  The Cosmic Microwave Background (CMB) anisotropy power on the largest angular
scales observed both by WMAP and COBE DMR appears to be lower than the one
predicted by the standard model of cosmology with almost scale free primordial
perturbations arising from a period of inflation
\cite{cobe,Bennett:2003bz,Spergel,Peiris}. One can either interpret this as a
manifestation of cosmic variance or as a physical effect that requires an
explanation. We discuss various mechanisms that could be responsible for the
suppression of such low $\ell$ multipoles. Features in the late time evolution
of metric fluctuations may do this via the integral Sachs-Wolfe effect. Another
possibility is a suppression of power at large scales in the primordial
spectrum induced by a fast rolling stage in the evolution of the inflaton field
at the beginning of the last 65 e-folds of inflation. We illustrate this effect
in a simple model of inflation and fit the resulting CMB spectrum to the
observed temperature-temperature (TT) power spectrum. We find that the WMAP
observations suggest a cutoff at $k_c=4.9^{+1.3}_{-1.6}\times
10^{-4}$Mpc$^{-1}$ at 68% confidence, while only an upper limit of $k_c <
7.4\times 10^{-4}$Mpc$^{-1}$ at 95%. Thus, although it improves the fit of the
data, the presence of a cutoff in power spectrum is only required at a level
close to $2\sigma$. This is obtained with a prior which corresponds to equal
distribution wrt $k_c$. We discuss how other choices (such as an equal
distribution wrt $\ln k_c$ which is natural in the context of inflation) can
affect the statistical interpretation.
