On the possibility of blue tensor spectrum within single field inflation
  We present a series of theoretical constraints on the potentially viable inflation models that might yield a blue spectrum for primordial tensor perturbations. By performing a detailed dynamical analysis we show that, while there exists such possibility, the corresponding phase space is strongly bounded. Our result implies that, in order to achieve a blue tilt for inflationary tensor perturbations, one may either construct a non-canonical inflation model delicately, or study the generation of primordial tensor modes beyond the standard scenario of single slow-roll field. 
Yi-Fu Cai, Jinn-Ouk Gong, Shi Pi, Emmanuel N. Saridakis and Shang-Yu   Wu
hep-th astro-ph.CO gr-qc hep-ph