Cloudscape

If either the age, size, energy or complexity of the universe are infinite, so are the others: if the universe is infinite in age, it must be infinite in size because a finite universe would keep expanding, ergo in energy, because it would otherwise be of infinitely low density due to this expansion, ergo in complexity because this energy would be distributed amongst the universe rather than remaining infinitely accumulated.
If the universe is infinite in size, it must be infinite in age because if it had a starting point it would originate from a singularity rather than popping into existence in infinite dimensions, and infinite in energy and complexity because it would otherwise be of infinitely low density as formerly said.
If the universe is infinite in energy, it must be infinite in age because in order to become of finite density it'd otherwise have to expand with infinite speed (this is the most plausible other possibility, as the absolute speed of light might not be absolute), infinite in size for the same reason, and infinite in complexity because of its infinite size.
Infinite complexity basically equals infinite size because size is relative. If the universe is infinite up or down, it makes little difference. Suppose the universe was contained inside a giant atom (which would have an infinitely complex substructure, so that this would be possible!), we'd still say the universe is tens of billions of light years in diameter instead of one and a half femtometer. Relative to an infinitely small world (at an infinitely complex level), everything is infinitely large. As we've said, infinite size and finite density means infinite energy. However, if the universe is infinite in complexity this does not necessarily mean that it is infinite in age.

Thus, we conclude that either:
1) the age, size, energy and complexity of the universe are all infinite,
2) neither the age, size, energy or complexity of the universe are infinite
3) the size, energy and complexity, but not the age, of the universe are infinite, and the Theory of Relativity is incomplete.

You can scratch the latter two possibilities, however, if you can accept the following argument. Existence cannot have had an actual cause, because that cause would itself have to be part of existence, otherwise it could not have existed because it would then not be part of existence. Why would there be a beginning? Where did it come from? What caused it? Now, I'm talking about the whole of existence, not just our own reality, but any reality at all, including hypothetical realities in which our own universe was created. Unless there already existed "something" which had caused the universe to arise, ie there was already something in *existence* (in other words, in the universe), such cause would necessarily have been acausal, and for something to be science it must obey causality. Causality, then, is its own only exception. Everything has a cause, but the chain of causes and consequences itself hasn't.

Following this line of reasoning we conclude that the universe is infinite in age, size, energy and complexity. This also implies a universe of infinite complexity. In such a universe, there would be an infinite number of phenomena; each of these would in some way have to influence each other, as they would otherwise not form one whole. Whatever phenomenon would not influence the rest of the Universe would not really be part of it, and therefore not really exist as far as we are concerned. In this way, all phenomena would be infinitely connected to one another, that is to say, each phenomenon would be influenced, directly or indirectly, by infinitely many others. One of such phenomena is our own will, or consciousness, which would likewise be causally interlinked to all other phenomena, meaning that it as well could influence and therefore control them. Thus, in principle, if one would find one's way through this web of causal connections, one could, in principle, control any phenomenon in the universe, meaning that one could be omnipotent. This appears to follow logically if the universe is of infinite complexity.