Equation (35) describes the inflaton density with w = [rho]/p = 1 and a

cosmological term varying with the speed [a.sup.-3].

Consider now the FLRW metric with a positive

cosmological term and homogeneous density - that is to say the [LAMBDA]CDM model.

The

cosmological term then becomes a ratio of photons to photon holes.

For a homogeneous, isotropic, and flat universe (k = 0) there are two independent Friedmann equations with the

cosmological term [LAMBDA]:

This lends support to the fact that only a 4th rank tensor theory can strictly describe a metric with a variable

cosmological term. Therefore, after interchanging [alpha] with [beta], we find:

Recently, embedding general relativity with varying

cosmological term in five-dimensional BDT of gravity in vacuum has been discussed by Reyes & Aguilar [26].

In addition, it implies a non zero

cosmological term and a constant scalar curvature, therefore it doesnot admit a Hubble expansion in the whole, which tends to contradict all current observations.

* We then include a variable term that supersedes the socalled

cosmological term Kgah in the field equations, still complying with the conservation property of the Einstein tensor density in GR;

Some Exact Solutions of the Friedmann Equations with the

Cosmological Term. Soviet Astronomy, 1976, v.

Next making use of a max quantum cosmic

cosmological term (lambda) we obtained the mass of the universe, which now appears quantized in the units of cosmic [[??].sub.g].

In the first one we used an exponential

cosmological term, for the second one we considered vanishing cosmological constant.

Its great brightness and protracted visibility is largely a result of its relative proximity in

cosmological terms.