Natural emergence of cosmological constant and dark radiation from the Stephenson-Kilmister-Yang- Camenzind theory of gravity

We show that the Stephenson-Kilmister-Yang (SKY) equation combined with Camenzind's matter current term naturally provides the cosmological constant and dark radiation as integration constants of the Stephenson-Kilmister-Yang-Camenzind (SKYC) field equation. To characterize the property of the dark radiation, we develop a method to separate it from the ordinary radiation. We find a special property of Camenzind's matter current, namely that the solution space for radiation in fact belongs to that of the vacuum solution of the SKY equation. We also find that this matter current does not obey the conservation condition suggested by Kilmister. Finally, we discuss the possible role of dark radiation emergent from the SKYC theory in recent cosmic microwave background observations and its implications to the inflation scenario.