The Cosmological Constant Constrained with Union2.1 Supernovae Type Ia Data. Derivation and evaluation of several FRW and Carmeli models presenting underwhelming support for the standard model

We derive several, detailed relationships in terms of the Friedmann, Robertson, Walker (FRW) generalization which describe the Universe during both the radiation and matter dominated epochs. We explicitly provide for the influence of radiation, rather than burying this term within the matter term. Several models allow the cosmological constant (CC) to vary with universe expansion in differing manners. We evaluate these and other popular models including the $\mathrm{\Lambda }$CDM({standard model}), quintessence as presented by Vishwakarma, Equation of State (EoS) and the Carmeli model with data from the 580 Union2.1 supernovae type Ia collection, using several minimization routines and find models built about the CC, the $\mathrm{\Lambda }$CDM models, fare no better than those without.