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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.
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