Secret interactions among sterile neutrinos have been recently proposed as an escape-route to reconcile eV sterile neutrino hints from short-baseline anomalies with cosmological observations .
In particular models with coupling g _ { X } \gtrsim 10 ^ { -2 } and gauge boson mediators X with M _ { X } \lesssim 10 MeV lead to large matter potential suppressing the sterile neutrino production before the neutrino decoupling .
With this choice of parameter ranges , big bang nucleosynthesis is left unchanged and gives no bound on the model .
However , we show that at lower temperatures when active-sterile oscillations are no longer matter suppressed , sterile neutrinos are still in a collisional regime , due to their secret self-interactions .
The interplay between vacuum oscillations and collisions leads to a scattering-induced decoherent production of sterile neutrinos with a fast rate .
This process is responsible for a flavor equilibration among the different neutrino species .
We explore the effect of this large sterile neutrino population on cosmological observables .
We find that a signature of strong secret interactions would be a reduction of the effective number of neutrinos N _ { eff } at matter radiation equality down to 2.7 .
Moreover , for M _ { X } \gtrsim g _ { X } MeV sterile neutrinos would be free-streaming before becoming non-relativistic and they would affect the large-scale structure power spectrum .
As a consequence , for this range of parameters we find a tension of a eV mass sterile state with cosmological neutrino mass bounds .