Inflation and Alternatives with Blue Tensor Spectra

TL;DR

The paper investigates whether the primordial tensor tilt $n_ ext{T}$ can be blue ($n_ ext{T}>0$) given the BICEP2/Planck/POLARBEAR data and what early-universe models can generate such a tilt. It analyzes NEC-violating inflation (G-inflation), generalized initial conditions, and string gas cosmology, highlighting that blue $n_ ext{T}$ is possible but often comes with large non-Gaussianities, except in string gas cosmology where fluctuations remain highly Gaussian. The analysis shows that blue $n_ ext{T}$ improves fits when Planck data are included, but different models make distinct predictions for non-Gaussianity, running, and the scalar tilt, providing a pathway to distinguish inflation from alternatives. Overall, the work underscores that a confirmed blue tensor tilt would favor non-standard or alternative scenarios and that precise measurements of non-Gaussianity will be crucial for model discrimination.

Abstract

We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe cosmology models, including null energy condition violating inflation, inflation with general initial conditions, and string gas cosmology, etc. For the simplest G-inflation, blue tensor spectrum also implies blue scalar spectrum. In general, the inflation models with blue tensor spectra indicate large non-Gaussianities. On the other hand, string gas cosmology predicts blue tensor spectrum with highly Gaussian fluctuations. If further experiments do confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test between inflation and alternatives.

Figures (8)

• Figure 1: The simulated $BB$ power spectrum with different $r_{0.002}$ and $n_\mathrm{T}$. Left panel: $r_{0.002}$ is fixed and variation of $n_\mathrm{T}$ is illustrated. Right panel: some sets of $r_{0.002}$ and $n_\mathrm{T}$ are chosen to get good fit against data. In both panels $r$ is calculated at pivot scale $k=0.002$ Mpc$^{-1}$.
• Figure 2: Contour plot of $r_{0.002}$ vs $n_\mathrm{T}$ to fit against the data. Left panel: fit the data of the BICEP2 and POLARBEAR. Right panel: fit the first five data bins of BICEP2 and treat the others as upper bound. Note that the strong correlation between $n_t$ and $r_{0.002}$ is an artifact from the choice of pivot scale. We have chosen $k=0.002 \mathrm{Mpc}^{-1}$ to match with BICEP2 conventions. However, the BICEP2 experiments measures $k\sim 0.01 \mathrm{Mpc}^{-1}$. Thus given a similar tensor spectrum at $k\sim 0.01 \mathrm{Mpc}^{-1}$, the large tilt modifies the $r_{0.002}$ value significantly.
• Figure 3: The $r-n_\mathrm{T}$ contour (left panel), and the likelihood for $r$ (middle panel) and $n_\mathrm{T}$ (right panel) from BICEP2 (9 bins).
• Figure 4: The $r-n_\mathrm{T}$ contour (left panel), and the likelihood for $r$ (middle panel) and $n_\mathrm{T}$ (right panel) from BICEP2 (9 bins) + Planck (2013) + WMAP polarization.
• Figure 5: The $r-n_\mathrm{T}$ contour (left panel), and the likelihood for $r$ (middle panel) and $n_\mathrm{T}$ (right panel) from BICEP2 (5 bins).