Quantifying the BICEP2-Planck Tension over Gravitational Waves

The recent BICEP2 measurement of $B$-mode polarization in the cosmic microwave background ($r={0.2}_{-0.05}^{+0.07}$), a possible indication of primordial gravity waves, appears to be in tension with the upper limit from WMAP ($r<0.13$ at 95% C.L.) and Planck ($r<0.11$ at 95% C.L.). We carefully quantify the level of tension and show that it is very significant (around 0.1% unlikely) when the observed deficit of large-scale temperature power is taken into account. We show that measurements of $TE$ and $EE$ power spectra in the near future will discriminate between the hypotheses that this tension is either a statistical fluke or a sign of new physics. We also discuss extensions of the standard cosmological model that relieve the tension and some novel ways to constrain them.

Figure 1

Current measurements of the CMB temperature power spectrum from Planck (open circles), WMAP (closed circles), ACT (squares), and SPT (triangles). Error bars include noise variance only; the shaded region represents cosmic variance. There is a small deficit of power on large angular scales relative to an $r=0$ model (solid curve) which becomes more statistically significant if $r=0.2$ as BICEP2 suggests (dashed curve).

Figure 2

1D probability distribution functions for the tensor-to-scalar ratio $r$ using $\text{Planck}+\text{WP}$ data (blue or leftmost curve), $\text{WMAP}+\text{SPT}+\text{BAO}+H_0$ data (green or middle curve), and BICEP2 data (red or rightmost curve). We use the COSOMC [5] code with the six cosmological parameters $\{{\mathrm{\Omega }}_b{h}^2,{\mathrm{\Omega }}_m{h}^2,{\mathrm{\Omega }}_{\mathrm{\Lambda }},A_{\zeta },\tau ,n_s\}$ marginalized. As discussed in the text, we allow $r$ to be negative in order to parametrize a possible power deficit on large angular scales.

Figure 3

$E$-mode power spectrum $C_{\ell }^{EE}$ (top) and dimensionless $TE$ correlation $C_{\ell }^{TE}/(C_{\ell }^{TT}{C}_{\ell }^{EE}{)}^{1/2}$ (bottom) compared for $r=0$ and $r=0.2$. An $r=0.2$ signal boosts $C_{\ell }^{EE}$ by $\approx 30\%$ in the range $15\lesssim \ell \lesssim 30$, making $E$ modes more sensitive to the tensor-to-scalar ratio $r$ than temperature.

Figure 4

Statistical errors on $r$ obtained from different combinations of temperature and $E$-mode power spectra, as a function of noise level. The six parameters $\{{\mathrm{\Omega }}_b{h}^2,{\mathrm{\Omega }}_c{h}^2,{\mathrm{\Omega }}_{\mathrm{\Lambda }},A_s,n_s,\tau \}$ have been marginalized.

Figure 5

Forecasted $1\sigma$ errors in the ($n_s$, ${\alpha }_s$) plane, obtained by combining the “standard Big Bang Observer” mission proposal [18] with a CMB detection of $r$ of 0.1 (red), 0.2 (green), or 0.3 (blue). The vertical lines show the current Planck value for $n_s$ (dotted), the corresponding 1$\sigma$ errors (dashed), and the forecasted 1$\sigma$ errors (solid) from a future cosmic-variance limited map of $T$ and $E$, with $f_{\max }=0.7$ and $l_{\max }=3000$.

Figure 6

Upper bounds in the $\{\widehat{w}(f),{\widehat{n}}_t(f)\}$ plane from combining CMB detection of $r\gtrsim 0.1$ with current pulsar timing constraints [25] (blue, top curve at extreme right), current LIGO constraints [26] (green, third curve from top at extreme right), big bang nucleosynthesis (red, last curve at extreme right), and the requirement that the primordial tensor power is less than unity on all scales to avoid overproduction of primordial black holes (magenta, second curve from top at extreme right). Here, ${\widehat{n}}_t(f)$ and $\widehat{w}(f)$ are appropriately averaged versions of $n_t(k)$ and $w(t)$: see Ref. [24] for details. (The standard radiation-dominated scenario is $\widehat{w}=1/3$.)