  We introduce a new family of primordial cosmological perturbations that are
not described by traditional power spectra. At the linear level, these
perturbations live in the kernel of the spatial Laplacian operator, and thus we
call them cosmological zero modes. We compute the cosmic microwave background
(CMB) temperature and polarization anisotropy induced by these modes, and
forecast their detection sensitivity using a cosmic-variance limited
experiment. In particular, we consider two configurations for the zero modes:
The first configuration consists of stochastic metric perturbations described
by white noise on a "holographic screen" located at our cosmological horizon.
The amplitude of the power spectrum of this white noise can be constrained to
be $\lesssim 9 \times 10^{-14}$. The second configuration is a primordial
monopole beyond our cosmological horizon. We show that such a monopole, with
"charge" $Q$, can be detected in the CMB sky up to a distance of $11.6 ~
Q^{1/4}\times$ horizon radius (or $160~ Q^{1/4}$ Gpc). More generally,
observational probes of cosmological zero modes can shed light on
non-perturbative phenomena in the primordial universe, beyond our observable
horizon.
