1. Evolution of perturbations and cosmological constraints in decaying dark matter models with arbitrary decay mass products Shohei Aoyama Nagoya University Collaborators: Toyokazu Sekiguchi, Kiyotomo Ichiki & Naoshi Sugiyama JCAP07(2014)021, arXiv: 1402.29721402.2972 KIAS workshop (2014) 3 rd November, 2014

2. CDM and its problem The ΛCDM model can predict numerous cosmological observations on large scales about temperature anisotropy of the CMB C l TT and the large scale structure. However the nature of dark matter (eg. the mass or interactions ) is still unknown. In addition, observations on the small scale, the discrepancies between the observations and the theoretical predictions. (eg. missing satellite problem) Moore et al. (1999) [astro-ph/9907411] http://cdn.arstechnica.net/wp- content/uploads/2013/03/Planck_cosmic_recipe.png

3. Planck anomaly Planck collaborations pointed out that σ8 which is estimated from C l TT is larger than that from the number counts of cluster by SZ effect on CMB by more than 2σ CL. Planck Collaboration(2013,XX)[1303.5080]

4. A prescription of these problems Some mechanisms that suppress small scale structure formation may rescue these problems. (Ostriker & Steinhardt (2003) [astro-ph/0306402]). Decaying dark matter (DDM) is a candidate of these problems because product particles are generated with large momentum and smear out of the gravitational potential which was originated by progenitor particles. Planck Collaboration(XX)[1303.5080] Moore+ (1999) [astro-ph/9907411]

5. We consider the DDM which decays into two product dark matter particles. In this case, the decaying process and the time evolutions of distribution functions of dark matter particles can be characterized by 4 parameters. In our calculation, by solving Boltzmann equations for these product particles directly, one can take the mass of one of daughter particles arbitrary and obtain the time evolutions of density perturbations, C l TT and σ 8. Our model of DDM

6. The effect on C l TT peak shift integrated SW

7. We consider the DDM which decays into two product dark matter particles. In this case, the decaying process and the time evolutions of distribution functions of dark matter particles can be characterized by 4 parameters. In this work, we set the constraint on the lifetime of DDM from σ8 estimated from BOSS III data. σ 8 =0.80±0.02 Sánchez et al.(2012)[arXiv: 1203.6616]) Our model of DDM

8. The constraint on the lifetime of DDM The lifetime of the DDM should be longer than 200Gyr in the case relativistic decay. This constraint is consistent with previous works (Ichiki et al. (2004), [astro-ph:astro-ph/0403164]). 2σ anomaly This SDSS data excluded σ 8 < 0.76 on 2 σ CL.

9. Planck anomaly Favored region The DDM whose lifetime of DDM is around 200 Gyr and which decays into two relativistic particles can explain observational C l TT and the number of clusters.

10. The power spectrum of CMB lens potential C l φφ ―m D1 /m M =0.3 ―m D1 /m M =0.9 ― Λ CDM The DDM which decays into two relativistic particles is not ruled out from the current CMB lensing observation.

11. Conclusion We consider the decaying dark matter which decays two particles and its effect on the cosmological observables. Even in the case that the finite mass of one of product particles, the lifetime should be larger than 200 Gyr. DDM may reconcile the tension between the observed σ 8 estimated from ClTT and that from number counts of cluster from SZ effect.