Natural Inflation

A pseudo-Nambu-Goldstone boson, with a potential of the form $ V(\phi) = \Lambda^4 [1 + \cos(\phi/f)]$, can naturally give rise to an epoch of inflation in the early universe (Freese, Frieman, and Olinto 1990). The potential is naturally flat (as required by microwave background limits on the amplitude of density fluctuations), without any fine-tuning. Successful inflation can be achieved if $f \sim m_{pl}$ and $\Lambda \sim m_{GUT}$. Such mass scales arise in particle physics models with a large gauge group that becomes strongly interacting at a scale $\sim \Lambda$, {\it e.g.,} as can happen in the hidden sector of superstring theories. The density fluctuation spectrum can be non-scale-invariant, with more power on large length scales (Adams, Bond, Freese, Frieman, and Olinto 1993). This enhanced power on large scales may be useful to explain the otherwise puzzling large-scale clustering of galaxies and clusters and their flows. Natural inflation differs from other models with extra large-scale power in that the contribution of the tensor modes to microwave background fluctuations is negligible; this difference should serve as a testable feature of the model.