### Empirical evidence for the p-adic evolution of cosmological constant?

The evolution of the cosmological constant Λ is different at each space-time sheet, and the value of Λ is determined by the p-adic length scale size of the space-time sheet according to the formula Λ (k)= Λ (2)× (L(2)/L(k))

^{2}, where L(k)=2

^{k}L

_{0}, k integer, is the p-adic length scale associated with prime p≈ 2

^{k}. L

_{0}is apart from a numerical constant CP

_{2}geodesic length. Prime values of k are especially interesting.

The formula is derived in the chapter TGD and Cosmology of TGD from the requirement that gravitational energy identfied as the difference of inertial energies and matter and antimatter (or vice versa) is non-negative. This means discrete evolution of cosmological constant with jumps in which cosmological constant is reduced by a power of 2.

In standard physics context piecewise constant cosmological constant would be naturally replaced by a cosmological constant behaving like 1/a^{2} as a function of cosmic time. p-Adic prediction is consistent with the study of Wang and Tegmark according to which cosmological constant has not changed during the last 8 billion years: the conclusion comes from the reshifts of supernovae of type I_{a}. If p-adic length scales L(k)= p ≈ 2^{k}, k any positive integer, are allowed, the finding gives the lower bound T_{M} > 2^{1/2}/( 2^{1/2}-1))× 8= 27.3 billion years for the recent age of the universe.

Now Brad Shaefer from Lousiana University has studied the red shifts of gamma ray bursters up to a red shift z=6.3, which corresponds to a distance of 13 billion light years, and claims that the fit to the data is not consistent with the time independence of the cosmological constant. In TGD framework this would mean that a phase transition scaling down the value of the cosmological constant by a power of 2 can be located in cosmological past at a temporal distance in the range 8--13 billion years.

For more details see the chapter Cosmic Strings of TGD.

Matti Pitkanen

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