Rollercoaster Cosmology
  (Abridged) Does inflation have to happen all in one go? The answer is a
resounding no! All cosmological problems can be solved by a sequence of short
bursts of cosmic acceleration, interrupted by short epochs of decelerated
expansion. The spectrum of perturbations will still match the CMB and LSS if
the earliest stage of the last ${\cal O}(50)-{\cal O}(60)$ efolds is at least
${\cal O}(15)$ efolds long. Other stages can be considerably shorter. But as
long as they add up to ${\cal O}(50)-{\cal O}(60)$ efolds and the stages of
decelerated expansion in between them are shorter and also overall last less,
the ensuing cosmology will pass muster. The presence of the interruptions
resets the efold clock of each accelerating stage, and changes its value at the
CMB pivot point. This change opens up the theory space, loosening the bounds.
In particular some models that seem excluded at ${\cal N}=60$ fit very well as
shorter stages with ${\cal N}=30$. Interesting predictions are that both the
scalar and tensor spectra of perturbations are rapidly modified at short
wavelengths. These features could be tested with future CMB spectroscopy
searches and with short wavelength primordial gravity probes. The spatial
curvature in these models can be larger than the largest wavelength scalar
perturbations, because $\Omega_{\tt k}$ evolves differently than the scalar
perturbations $\frac{\delta \rho}{\rho}|_{\tt S}$. Finally, with many short
stages of accelerated expansion, the abundance of reheating products from
previous accelerated stages does not get completely wiped out. This implies
that the universe may contain additional populations of particles, more rare
than the visible ones, or even primordial black holes, created during a late
decelerated epoch before last reheating, which may be dark matter.
