The answer to this question will depend on what one means by the significant terms used in the question.
First the universe. We live in the only universe we know. It is entirely possible – and some theories in physics make this a not implausible possibility – that there are several other universes, There may or may not be any life in many of them. So there is nothing unique in the phenomenon of life to warrant a universe that is specially intended to make life a possibility in a remote niche of its stupendously vast stretch.
Next is fine-tuned. The implication is that conditions and parameters that could be arbitrarily arranged have been given optimal values for the attainment of a specific goal. Indeed, if the initial assignment of values had been different ever so slightly, the intended goal or current situation would and could not have been achieved. Note that the verb is used in the passive voice, but the customary by X has been omitted. That is to say, one leaves open the question: fine-tuned by whom? Perhaps the implication is that it was by an intelligent designer, but this is not a phrase one dares to use in scientific discussion these days. This is also a reason why most hard-core atheist physicists and biologists shudder to contemplate this sort of anthropic or biopic principle.
The third important word is life. That life is a remarkable property of agglomerations of inert matter on our planet is undoubtedly a perplexing situation. We know that life emerged on our planet because of the external conditions of temperature and atmospheric pressure for a sufficiently long time period of time, and the abundant availability of certain elements and compounds. Unique as life seems to be on our solar system, one can also imagine other entities in the universe that are unique to some planets and satellites: volcanoes, atmosphere, water/ice, common salt, and clay. Or again, orbiting planets and comets may be unique to some stars. On the basis of these could one argue, for example, that the universe was fine-tuned for rings around Saturn or planets with satellites?
In sum, then, the question cannot be answered with a simple yes or a no, although in probabilistic and cosmic history terms it seems highly unlikely that parameters were fine-tuned for such a late and fleeting event that was to occur several billions of years after the big bang genesis.
But the simplistic answer to the question could be, of course yes. Otherwise how could life have arisen at all?
V. V. Raman
May 9, 2009