Self-Reproduction of the Universe

Self-Reproduction of the Universe

Self-Reproduction of the Universe
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Here we come to the central part of our story, to the theory of eternally existing self-reproducing inflationary universe. As we already mentioned, one can visualize quantum fluctuations of the scalar field in inflationary universe as waves, which first move in all possible directions, and then freeze on the top of each other. Each freezing wave slightly increased the value of the scalar field in some parts of the universe, and slightly decreased this field in other parts of the universe.

Now let us consider those rare parts of the universe where these freezing waves always increased the value of the scalar field , persistently pushing the scalar field uphill, to the greater values of its potential energy V. This is a very strange and obviously improbable regime. Indeed, the probability that the field will make one jump up (instead of jump down), is equal to ½. The probability that the next time it also jumps up is also ½. Therefore the probability that the field without any special reason will make N consecutive jumps in the same direction is extremely small; it will be proportional to 1/ 2N.

Normally one neglects such fluctuations. However, in our case they can be extremely important. Indeed, those rare domains of the universe where the field jumps high enough begin exponentially expanding with ever increasing speed. Remember that inflationary universe expands as eHt, where the Hubble constant is proportional to the square root of the energy density of the field . In our simple model with V 2 the Hubble constant H will be simply proportional to . Thus, the higher the field  jumps, the faster the universe expands. Very soon those rare domains, where the field  persistently climbs up the wall, will acquire a much greater volume than those domains which keep sliding to the minimum of V in accordance with the laws of classical physics.

From this theory it follows that if the universe contains at least one inflationary domain of a sufficiently large size, it begins unceasingly producing new and new inflationary domains. Inflation in each particular point may end up very quickly, but there will be many other places which will continue expanding exponentially. The total volume of all inflationary domains will grow without end.

Eternal inflation implies that the universe as a whole is immortal. Each particular part of the universe may appear from a singularity somewhere in the past, and it may end up in a singularity somewhere in the future. However, there is no end for the evolution of the whole universe. The situation with the beginning is less certain. It is most probable that each part of inflationary universe has originated from some singularity in the past. However, at present we do not have any proof that all parts of the universe were created simultaneously in a general cosmological singularity, before which there was no space and time at all. Moreover, the total number of inflationary bubbles on our “cosmic tree” exponentially grows in time. Therefore most of the bubbles (including our own part of the universe) grow indefinitely far away from the root of this tree. This removes the possible beginning of the whole universe to indefinite past.

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