Natural inflation: Particle physics models, power-law spectra for large-scale structure, and constraints from the Cosmic Background Explorer

The particle physics basis for models of natural inflation with pseudo Nambu-Goldstone bosons are discussed and the consequences for large-scale structure of the nonscale-invariant density fluctuation spectra that arise in natural inflation and other models are studied.

Abstract

A pseudo-Nambu-Goldstone boson, with a potential of the form $V(\\phi) =\n\\Lambda^4[1 \\pm \\cos(\\phi/f)], naturally gives rise to inflation if $f \\sim\nM_{Pl}$ and $\\Lambda \\sim M_{GUT}$. We show how this can arise in\ntechnicolor-like and superstring models, and work out an explicit string\nexample in the context of multiple gaugino condensation models. We study the\ncosmology of this model in detail, and find that sufficient reheating to ensure\nthat baryogenesis can take place requires $f > 0.3 M_{Pl}$. The primordial\ndensity fluctuation spectrum generated is a non-scale-invariant power law,\n$P(k) \\propto k^{n_s}$, with $n_s \\simeq 1 - (M^2_{Pl}/8\\pi f^2)$, leading to\nmore power on large length scales than the $n_s = 1$ Harrison-Zeldovich\nspectrum. The standard CDM model with $0 \\la n_s \\la 0.6-0.7$ could in\nprinciple explain the large-scale clustering observed in the APM and IRAS\ngalaxy surveys as well as large-scale flows, but the COBE microwave anisotropy\nimplies such low amplitudes (or high bias factors, $b>2$) for these CDM models\nthat galaxy formation occurs too late to be viable; combining COBE with\nsufficiently early galaxy formation or the large-scale flows leads to $n_s\n>0.6$, or $f > 0.3 M_{Pl}$ as well. For extended and power law inflation\nmodels, this constraint is even tighter, $n_s > 0.7$; combined with other\nbounds on large bubbles in extended inflation, this leaves little room for most\nextended models.\n