With his eqs.[1,(28)-(29)] Evans arrives at a remarkable realization:

Christoffel connection:

                Γ^λ_μν = Γ^λ_νμ .                                 [1,(28)]

However, for the connection [1,(28)] the torsion must be zero:

                T^λ_μν = Γ^λ_μν − Γ^λ_νμ = 0.                 [1,(29)]

Therefore the Bianchi identity and Christoffel connection are incompatible in general. The Christoffel connection can be a solution of the Bianchi identity if and only if the metric defines a Ricci flat space-time where all elements of the Ricci tensor vanish.

There is no way in which the EH theory can escape its inherent weaknesses. Furthermore it is almost entirely based on the use of the Christoffel symbol, which as we have shown, violates the fundamental geometry [1,(1)]. It is concluded that all cosmologies based on EH theory are physically meaningless . . . The Christoffel symbol can be used if and only if

                R^κ_μ^μν = 0.                                 [1,(30)]

The reader is kindly requested have a look at the eqs. (3.80-95) of Evans' standard text book [2]. He'll find that at least S.M. Carroll (and a tiny minority of some other mislead guys) does not follow the above conclusion that vanishing torsion implies vanishing Ricci tensor.

The opinion of that tiny minority: In torsion free case due to T^a = 0 the 1st Bianchi identity D Ù T^a = R^a_b Ù q^b yields R^a_b Ù q^b = 0, i.e.

                R^λ_ρμν + R^λ_νρμ + R^λ_μνρ = 0 ,                                 [1,(32)]

for short R^λ_[ρμν] = 0, however, that does NOT imply the vanishing of the Ricci tensor.

S.M. Carroll [2, eqs.(3.100)ff.] considers the two-sphere as his favorite (counter-)example: In [2, eqs.(3.101)] the Christoffels are displayed to show the vanishing of torsion. Then Carroll calculates the Riemann tensor [2, eqs.(3.102-103)] finally followed by the Ricci tensor in [2,eqs.(3.104)]. For everybody who has eyes to see:

The Ricci tensor in [2, eqs.(3.104)] is NOT ZERO.