Recent B-mode polarization observation seems to imply the tensor tilt n _ { T } \gtrsim 1 at large angular scale , if the primordial signal is dominated .
We show that for a primordial universe , which is in a slowly expanding genesis phase before the slow-roll inflation , the primordial tensor spectrum will get a large-scale cutoff , i.e . n _ { T } \gtrsim 1 at large scales while n _ { T } \simeq 0 at small scale .
We find that this inflationary scenario not only may be consistent with the observation , but also predicts a large-scale anomaly in BB power spectrum , i.e .
due to the large suppression of tensor perturbation amplitude we will hardly see the reionization bump at low- l , which may be falsified by the Planck polarization data .