Evolution mapping: a new approach to describe matter clustering in the non-linear regime

Understand

We present a new approach to describe statistics of the non-linear matter density field that exploits a degeneracy in the impact of different cosmological parameters on the linear dimensionless matter power spectrum, $\Delta^2_{\rm L}(k)$.

• We classify all cosmological parameters into two groups, shape parameters, which determine the shape of $\Delta^2_{\rm L}(k)$, and evolution parameters, which only affect its amplitude at any given redshift.
• With this definition, the time evolution of $\Delta^2_{\rm L}(k)$ in models with identical shape parameters but different evolution parameters can be mapped from one to the other by relabelling the redshifts that correspond to the same clustering amplitude, which we characterize by the linear mass fluctuation in spheres of radius $12\,{\rm Mpc}$, $\sigma_{12}(z)$.
• We use N-body simulations to show that the same evolution mapping relation gives a good description of the non-linear power spectrum, the halo mass function, or the full density field.