1.3.6 Cosmological Constant Problem
In order to make the Universe static, Einstein first added the cosmological constant to his field equations so that the positive attraction of matter may balance the cosmological constant repulsion. This was later discarded after Hubble’s discovery of the expansion of the Universe in 1929. However, in 1998, after the discovery of the accelerating Universe from distant Type Ia supernovae, in addition to the data from the cosmic microwave background and large galaxy redshift surveys, astronomers were able to measure the evolution of the expansion rate of the Universe, which lead to the current standard model of cosmology, the Lambda-Cold-Dark-Matter model, (
).
On the other hand, as early as 1960s, Quantum Field Theory predicted that quantum fluctuations would make huge contributions to the vacuum energy, much larger than the energy due to the cosmological constant which was known to be either zero or very small. The problem became extremely critical after the development of inflationary models in the 1980s, since the cosmic inflation is driven by vacuum energy and even the smallest changes in its value will lead to different expansion scenarios.
As Weinberg showed, there are many problems associated with the cosmological constant. The observed acceleration of the expansion simply means that the cosmological constant is about 120 orders of magnitude smaller than the density of vacuum energy, the Planck density, that can be calculated from Quantum Field Theory. This is known as the problem of smallness. Moreover, being so small, why it just happens to have exactly the value that makes its density similar to the average matter density, which is called the coincidence problem.
Many solutions have been suggested in this regard, as it was reviewed by Weinberg and Sanhi, but because the discrepancy is so huge, none of the speculations came ever close to solving the puzzle. The huge discrepancy indicates that there is something substantially wrong in our understanding of quantum physical processes.
The number of atoms in the visible Universe is usually estimated at
, which is called Eddington number, so the discrepancy in the cosmological constant problem is still forty orders of magnitudes larger than the number of all atoms in the Universe. It would not be strange, therefore, if we postulate that this huge physical multiplicity could be deceiving! Yet since we clearly observe this multiplicity in our normal time level, the only way out is to consider that the whole Universe is being created from only one ultimate, or metaphysical, elementary particle, that we call the Single Monad, that is perpetually being multiplied in the inner levels of time to create the whole physical Universe.
Accordingly, the huge discrepancy in the cosmological constant is diminished and even eliminated because the vacuum energy should be calculated from the average of all states, and not their collective summation as it is currently treated in Quantum Field Theory. This means that we should divide the vacuum energy density by the number of modes included in the unit volume, which can be calculated by:
, because the cutoff is usually applied at the Planck scale. This will reduce the discrepancy between the observed and the predicted vacuum energy density from 120 into only three orders of magnitudes. The remaining very small discrepancy could be explained according to quintessence models, but a more accurate calculation is needed first because all the current methods are approximate.