Alternative to the Epoch Time Solution Patching Structure of the Cosmological Standard Model in the Friedman Dust Universe with Einstein's Lambda
James G. Gilson
The need for the cosmological constant, Lambda, in Einstein's field equations to be an absolute mathematical constant over all the time that they are used to describe some astrophysics process is demonstrated. Only if that condition holds will the conservation laws of mass and momentum hold as in classical physics. The Friedman equations that can be deduced rigorously from general relativity are consequently equally restricted to a constant valued Lambda and for the same reasons. However, the standard cosmological model, is not constructed from one solution of the Friedman equations but rather from at least three different but rigorous solutions patched together at times where they are physically thought to join. This is because the known solutions are thought to represent different conditions of mass movement, highly erratic or thermal at time near the big bang or more particle like and organized into systems at time near now, just to mention two types of activity when there obviously could be a continuous range of activities of mass types. Clearly this idea of how things have evolved after the big bang is very plausible, if the big bang idea is accepted as fact. The apparent need to patch solutions together over time creates great mathematical difficulties for cosmology because the three functions selected have to join smoothly which is the same as saying that they have to be differentiable not once but twice if accelerations are taken into account as they must be if the Friedman equations are to hold through the join. It is not clear whether or not this patching process can be rigorously achieved. However it is clear that the big bang concept does violate Einstein's field equations at $t=0$ because this concept implies that mass and momentum comes from nowhere. It is shown that all of these problems can be removed by introducing a continuously variable over time structure into the definition of temperature for the dust universe model. This only affects the value of the temperature that is associated with a given time and make no difference to the validity of the dust universe model with regard to it being a rigorous solution to the Einstein Field equations for all time from minus infinity to plus infinity.
