The cosmology of minimal varying Lambda theories
  Inserting a varying Lambda in Einstein's field equations can be made
consistent with the Bianchi identities by allowing for torsion, without the
need to add scalar field degrees of freedom. In the minimal such theory, Lambda
is totally free and undetermined by the field equations in the absence of
matter. Inclusion of matter ties Lambda algebraically to it, at least when
homogeneity and isotropy are assumed, i.e. when there is no Weyl curvature. We
show that Lambda is proportional to the matter density, with a proportionality
constant depending on the equation of state. Unfortunately, the proportionality
constant becomes infinite for pure radiation, ruling out the minimal theory
prima facie despite of its novel internal consistency. It is possible to
generalize the theory still without the addition of kinetic terms, leading to a
new algebraically-enforced proportionality between Lambda and the matter
density. Lambda and radiation may now coexist in a form consistent with Big
Bang Nucleosynthesis, though this places strict constraints on the single free
parameter of the theory, $\theta$. In the matter epoch Lambda behaves just like
a dark matter component. Its density is proportional to the baryonic and/or
dark matter, and its presence and gravitational effects would need to be
included in accounting for the necessary dark matter in our Universe. This is a
companion paper to Ref. [1] where the underlying gravitational theory is
developed in detail.
