Spatial Curvatures In The Evolution Of The Universe Viewed Through Systemic Functional Linguistics

Penrose (2004: 719-20):

In Fig. 27.13a,b,c, I have tried to depict the time-evolution of the universe, according to Friedmann’s original analysis of the Einstein equation, for the different alternative choices of spatial curvature [K]. In each case, the universe starts from a singularity — the so-called Big Bang — where spacetime curvatures become infinite and then it expands rapidly outwards. 

The ultimate behaviour depends critically on the value of K. If K > 0 (Fig. 27.13a), the expansion eventually reverses, and the universe returns to a singularity, often referred to as the Big Crunch, which is a precise time-reverse of the initial Big Bang in the exact Friedmann model. If K = 0 (Fig. 27.13b), then the expansion just manages to hang on and a collapse phase does not take place. If K < 0 (Fig. 27.13c), then there is no prospect of collapse, as the expansion ultimately approaches a constant rate. 

(There is an analogy, here, with the stone thrown upwards from the ground. If the stone’s initial speed is less than escape velocity, then it eventually falls back to the ground, like Friedmann’s universe for K > 0; if equal to escape velocity, then it just fails to fall back, like K = 0; if greater than escape velocity, then it continues and approaches a limiting rate which does not slow down, like K < 0.)

 

Blogger Comments:

For reasons previously given, from the perspective of Systemic Functional Linguistic Theory, 'spatial curvature' is not the curvature of space, but the curvature of geodesic trajectories (processes) in space. (This is borne out by the explanatory analogy, which is concerned with the trajectories of stones in space.)