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We study the implications of recent indications for a red spectrum ofprimordial density perturbations for the detection of inflationarygravitational waves (IGWs) with forthcoming cosmic microwave backgroundexperiments. We find that if inflation occurs with a single field with aninflaton potential minimized at V=0, then Planck will be able to detect IGWs atbetter than 2$\sigma$ confidence level, unless the inflaton potential is apower law with a very weak power. The proposed satellite missions of the CosmicVision and Inflation Probe programs will be able to detect IGWs from all themodels we have surveyed at better than 5$\sigma$ confidence level. We providean example of what is required if the IGW background is to remain undetectedeven by these latter experiments.

Red Density Perturbations and Inflationary Gravitational Waves