Graduate Can an Oscillating Eternal Universe be Described without Singularity?

[victorvmotti]

Consider the FLRW metric.

We pick a specific definition for the scale factor as suggested bellow.

Suppose we have a hypothetical metric having the scale factor defined by

$a(t)=\sin(t) (1+ \text {sgn}(\sin(t)) +\epsilon$

Does this make sense, mathematically (and physically)?

Like having a continuous smooth (differentiable) manifold. Or relating to the geometric properties of homogeneity and isotropy, an expanding and contracting universe?

Can this describe an oscillating eternal infinite universe without singularity?

If it does not, how to write a metric that can do so?

 

[PeterDonis]

Suppose we have a hypothetical metric having the scale factor

Just giving a scale factor doesn't tell us what the metric is. You need to write down the entire line element.

 

[victorvmotti]

Just giving a scale factor doesn't tell us what the metric is. You need to write down the entire line element.

Actually, I meant that the Standard Model of cosmology and its metric to be used, only that we pick a specific definition for the scale factor as suggested.

 

[PeterDonis]

Actually, I meant that the Standard Model of cosmology and its metric to be used, only that we pick a specific definition for the scale factor as suggested.

The Standard Model of cosmology already includes a definition for the scale factor, which is not yours.

If you mean the general FRW metric, you should be able to write it down. And you should also be able to plug your ansatz for the scale factor into the equations that that metric gives (the Friedmann Equations) to see whether they make sense. Anyone with the background knowledge for an "A" level thread on this topic should be able to do that.