To me, 'size' is relative.

I believe the universe as in stable energy (matter, you can call it that way) flows through an infinite stream, not in depth or width, but instead infinitely long.

Putting this possibility, many things are possible. The fact that the space is expanding itself every moment as in broadening its 'boundaries' doesn't mean it's infinite, but it scatters using the same torrent through all eternity.

However, assuming space and its respective curvature (time) are infinite, it's a little paradoxical to say it's expanding, isn't it? We can add 1 or 2 to infinite, but we still get infinite.