- #1

victorvmotti

- 155

- 5

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?

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?

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