Decaying cosmological parameter in the early universe from NKK theory of gravity

Cosmological observations imply that there exists an extremely small upper limit on the vacuum energy density in the present state of our universe. This stands in sharp contradiction with theoretical predictions [1]. In fact, any mass scale in particle physics contributes to the vacuum energy density much larger than this upper bound [2]. According to modern quantum field theory, the structure of the vacuum is turned out to be interrelated with some spontaneous symmetry-breaking effects through the condensation of quantum scalar fields. This phenomenon gives rise to a non-vanishing vacuum energy density ρvac ∼ M p (Mp = G −1/2 is the Planckian mass and G is the gravitational constant). The appearance of this characteristic mass scale may have an important effect on the cosmological constant because it receives potential contributions from this mass scale due to mass spectrum of corresponding physical fields in quantum field theory. By taking into account this contribution, an effective cosmological constant is defined as the sum of the bare cosmological constant λ and 8πGρvac [3]. This type of contribution gives rise to an immediate difficulty called the cosmological constant problem. There are some possible solutions to this problem rendering Λ exactly or almost vanishing [4]. One of them consists to find some relaxation mechanism by which Λ could relax to its present day small value [5,6]. A credible mechanism for obtaining such a decay already exists, which is to assume the existence of a scalar field