Observing the Structure of the Landscape with the CMB Experiments
  Assuming that inflation happened through a series of tunneling in the string
theory landscape, it is argued that one can determine the structure of vacua
using precise measurements of the scalar spectral index and tensor
perturbations at large scales. It is shown that for a vacuum structure where
the energy gap between the minima is constant, i.e. $\epsilon_i=i m_f^4$, one
obtains the scalar spectral index, $n_s$, to be $\simeq 0.9687$, for the modes
that exit the horizon 60 e-folds before the end of inflation. Alternatively,
for a vacuum structure in which the energy gap increases linearly with the
vacuum index, i.e. $\epsilon_i=\frac{i^2}{2} m_f^4$, $n_s$ turns out to be
$\simeq 0.9614$. Both these two models are motivated within the string theory
landscape using flux-compactification and their predictions for scalar spectral
index are compatible with WMAP results. For both these two models, the results
for the scalar spectral index turn out to be independent of $m_f$. Nonetheless,
assuming that inflation started at Planckian energies and that there had been
successful thermalization at each step, one can constrain $m_f<2.6069\times
10^{-5} m_P$ and $m_f<6.5396\times 10^{-7} m_P$ in these two models,
respectively. Violation of the single-field consistency relation between the
tensor and scalar spectra is another prediction of chain inflation models. This
corresponds to having a smaller tensor/scalar ratio at large scales in
comparison with the slow-roll counterparts. Similar to slow-roll inflation, it
is argued that one can reconstruct the vacuum structure using the CMB
experiments.
