A Solution to the Cosmological Constant Problem in Two Time Dimensions

For the last hundred years, the existence and the value of the cosmological constant Λ has been a great enigma. So far, any theoretical model has failed to predict the value of Λ by several orders of magnitude. We here offer a solution to the cosmological constant problem by extending the Einstein-Friedmann equations by one additional time dimension. Solving these equations, we find that the Universe is flat on a global scale and that the cosmological constant lies between 10-90 m-2 and 10-51 m-2 which is in range observed by experiments. It also proposes a mean to explain the Planck length and to mitigate the singularity at the Big Bang.

Cosmological application on five-dimensional teleparallel theory equivalent to general relativity

A theory of（4＋1）-dimensional gravity has been developed on the basis of which equivalent to the theory of general relativity by teleparallel.The fundamental gravitational field variables are the 5-dimensional（5D） vector fields（pentad）,defined globally on a manifold M,and gravity is attributed to the torsion.The Lagrangian density is quadratic in the torsion tensor.We then apply the field equations to two different homogenous and isotropic geometric structures which give the same line element,i.e.,FRW in five dimensions.The cosmological parameters are calculated and some cosmological problems are discussed.

Mysteries of the geometrization of gravitation

As we now know, there are at least two major difficulties with general rel- ativity （GR）. The first one is related to its incompatibility with quantum mechanics, in the absence of a consistent, widely accepted theory that combines the two theo- ries. The second problem is related to the requirement of the dark sectors-inflaton, dark matter and dark energy by the energy-stress tensor, which are needed to explain a variety of astronomical and cosmological observations. Research has indicated that the dark sectors themselves do not have any non-gravitational or laboratory evidence. Moreover, the dark energy poses, in addition, a serious confrontation between funda- mental physics and cosmology. Guided by theoretical and observational evidences, we are led to an idea that the source of gravitation and its manifestation in GR should be modified. The result is in striking agreement with not only the theory, but also the ob- servations, without requiring the dark sectors of the standard approach. Additionally, it provides natural explanations to some unexplained puzzles.

An approach to dark energy problem through linear invariants

The time evolution of vacuum energy density is investigated in the coherent states of inflationary universe using a linear invariant approach. The linear invariants we derived are represented in terms of annihilation operators. On account of the fact that the coherent state is an eigenstate of an annihilation operator, the wave function in the coherent state is easily evaluated by solving the eigenvalue equation of the linear invariants. The expectation value of the vacuum energy density is derived using this wave function. Fluctuations of the scalar field and its conjugate momentum are also investigated. Our theory based on the linear invariant shows that the vacuum energy density of the universe in a coherent state is decreased continuously with time due to nonconservative force acting on the coherent oscillations of the scalar field, which is provided by the expansion of the universe. In effect, our analysis reveals that the vacuum energy density decreases in proportion to t-β where β is 3/2 for radiation-dominated era and 2 for matter-dominated era. In the case where the duration term of radiation-dominated era is short enough to be negligible, the estimation of the relic vacuum energy density agrees well with the current observational data.