I think typical discussions of the Fermi Paradox, such as this one, focus on the observable universe, which is finite. Assuming the universe (observable or not) is infinite, would the probability of intelligent life be 1?
If you assume the cosmological principle (i.e. that the universe in homogeneous and isotropic at the largest scales), as all modern cosmologists do, then yes. Indeed, the implication would be even more extreme, namely that the number of other civilisations in the universe is infinite as well. Whether the universe is infinite or not is an open question and depends on its curvature, which is determined by the energy density of the universe. According to our best current observations, the energy density of the universe is exactly equal to the critical density, and the universe therefore infinite and flat with zero curvature. However, a slightly higher energy density, resulting in positive curvature and a closed, i.e. finite universe, is well within our range of uncertainty. Except maybe for speculative multiverse-wide cooperation, this is of no practical relevance though, as we cannot influence anything outside of the observable universe. In fact, we can only influence events within our cosmological event horizon, which (assuming a cosmological constant) is only 16 billion light years, compared to the 46 billion light years radius of the observable universe (anything we can ever see).
Thanks for the follow-up, Jan! I agree with all your points except one. I think the best guess distribution about the energy density should be roughly continuous, which implies an infinitesimal probability of any specific value, including that implying a flat universe (which should be very close to the mode of the distribution).
That’s fair. Personally, I think there is a substantive chance that an underlying theory requires the relative density to be one. This would also resolve the question of why the value is so close to one in the first place if it could’ve been very different (bounded by anthropic arguments I assume).
I think typical discussions of the Fermi Paradox, such as this one, focus on the observable universe, which is finite. Assuming the universe (observable or not) is infinite, would the probability of intelligent life be 1?
If you assume the cosmological principle (i.e. that the universe in homogeneous and isotropic at the largest scales), as all modern cosmologists do, then yes. Indeed, the implication would be even more extreme, namely that the number of other civilisations in the universe is infinite as well. Whether the universe is infinite or not is an open question and depends on its curvature, which is determined by the energy density of the universe. According to our best current observations, the energy density of the universe is exactly equal to the critical density, and the universe therefore infinite and flat with zero curvature. However, a slightly higher energy density, resulting in positive curvature and a closed, i.e. finite universe, is well within our range of uncertainty. Except maybe for speculative multiverse-wide cooperation, this is of no practical relevance though, as we cannot influence anything outside of the observable universe. In fact, we can only influence events within our cosmological event horizon, which (assuming a cosmological constant) is only 16 billion light years, compared to the 46 billion light years radius of the observable universe (anything we can ever see).
Thanks for the follow-up, Jan! I agree with all your points except one. I think the best guess distribution about the energy density should be roughly continuous, which implies an infinitesimal probability of any specific value, including that implying a flat universe (which should be very close to the mode of the distribution).
That’s fair. Personally, I think there is a substantive chance that an underlying theory requires the relative density to be one. This would also resolve the question of why the value is so close to one in the first place if it could’ve been very different (bounded by anthropic arguments I assume).