Axion as a Cold Dark Matter Candidate: Proof to Second order

Understand

We prove that the axion as a coherently oscillating scalar field acts as a cold dark matter (CDM) to the second-order perturbations in all cosmological scales including the super-horizon scale.

• The proof is made in the axion-comoving gauge.
• For a canonical mass, the axion pressure term causes deviation from the CDM only on scales smaller than the Solar System size.
• Beyond such a small scale the equations of the axion fluid are the same as the ones of the CDM based on the CDM-comoving gauge which are exactly identical to the Newtonian equations to the second order.