We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors which leads to greater geometric insight and a higher degree of organization in analytical expressions. We demonstrate t...We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors which leads to greater geometric insight and a higher degree of organization in analytical expressions. We demonstrate the effectiveness of the approach by proving a number of integral identities with vector integrands. The presented approach may be aptly described as absolute vector calculus or as vector tensor calculus.展开更多
The cosmological constant, Λ, represents dark energy. The dark energy hypothesis (DEH) replaces Λ with a variable quantity, the cosmological parameter: Λ=1a2η2In this formula, “a” is the scale factor and η the ...The cosmological constant, Λ, represents dark energy. The dark energy hypothesis (DEH) replaces Λ with a variable quantity, the cosmological parameter: Λ=1a2η2In this formula, “a” is the scale factor and η the conformal time: adη = cdt. A companion paper (DEH II) develops and explores a cosmological model with this variable parameter. This paper portrays the origin of the cosmological parameter in the uncoupling of time and space in the early universe from a prior state in which the comoving coordinates x0 = η and x1 = χ, the cosmic latitude, are coupled. In this hypothesis dark matter is a co-product of the decoupling, but its nature remains mysterious.展开更多
文摘We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors which leads to greater geometric insight and a higher degree of organization in analytical expressions. We demonstrate the effectiveness of the approach by proving a number of integral identities with vector integrands. The presented approach may be aptly described as absolute vector calculus or as vector tensor calculus.
文摘The cosmological constant, Λ, represents dark energy. The dark energy hypothesis (DEH) replaces Λ with a variable quantity, the cosmological parameter: Λ=1a2η2In this formula, “a” is the scale factor and η the conformal time: adη = cdt. A companion paper (DEH II) develops and explores a cosmological model with this variable parameter. This paper portrays the origin of the cosmological parameter in the uncoupling of time and space in the early universe from a prior state in which the comoving coordinates x0 = η and x1 = χ, the cosmic latitude, are coupled. In this hypothesis dark matter is a co-product of the decoupling, but its nature remains mysterious.
