![]() ![]() ![]() We see trillions of stellar systems, many more than are necessary for life to emerge (we believe), so the anthropic principle cannot be a factor in this argument. The Universe does not need to be this big for sentient beings to exist within it. But this is where the Boltzmann hypothesis breaks down. ![]() This idea of an equilibrium state permitting a low entropy fluctuation is an accepted notion of why the \(\varLambda \)CDM Universe might have begun its expansion with an incredibly low entropy, but detractors question the size of the Universe in such a state.Ĭoupled with an anthropic hypothesis, the fluctuation theorem allows one to quantify the relative probabilities of us living in a Universe of various sizes, showing that small low-entropy universes are exponentially more likely than large ones. This is a highly unlikely event, of course, and the probability of it happening drops sharply as the size of the fluctuation increases but, given an infinite timeline, it is bound to happen sooner or later. It therefore appears very unlikely that the very low entropy in the early \(\varLambda \)CDM Universe could have been due to inflation as we know it today.Īn alternative explanation for the very low initial entropy has been around much longer, and began with Boltzmann himself, who proposed that the low-entropy Universe we live in started as a random fluctuation in an otherwise maximal entropy state. Even extensions to the basic picture, incorporating kinetic-dominated or radiation-dominated pre-inflationary phases, have no impact on this conclusion. As a result, most (if not all) slow-roll inflationary models proposed thus far, fail to accommodate this minimum cutoff. There does not appear to be a viable explanation for this ‘unnatural’ history, other than via the generalized second law of thermodynamics (GSL), in which the entropy of the bulk, \(S_\mathrm\). In the standard model of cosmology, the Universe began its expansion with an anomalously low entropy, which then grew dramatically to much larger values consistent with the physical conditions at decoupling, roughly 380,000 years after the Big Bang. ![]()
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