First, this paper broaches the definition of science and the epistemic yield of tenets and approaches: phenomenological (descriptive only), well founded (solid first principles, conducive to deep understanding), provisional (falsifiable if universal, verifiable if existential), and imaginary (fictitious entities or processes, conducive to empirically unsupported beliefs). The Big Bang paradigm and the ΛCDM `concordance model' involve such beliefs: the emanation of the universe out of a non-physical stage, cosmic inflation (hardly testable), Λ (fictitious energy), and `exotic' dark matter. They fail in the confidence check that empirical science requires. They also face a problem in delimiting what expands from what does not. In the more well-founded cosmology that emerges, energy is conserved, the universe is persistent (not transient), and the `perfect cosmological principle' holds. Waves and other field perturbations that propagate at c (the escape velocity of the universe) expand exponentially with distance. This results from gravitation. The galaxy web does not expand. Potential Φ varies as -H/(cz) instead of -1/r. Inertial forces reflect gradients present in comoving frames of accelerated bodies (interaction with the rest of the universe - not with space). They are increased where the universe appears blue-shifted and decreased more than proportionately at very low accelerations. A cut-off acceleration a0 = 0.168 cH is deduced. This explains the successful description of galaxy rotation curves by "Modified Newtonian Dynamics". A fully elaborated physical theory is still pending. The recycling of energy via a cosmic ocean filled with photons (the cosmic microwave background), neutrinos and gravitons, and the wider implications for science are briefly discussed.