Relic gravitational waves in light of the 7-year Wilkinson Microwave Anisotropy Probe data and improved prospects for the Planck mission

The new release of data from Wilkinson Microwave Anisotropy Probe improves the observational status of relic gravitational waves. The 7-year results enhance the indications of relic gravitational waves in the existing data and change to the better the prospects of confident detection of relic gravitational waves by the currently operating Planck satellite. We apply to WMAP7 data the same methods of analysis that we used earlier [W. Zhao, D. Baskaran, and L. P. Grishchuk, Phys. Rev. D 80, 083005 (2009)] with WMAP5 data. We also revised by the same methods our previous analysis of WMAP3 data. It follows from the examination of consecutive WMAP data releases that the maximum likelihood value of the quadrupole ratio $R$, which characterizes the amount of relic gravitational waves, increases up to $R=0.264$, and the interval separating this value from the point $R=0$ (the hypothesis of no gravitational waves) increases up to a $2\sigma$ level. The primordial spectra of density perturbations and gravitational waves remain blue in the relevant interval of wavelengths, but the spectral indices increase up to $n_s=1.111$ and $n_t=0.111$. Assuming that the maximum likelihood estimates of the perturbation parameters that we found from WMAP7 data are the true values of the parameters, we find that the signal-to-noise ratio $S/N$ for the detection of relic gravitational waves by the Planck experiment increases up to $S/N=4.04$, even under pessimistic assumptions with regard to residual foreground contamination and instrumental noises. We comment on theoretical frameworks that, in the case of success, will be accepted or decisively rejected by the Planck observations.

Figure 1

The relation between $R$ and $r$ for different values of the spectral index $n_s$. From top to bottom the $n_s$ changes from $n_s=0.8$ to $n_s=1.2$.

Figure 2

The projection of 10 000 samples of the 3-dimensional likelihood function, based on the WMAP7 data, onto the $R-n_s$ (left panel) and $R-A_s$ (right panel) planes. The black $+$ indicates the maximum likelihood parameters listed in (12).

Figure 3

The ML point (red $\times$) and the 68.3% and 95.4% confidence intervals (red solid lines) for the 2-dimensional distributions $R-n_s$ (left panel) and $R-A_s$ (right panel). The left panel shows also the WMAP7 confidence contours (black dashed line) derived under the assumption that the spectral index $n_s$ is one and the same constant throughout all measured multipoles [1, 2]. The WMAP7 papers do not show the confidence contours in the $R-A_s$ plane.

Figure 4

The 1-dimensional likelihoods for $R$. The results of the analysis of WMAP7, WMAP5, and WMAP3 data are shown, respectively, by the red (solid), black (dashed), and blue (dotted) curves. The shaded regions indicate the 68.3% and 95.4% confidence intervals for WMAP7 likelihood.

Figure 5

The 1-dimensional likelihoods for $n_s$ (left) and $A_s$ (right). In both panels the red (solid), black (dashed), and blue (dotted) curves show the results for WMAP7, WMAP5, and WMAP3 data, respectively.

Figure 6

The spectral index $n_s$ as a function of the wave number $k$. The ML results of this work are shown by red lines. Other lines are our plots of WMAP7 findings [1], Table 7.

Figure 7

The total signal-to-noise ratio $S/N$ as a function of $R$. The left panel shows $S/N$ with $\Delta R=1/\sqrt{F_{RR}}$, while the right panel shows $S/N$ with $\Delta R=\sqrt{(F^{-1}{)}_{RR}}$.

Figure 8

The decomposition of the total $S/N$ into contributions from different information channels. Four panels describe different assumptions about foreground cleaning and noises. The $S/N$ line from the upper left panel for the optimistic case ${\sigma }^{\mathrm{fg}}=0.01$ is copied as a broken line in other panels.

Figure 9

The individual terms $(S/N{)}_{\ell }^2$ as functions of $\ell$ for various combinations of information channels and two opposite assumptions about residual foreground contamination and noises. The calculations are done for the ML model (12) with $R=0.264$.

Figure 10

The improved signal-to-noise ratio $S/N$ for the scenario where the Dust B model is correct and the instrumental noises are smaller because of the 7 frequency channels used, instead of 3, in data analysis. The left panel shows $S/N$ with $\Delta R=1/\sqrt{F_{RR}}$, while the right panel shows $S/N$ with $\Delta R=\sqrt{(F^{-1}{)}_{RR}}$.

Figure 11

The improved $S/N$ for 28 months of observations. Other assumptions are the same as in Fig. 7.

Figure 12

Decomposition of the total $S/N$ figuring in the left panel of Fig. 11 into contributions from different information channels. In the assumed conditions of deep cleaning ${\sigma }^{\mathrm{fg}}=0.01$, the $BB$ alone is more informative than the combination $TT+TE+EE$.