Dark energy cosmologies and other solutions in extended general relativity

Most extensions of general relativity involve hypothetical new dimensions. Here, the use of tensor multinomials creates extensions of Einstein’s theory without extra dimensions of spacetime. This mathematical space of tensor multinomials is in fact the universal covering algebra of the tensor algebra. A Lagrange multiplier system is used to determine the equations in this extension. Here, 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. Also presented is further work giving static, spherically-symmetric solutions. This version of extended general relativity is what a trial model of a unification of gravity, electromagnetism, and a scalar field might look like when represented by a second-order tensor multinomial.