A (Dτ,Dx)-manifold with N-correlators of Ns-objects

Context. In this paper, we describe a mathematical formalism for a [Formula: see text]-dimensional manifold with [Formula: see text]-correlators of [Formula: see text] types of targeted source objects, with cross correlations and contaminants. Methodology. In particular, we build this formalism using simple notions of mathematical physics, field theory, topology, algebra, statistics [Formula: see text]-correlators and Fourier transform. Results. We present and discuss the applicability of this formalism in the context of cosmological scales, i.e. from astronomical scales to quantum scales, for which we give some intuitive examples, explicitly, for standard spacetime dimensions and extra dimensions. Conclusion. We conclude that this study can be used as a guide to analyze and build models for future cosmological and collider experiments. Furthermore, this study opens the road of extra dimension studies.