  We introduce Sinyukov-like tensors, a special kind of conformal Killing
tensors. In Robertson-Walker space-times they have the perfect-fluid form and
only depend on two constants and the scale factor. They are the candidate for
the dark term of the newly proposed Conformal Killing Gravity, by Harada. In
addition to ordinary matter, the Friedmann equations contain a dark term and a
Lambda term that parametrize the Sinyukov-like tensor. The expression of H(z)
is tested on cosmological data based on cosmic chronometers CC or including
baryon acoustic oscillations BAO. There is a large incertitude in Omega_Lambda
and Omega_dark that may become negative, but their sum is close to Omega_Lambda
of Lambda-CDM. In any case, there is a future singularity, that is a big rip
for all Omegas positive. We solve the equation for the evolution, in linear
approximation, of the density contrast in matter-dominated universe. The dark
sector and the Lambda term give no significative deviation from Lambda-CDM and
GR results.
