Is the universe truly infinite

Answer 1

The theory is that the universe 13.5-14.0 billions year ago was infinitely small but expanded very rapidly after the big bang.

e.g. an expanding universe could
1) expand until it reaches a size where it starts to contract
2) expand forever but the speed of the expansion slows down in time until the expansion is almost not measurable
3) expand forever at a fixed rate
4) expand forever at an increasing rate (gets bigger, faster)

The current theory is that the universe continues to expand and does so at an increasingly fast rate (e.g. item 4 above)

Therefore, the best answer to your question is yes: the universe is truly infinitive because it will continue to expand and this expansions will be faster and faster the more time that goes by.