but they
encounter a singular end-state when inflation ends. We term this singular
inflation.
