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Using the Big Bang model it is possible to calculate the concentration of helium-4, helium-3, deuterium and lithium-7 in the universe. All the abundances depend on a single parameter, the ratio of photons to baryons. The abundances predicted are about 25 percent for 4He, a 2H/H ratio of about 10-3, a 3He/H of about 10-4 and a 7Li/H abundance of about 10-9.
Measurements of primordial abundances for all four isotopes are consistent with a unique value of that parameter (see Big Bang nucleosynthesis), and the fact that the measured abundances are in the same range as the predicted ones is considered strong evidence for the Big Bang. There is no obvious reason outside of the Big Bang that, for example, the universe should have more helium than deuterium or more deuterium than 3He. Thus far, no other theory has attempted to make the nucleosynthetic predictions that the Big Bang does.
Theories which assert that the universe has an infinite life such as the steady state theory fail to account for the abundance of deuterium in the cosmos, because deuterium easily undergoes nuclear fusion in stars and there are no known astrophysical processes other than the Big Bang itself that can produce it in large quantities. Hence the fact that deuterium is not an extremely rare component of the universe suggests that the universe has a finite age.
Theories which assert that the universe has a finite life but that the Big Bang did not happen have problems with the abundance of helium-4. The observed amount of 4He is far larger than what could be created via stars or any other known process. By contrast, the abundance of 4He are very insensitive to assumptions about baryon density changing only a few percent, as the baryon density changes by several orders of magnitude. The observed value of 4He appears to be within the range calculated.
This having been said, there are three theoretical issues with Big Bang nucleosynthesis which have some potential of undermining the theory. The first is that the baryon concentration necessary to get an exact match with the current abundances is inconsistent with a universe with mostly baryons. The second is that the Big Bang predicts that no elements heavier than lithium would have been created in the Big Bang, yet elements heavier than lithium are observed in quasars, which presumably are some of the oldest galaxies in the universe. The third problem is since big bang nucleosynthesis produces no elements heavier than lithium, then we ought to see some long lived remnant stars which have no heavy elements in them. We don't.
The standard explanation for the first are that most of the universe isn't composed of baryons. This explanation fits nicely with other evidence of dark matter such as galaxy rotation curves. The standard explanation for the second and third is that the universe underwent a period of massive star formation creating large high mass stars and that without heavy elements, forming low mass red dwarf stars is impossible. This explanation has the feature that it predicts a class of stars that, as of 2004, have not been observed. Hence, in a few years we should have either seen them, which would support the big bang scenario, or we won't, in which case there is a possibility that we will have to fundamentally alter our views of the universe.
Critics of big bang point to the claim that there is an abundance of primordial elements in the universe as circular logic. It is assumed by big bang proponents that only big bang could produce deuterium, so any deuterium in a big bang universe must be a result of the big bang, and since deuterium is believed to be rapidly consumed by stars, the age of a big bang universe therefore is finite. Critics note that if big bang did not occur, then there is another way for deuterium to be created. Critics also remark that no evidence has yet surfaced that suggests the universe is being depleted of deuterium. Assumed abundance of deuterium neither verifies nor falsifies big bang hypotheses.
One observation that has become increasingly apparent since the early 1970s is that while the universe appears to be isotropic in space (i.e. the universe in one direction looks very much like the universe in another direction) it is not uniform with respect to distance (due to the finite speed of light, greater distances represent earlier times in the past). As one looks to increasingly large distances, the universe looks very different. For example, there are no nearby quasars, but there are many quasars once you pass a given redshift, and then the quasars disappear at a still further distance. Similarly, the types and distribution of galaxies appears to change markedly over time and once one passes a given distance, the number of galaxies fall off considerably.
Critics of big bang have suggested that presuppositions about the extreme distance of all quasars may be overstated. Recent reviews of the proper motion of many quasars has shown that extreme distances are not possible. In one review a quasar was found to have a calculated proper motion on the order of one thousand times the speed of light, with proper motion perpindicular to its radio jets or lobes[5]. Only an object within our own galaxy could have such extreme observed proper motion, which challenges the conclusion that all quasars are extremely distant (at least intergalactic) and the assumption that redshift equals distance equals age equals velocity.
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