1. Axion as a Cold Dark Matter Candidate J. Hwang, H. Noh & C-G Park

2. Convention: no tensor-pert. Spatial gauge condition: anisotropic stress

3. Axion as a CDM

4. Scalar field: Axion: PLB 126, 179 (1991) Axenides et al

5. Axion: PRD 44, 352 (1991) Ratra Strictly ignore: Ansatz: EOM: Fluid quantities: ⇒ ∴ Pressureless fluid!

6. Axion: PLB 680, 1 (2009) JH, Noh Axion-comoving gauge: Ansatz: Fluids: EOM:

7. Jeans scale: (Khlopov, Malomed, Zeldovich, MN 1985; Nambu, Sasaki PRD 1990) Sound speed: Axion (K = 0): PRD 86, 083535 (2012) Park, JH, Noh; PRL 103, 111301 (2009) Sikivie, Yang in zero-shear gauge ∴ CDM in ALL cosmological scales

8. Axion (K = 0): Exact solution in mde with K=0=Lambda: Large-scale asymptotic solution in mde with K=0=Lambda: PLB 680, 1 (2009) JH, Noh

9. To second order

10. Axion (K = 0): PLB 726, 559 (2013) JH, Noh ⇒ with perturbed trace of extrinsic curvature

11. Low-mass Axion

12. Axion: } ⇒ Boltzmann eq. Tight coupling PRD 86, 083535 (2012) Park, JH, Noh G i j - … T (a)c 0;c T (b)c i;c T (b)c 0;c T (r)c 0;c T (r)c i;c EOM

13. Axion: PRD 86, 083535 (2012) Park, JH, Noh

14. Axion: Constant mass: Evolving mass: PRD 86, 083535 (2012) Park, JH, Noh

15. Low-mass axion as a CDM with SS cut: PRD 86, 083535 (2012) Park, JH, Noh

16. Neutrino as a HDM: PRD 86, 083535 (2012) Park, JH, Noh

17. Summary - Axion as a CDM, shown to second order pert. -Roles of low-mass axion as a CDM with small-scale cut off in the power spectrum -Axion mass smaller than 10 24 eV induces a significant damping in the baryonic density power spectrum in cosmologically relevant scales Future -Third order perturbation and NL power spectra -Axion as a Bose-Einstein condensate -Axion generated as isocurvature perturbation

18. The 6th KIAS Workshop on Cosmology and Structure Formation Nov. 3 - 7, 2014 KIAS, Seoul