Exact dark energy cosmologies in extended general relativity

Tensor multinomials, elements of the universal covering algebra of the tensor algebra, 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 [Formula: see text], where [Formula: see text] is a constant. These solutions include three- and four-parameter families of dark energy cosmologies, some nonsingular everywhere, albeit with negative energy density in the latter case. The theory permits a time-dependent source, [Formula: see text], 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 positive and negative 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, [Formula: see text] naturally declines by many orders of magnitude. An example of such a function is given when [Formula: see text] is proportional to the energy density, and leads to a choice of cosmologies, including de Sitter and power-law accelerating spacetimes, with the power taking arbitrarily large values. 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.