Closed string thermodynamics and a blue tensor spectrum

The BICEP-2 team has recently reported the positive detection of cosmic microwave background $B$-mode polarization. Although uncertainties due to galactic dust foregrounds remain, it is a constructive exercise to work out the implications of presuming some part of the detected $B$-mode signal to be due to primordial gravitational waves. Were a positive detection of a tensor-to-scalar ratio larger than $r\gtrsim \mathcal{O}({10}^{-2})$ confirmed, detecting a tilt in the tensor spectrum comparable to that observed for the scalar power spectrum becomes in principle possible. We wish to explore in this brief paper the possibility of there being a blue tilt to the primordial gravitational-wave spectrum. Such a tilt would be incompatible with standard inflationary models, although it was predicted some years ago in the context of a mechanism that thermally generates the primordial perturbations through a Hagedorn phase of string cosmology. By scrutinizing the data with priors informed by a model that is immediately falsifiable, but which predicts features that may be favored by the data—namely a blue tensor tilt with an induced and complementary red tilt to the scalar spectrum, with a naturally large tensor-to-scalar ratio that relates to both—we offer a useful straw model against which to test the predictions of single-field inflation.

Figure 1

Space-time sketch of the evolution in string gas cosmology. The vertical axis is time, and the horizontal axis is physical distance. The time $t_R$ corresponds to the transition between the Hagedorn phase and the radiation phase. The thick blue curve labeled by $H^{-1}$ indicates the Hubble radius, and the two thin red curves which are vertical during the Hagedorn phase correspond to the physical wavelengths of fluctuation modes labeled by $k_1$ and $k_2$.