Exact dark energy cosmologies in extended general relativity

Tensor multinomials can be used to create extensions of Einstein's theory of general relativity without introducing extra dimensions of spacetime. One version of such an extended theory was recently shown to have accelerating vacuum and dust solutions. Using the same formulation and a simpler Lagrangian, it is possible to find all plane-symmetric cosmologies with P = ωρ, where ω is a constant. These solutions include three and four-parameter families of dark energy cosmologies, some non-singular everywhere, albeit with negative energy density in the latter case. The theory permits a time-dependent source, μ(τ). for the scalar field equation, equivalent to a ``time-dependent cosmological constant", or quintessence function. The physical source of the scalar field has a possible interpretation as a charge-squared distribution, with both like and unlike charges contributing equally as sources. In the plasma of the early universe, separated charges drive universal inflation. As matter and anti-matter annihilate and the universe expands, μ(τ) naturally declines by many orders of magnitude. An example of such a function is given when μ(τ) is proportional to the energy density, and leads to de Sitter, forcing ω = -1, as it should. This version of extended general relativity can be considered a trial model of what a unification of gravity, electromagnetism, and dark energy might look like when represented by a second-order tensor multinomial.