Is cosmology compatible with blue gravity waves?

A primordial gravitational wave background with positive (blue) spectral index is expected in several nonstandard inflationary cosmologies where the stress-energy tensor violates the null energy condition. Here we show that a sizable amount of blue gravitational waves is compatible with current cosmological and astrophysical data. So far most of the works on parameter estimation from cosmic microwave background data have assumed a negative or negligible spectral index. The present limits on cosmological parameters, especially on the scalar spectral index, widen up considerably when one allows also for blue tilts of the tensor spectrum. Since the amplitude of the cosmic microwave background (CMB) B-mode polarization is larger in these models, future data from Planck are likely to provide crucial measurements.

Figure 1

68% and 95% likelihood contour plots from WMAP data where no external prior on the spectral index of the gravity wave background is assumed.

Figure 2

95% likelihood contour plots on the $n_T$-$r$ plane from WMAP data when external prior on the spectral index of the gravity wave background are assumed.

Figure 3

95% likelihood contour plots on the $n_S$-$r$ plane from WMAP data when external prior on the spectral index of the gravity wave background are assumed.

Figure 4

95% likelihood contour plots on the ${\omega }_b$-${\omega }_c$ plane from WMAP data when external priors on $n_T$ are assumed. The solid line corresponds to the $\mathrm{WMAP}+\mathrm{PULSAR}$, the dashed line to $\mathrm{WMAP}+\mathrm{LIGO}$, the long-short dashed line to $\mathrm{WMAP}+\mathrm{BBN}$, and the dotted line to the $\mathrm{WMAP}+n_T<0$ case.

Figure 5

Top Panel: CMB temperature anisotropy angular power spectra for the best-fit models to current WMAP data for different choices of external priors on $n_T$. Bottom Panel: Contribution to the $B$B-mode polarization.