Evolving laws and cosmological energy

We couple the issue of evolution in the laws of physics with that of violations of energy conservation. Avoiding a time dependence in terms of coordinate time, we define evolution as a function of time variables canonically dual to ``constants'' (such as, the Planck mass, or the gravitational coupling), mimicking a procedure associated with one formulation of unimodular gravity. We then introduce variability via a dependence of other fundamental ``constants'' on these clocks. Although this is not needed, sharper results are obtained if this procedure violates local Lorentz invariance, which we define in the spirit of Horava-Lifshitz theories (modifying a 3+1 split action, so that a Lorentz invariant 4D reassembly is no longer possible). We find that variability in the ``laws of physics'' generically leads to violations of energy conservation if either a matter parameter varies as a function of a gravitational clock, or a gravity parameter depends on a matter clock, with the other combinations sterile. In general the matter components associated with the varying parameter or the clock absorb or give off the violated energy. We illustrate this with a variety of clocks (ticking unimodular time, Ricci time, etc. ) and parameters (mainly the gravitational and matter speed of light, but also). We can accommodate in this construction (and improve on) several early varying speed of light models, allowing for variability effects related to the spatial curvature and to cause creation of radiation and a hot big bang.