Conformal Killing cosmology with Sinyukov tensors: geometry and growth of structures

We introduce perfect fluid Sinyukov-like tensors, a special kind of conformal Killing tensors, and prove a characterization of generalized RW spacetimes. In cosmological (RW) framework, we study the Friedmann equations of Conformal Killing Gravity. In addition to ordinary matter they contain a dark fluid and a Lambda term emergent from the conformal Killing extension. We then solve the equation for the evolution of the density contrast in matter-dominated universe. The main result is that the simultaneous presence of the dark sector and the Lambda term gives a deviation from Lambda-CDM and ordinary GR towards an enhancement of the overdensity growth.