Detecting relic gravitational waves in the CMB: Optimal parameters and
  their constraints
  The prospect of detecting relic gravitational waves (RGWs), through their
imprint in the cosmic microwave background radiation, provides an excellent
opportunity to study the very early Universe. In simplest viable theoretical
models the RGW background is characterized by two parameters, the
tensor-to-scalar ratio $r$ and the tensor spectral index $n_t$. In this paper,
we analyze the potential joint constraints on these two parameters, $r$ and
$n_t$, using the data from the upcoming cosmic microwave background radiation
experiments. Introducing the notion of the best pivot multipole $\ell_t^*$, we
find that at this pivot multipole the parameters $r$ and $n_t$ are
uncorrelated, and have the smallest variances. We derive the analytical
formulae for the best pivot multipole number $\ell_t^*$, and the variances of
the parameters $r$ and $n_t$. We verify these analytical calculations using
numerical simulation methods, and find agreement to within 20%. The analytical
results provides a simple way to estimate the detection ability for the relic
gravitational waves by the future observations of the cosmic microwave
background radiation.
