On a principle of cosmological uncertainty

We show that cosmological observations are subject to an intrinsic uncertainty which can be expressed in the form of an uncertainty relation similar to the Heisenberg principle. This is a consequence of the fact that the four dimensional space-time metric information is projected into the one-dimensional observational red-shift space, implying a limit on the amount of information which can be extracted about the underlying geometry. Since multiple space-time configurations can lead to the same red-shift, there is an unavoidable uncertainty about the determination of the space-time geometry. This suggests the existence of a limit about of the amount of information that cosmological observations can reveal about our Universe that no experiment could ever overcame, conceptually similar to what happens in quantum mechanics.We develop a discrete model to account for the effects of inhomogeneities on the redshift of photons. Using this model we compute the probability distribution of the observed redshift respect to the background value, obtaining that its dispersion around the central value is proportional the square root of the comoving distance. This implies that data analysis should include a contribution to the total error budget which depends on the distance of the source. Assuming large scale inhomogeneities with a power spectrum given by primordial curvature perturbations the effect is expected to be small at low red-shift, and to become important only at very high redshift. We then consider what are the general implications for the estimation of background cosmological parameters, giving some example for the case of quantities related to the luminosity distance such as the Hubble parameter and the cosmological constant. The model correctly reproduces the expected stochastic properties of the propagation of photons in inhomogeneous media and due to its computational simplicity it could be particularly suitable for the numerical estimation of the effects of inhomogeneities on cosmological observables using Montecarlo methods