  We demonstrate that for a cosmic variance limited experiment, CMB E
polarization alone places stronger constraints on cosmological parameters than
CMB temperature. For example, we show that EE can constrain parameters better
than TT by up to a factor 2.8 when a multipole range of l=30-2500 is
considered. We expose the physical effects at play behind this remarkable
result and study how it depends on the multipole range included in the
analysis. In most relevant cases, TE or EE surpass the TT based cosmological
constraints. This result is important as the small scale astrophysical
foregrounds are expected to have a much reduced impact on polarization, thus
opening the possibility of building cleaner and more stringent constraints of
the LCDM model. This is relevant specially for proposed future CMB satellite
missions, such as CORE or PRISM, that are designed to be cosmic variance
limited in polarization till very large multipoles. We perform the same
analysis for a Planck-like experiment, and conclude that even in this case TE
alone should determine the constraint on $\Omega_ch^2$ better than TT by 15%,
while determining $\Omega_bh^2$, $n_s$ and $\theta$ with comparable accuracy.
Finally, we explore a few classical extensions of the LCDM model and show again
that CMB polarization alone provides more stringent constraints than CMB
temperature in case of a cosmic variance limited experiment.
