Observing the Structure of the Landscape with the CMB Experiments

TL;DR

This paper explores how precise measurements of the CMB can reveal the structure of the string theory landscape, focusing on scalar spectral index predictions for different vacuum energy gap models and their compatibility with observations.

Contribution

It introduces specific models of vacuum energy gaps in the string landscape and demonstrates how their predictions for the scalar spectral index can be used to infer landscape structure from CMB data.

Findings

Predicted scalar spectral index for constant energy gap model is ~0.9687.

Predicted scalar spectral index for linearly increasing energy gap model is ~0.9614.

Constraints on the energy scale parameter m_f are derived from observational data.

Abstract

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.