Toward physical cosmology: focus on inhomogeneous geometry and its
  non-perturbative effects
  We outline the key-steps toward the construction of a physical, fully
relativistic cosmology. The influence of inhomogeneities on the effective
evolution history of the Universe is encoded in backreaction terms and
expressed through spatially averaged geometrical invariants. These are absent
and potential candidates for the missing dark sources in the standard model.
Since they can be interpreted as energies of an emerging scalar field (the
morphon), we are in the position to propose a strategy of how phenomenological
scalar field models for Dark Energy, Dark Matter and Inflation, that are
usually added as fundamental sources to a homogeneous-geometry (FLRW)
cosmology, can be potentially traced back to inhomogeneous geometrical
properties of space and its embedding into spacetime. We lay down a line of
arguments that is - thus far only qualitatively - conclusive, and we address
open problems of quantitative nature, related to the interpretation of
observations. We discuss within a covariant framework ... [abridged]
