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We show that a detectable tensor-to-scalar ratio $(r\ge 10^{-3})$ on the CMBscale can be generated even during extremely low energy inflation whichsaturates the BBN bound $\rho_{\rm inf}\approx (30 {\rm MeV})^4$. The source ofthe gravitational waves is not quantum fluctuations of graviton but those of$SU(2)$ gauge fields, energetically supported by coupled axion fields. Thecurvature perturbation, the backreaction effect and the validity ofperturbative treatment are carefully checked. Our result indicates thatmeasuring $r$ alone does not immediately fix the inflationary energy scale.

Does the detection of primordial gravitational waves exclude low energy inflation?