## Why ratios of the scale factor?

I introduced the notion of a scale factor as a concept separate from a fixed and comoving cosmological lattice in a previous post. Developing that idea lead to the Hubble non-constant, . Later, in developing a couple of simple forms of the Friedmann equations, we encountered something of the form . This raises a question. Why all these ratios of a(t)? The answer is simple. The scale factor depends on the scale of the comoving cosmological grid that’s being used. Since proper distances depend upon the product of the scale factor and the size of the grid, , changing the size of the...

Read More## The Hubble non-constant

In a previous post, I introduced the notion of a 3-dimensional cosmological lattice. The idea is that, very roughly, the grid spacing is about the mean spacing between galaxies now. We break the order on the grid into two components, an ordinal part against which the position of the galaxies is fixed, or nearly fixed; and a scale part, which is a function of time, . One cell of this grid looks like this: The distance between any two galaxies, say and , will be assuming a Euclidean space. Since it transpires that experimental evidence indicates that the assumption that our visible universe...

Read More## A lattice for cosmology

I am going to introduce the idea of a lattice on cosmological space. To do this, I am going to introduce first the notion of an integer lattice on the space. A very simple lattice would look like this: This lattice could be continued forever in every direction in 3-space. Ultimately, the space could be coarsely grained in terms of such a lattice. Other, more complex lattices are possible; for example, Or, However, these are more complex than necessary. The essential notion is that the points on the grid are associated with a well-ordered set of numbers in each dimension. Consider these three...

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