Bosonic dark matter, misalignment
mechanism, and cosmic BoseEinstein condensation
Qiaoli Yang
Jinan University

12-20-2017
Osaka University

Dark Matter• leading candidates:
1. WIMPs
2. Axions ~ 10 5 eV .
3. ALPs
4. Dark Photons.....

To solve the strong CP problem, one
introduces the U (1) symmetry whichis spontaneously broken
PQ

relaxes to zero during
QCD phase transition.

An example: the KSVZ axion• one introduces an new complex scalar
and a new heavy quark Q.

=>

Axion like particles• alps arises due to compactification ofthe antisymmetric tensor fields• the x are non-compact coordinate, y arecompact coordinates.

Axion like particles• the zero mode acquires a potential due
to non-perturbative effects on thecompactifying cycle.
• the effective Lagrangian in four
dimension:

ALPs

So if extra dimension is exist, alps
seems inevitably.
Question is: what is the mass?

Misalignment mechanism:

during the radiation dominated era:

The cold axion (like) parties• can be a major part of dark matter.
• have a very small velocity
V=[1/(t_1*m)]*[a(t_1)/a(t)]m<10^(-6)eV. They are ultra light nonrelativistic bosons.

Cosmic condensate• cold alps phase space density is>10^26, so they behave likecondensate instead of thermal particles.
• the excited thermal states can only
accommodate a given number ofparticles for a given temperature, therest have to go to the ground state.

Axion/ALPs BEC• the Lagrange in unperturbed flat FRW
universe:• we can derive the equation of motion•••

PRL 103(2009) 111301 (QCD Axions)
Int.J.Mod.Phys. A32, (2017) 1750051 (ALPs)
PRD 95 (2017), 043541 (fuzzy dark matter) ...

Axion/ALPs BEC
alps are non-relativistic, so slow varying
terms are interested. We factor out termsof order, then we have a nonlinear wave equation.

Axion/ALPs BEC• if we consider gravitational inhomogeneity, then we have:Perturbative regime• from the wave function, we derive thegeneralized continuity equation:

which is the same as the equation of point
like CDM.

Perturbative regime• the first order velocity equation isdifferent:
comparing with point like CDM:
we see two additional terms
which are due to quantum pressure andself interaction.

The jeans length• combined all interactions (gravity, selfinteractions), we find perturbation
spectrum in k space:

Int.J.Mod.Phys. A32, (2017) 1750051

None-linear evolution• occupation number change• therefore the thermalization rate is:leading to a different cosmologicalstructure formations.

Misalignment mechanism•

1: Spin 0 axions, axion like particles•

2: Spin 1 Dark Photons

ALPs• decay channel• decay rate:• QCD Axions:• Cosmological density ratio during thematter dominate era:

Dark photons
hidden sector particles

Dark photons

Dark photons• Decay channel• Decay rate:

Dark Photons• Spectrum:• orthopositronium：Dark matter halos• up to 95% percent galaxy
mass which is of order
10^(12) solar mass.

The distortion of spectrum• Cosmology red-shift, Gravitational redshift, Kinetic red-shift...

The parameter space of ALPs

PRD 95 (2017), 075032.

The flux from the M31
received on the earth

PRD 95 (2017), 075032.

Dark photon detection
arXiv:1606.01492

Interactions in non-relativistic limit:• in atomic scale，DP behaves like laserDark photons
experiment detection:

Dark Photon Detection