Testing chirality of primordial gravitational waves with Planck and   future CMB data: no hope from angular power spectra
  We use the 2015 Planck likelihood in combination with the Bicep2/Keck likelihood (BKP and BK14) to constrain the chirality, $\chi$, of primordial gravitational waves in a scale-invariant scenario. In this framework, the parameter $\chi$ enters theory always coupled to the tensor-to-scalar ratio, $r$, e.g. in combination of the form $\chi \cdot r$. Thus, the capability to detect $\chi$ critically depends on the value of $r$. We find that with present data set $\chi$ is \textit{de facto}unconstrained. We also provide forecasts for $\chi$ from future CMB experiments, including COrE+, exploring several fiducial values of $r$. We find that the current limit on $r$ is tight enough to disfavor a neat detection of $\chi$. For example, in the unlikely case in which $r\sim0.1(0.05)$, the maximal chirality case, i.e. $\chi = \pm1$, could be detected with a significance of $\sim2.5(1.5)\sigma$ at best. We conclude that the two-point statistics at the basis of CMB likelihood functions is currently unable to constrain chirality and may only provide weak limits on $\chi$ in the most optimistic scenarios. Hence, it is crucial to investigate the use of other observables, e.g. provided by higher order statistics, to constrain these kind of parity violating theories with the CMB. 
Martina Gerbino, Alessandro Gruppuso, Paolo Natoli, Maresuke   Shiraishi, Alessandro Melchiorri
astro-ph.CO