Motivated by the string gas cosmological model , which predicts a blue tilt of the primordial gravitational wave spectrum , we examine the constraints imposed by current and planned observations on a blue tilted tensor spectrum .
Starting from an expression for the primordial gravitational wave spectrum normalised using cosmic microwave background observations , pulsar timing , direct detection and nucleosynthesis bounds are examined .
If we assume a tensor to scalar ratio on scales of the CMB which equals the current observational upper bound , we obtain from these current observations constraints on the tensor spectral index of n _ { T } \lesssim 0.79 , n _ { T } \lesssim 0.53 , and n _ { T } \lesssim 0.15 respectively .