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 } = im _ { 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 .