Ask what "infinite" -- having no limit -- could physically mean.  Taken
literally, it means "having features or attributes embodying amount, but
at the same time *beyond* any particular amount".  This means, having no
identity.

If infinity does not name a specific amount, then it isn't a number that
can be applied to reality.  More precisely, the strategy (discovered by
Cantor) that gives it numerical meaning is indulged at the expense of
entirely abstracting away the connection to existence that gives numbers
their objective status (i.e., their connection to reality).  It cannot
name any specific amount in reality.

"Infinity" is still a valid mathematical concept, however, so that in
a certain non-numerical sense Objectivism *does* allow an infinite
universe.  Rand said in _Introduction to Objectivist Epistemology_, "An
arithmetical sequence extends into infinity, without implying that
infinity actually exists; such extension means only that whatever
number of units does exist, it is to be included in the same sequence."
(This makes "infinity" what her epistemological view calls a concept of
method.)

The application of her statement to the physical universe is that
"whatever number of existents (or measures of their attributes) exists,
it is to be included in the same sequence" of progressively larger
numbers.