A toy model of the five-dimensional universe with the cosmological constant

A value of the cosmological constant in a toy model of the five-dimensional universe is calculated in such a manner that it remains in agreement with both astronomical observations and the quantum field theory concerning the zero-point fluctuations of the vacuum. The (negative) cosmological constant is equal to the inverse of the Planck length squared, which means that in the toy model the vanishing of the observed value of the cosmological constant is a consequence of the existence of an energy cutoff exactly at the level of the Planck scale. In turn, a model for both a virtual and a real particle-antiparticle pair is proposed which describes properly some energetic properties of both the vacuum fluctuations and created particles, as well as it allows one to calculate the discrete "bare" values of an elementary-particle mass, electric charge and intrinsic angular momentum (spin) at the energy cutoff. The relationships between the discussed model and some phenomena such as the Zitterbewegung and the Unruh-Davies effect are briefly analyzed, too. The proposed model also allows one to derive the Lorentz transformation and the Maxwell equations while considering the properties of the vacuum filled with the sea of virtual particles and their antiparticles. Finally, the existence of a finite value of the vacuum-energy density resulting from the toy model leads us to the formulation of dimensionless Einstein field equations which can be derived from the Lagrangian with a dimensionless (naively renormalized) coupling constant.Comment: 52 pages, 1 figure; a post-final, rewritten version with a number of new remarks and conclusion

Origin of Magnetic Fields in the Universe Due to Nonminimal Gravitational-Electromagnetic Coupling

Basically the only existing theories for the creation of a magnetic field B in the Universe are the creation of a seed field of order 10^{-20} G in spiral galaxy which is subsequently supposedly amplified up to the observed 10^{-6} - 10^{-5} G by a dynamo process or a seed intergalactic field of magnitude 10^{-12} - 10^{-10} G which is amplified by collapse and differential rotation. No satisfactory dynamo theory, however, exists today. We show that a 10^{-6} - 10^{-5} G magnetic field in spiral galaxies is directly obtained from a nonminimal gravitational-electromagnetic coupling, without the need of significant dynamo amplification.Comment: 5 pages, Latex (Revtex), no figures, To appear in PR