A Back-reaction Induced Lower Bound on the Tensor-to-Scalar Ratio

Abstract

There are large classes of inflationary models, particularly popular in the context of string theory and brane world approaches to inflation, in which the ratio of linearized tensor to scalar metric fluctuations is very small. In such models, however, gravitational waves produced by scalar modes cannot be neglected. We derive the lower bound on the tensor-to-scalar ratio by considering the back-reaction of the scalar perturbations as a source of gravitational waves. These results show that no cosmological model that is compatible with a metric scalar amplitude of $\approx 10^{-5}$ can have a ratio of the tensor to scalar power spectra less than $\approx 10^{-8}$ at recombination and that higher-order terms leads to logarithmic growth for r during radiation domination. Our lower bound also applies to non-inflationary models which produce an almost scale-invariant spectrum of coherent super-Hubble scale metric fluctuations.

5 pages, version 3, minor changes from version 2

References in corpus (10)

• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• Theory and Numerics of Gravitational Waves from Preheating after Inflation
• A Gravitational Wave Background from Reheating after Hybrid Inflation
• Gravitational Wave Production At The End Of Inflation
• A stochastic background of gravitational waves from hybrid preheating
• A Microscopic Limit on Gravitational Waves from D-brane Inflation
• Unified treatment of cosmological perturbations from super-horizon to small scales
• Vector modes generated by primordial density fluctuations
• The Maximal Amount of Gravitational Waves in the Curvaton Scenario

Cited by in corpus (1)

• A Study of Structure Formation and Reheating in the D3/D7 Brane Inflation Model