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.

Oscillating Spacetime: The Foundation of the Universe

In this article, spacetime is modeled as a quantum mechanical sonic medium consisting of Planck length oscillations at Planck frequency. Planck length-time oscillations give spacetime its physical constants of c, G and ħ. Oscillating spacetime is proposed to be the single universal field that generates and unifies everything in the universe. The 17 fields of quantum field theory are modeled as lower frequency resonances of oscillating spacetime. A model of an electron is proposed to be a rotating soliton wave in this medium. An electron appears to have wave-particle duality even though it is fundamentally a quantized wave. This soliton wave can momentarily be smaller than a proton in a high energy collision or can have a relatively large volume of an atom’s orbital wave function. Finding an electron causes it to undergo a superluminal collapse to a smaller wave size. This gives an electron its particle-like properties when detected. The proposed wave-based electron model is tested and shown to have an electron’s approximate energy, de Broglie wave properties and undetectable volume. Most important, this electron model is shown to also generate an electron’s electrostatic and gravitational forces. The gravitational properties are derived from the nonlinearity of this medium. When an electron’s gravitational and electrostatic forces are modeled as distortions of soliton waves, the equations become very simple, and a clear connection emerges between these forces. For example, the gravitational force between two Planck masses equals the electrostatic force between two Planck charges. Both force magnitudes equal ħc/r2.

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.