Non-Linear Fuzzy Dark Matter Modelling with Extended LPTAlex Laguë, Renée Hložek, George Stein, and Dick Bond
Fuzzy Dark Matter (FDM)
✤ Ultra-light boson:
✤ Scale-dependent sound speed:
✤ Jeans scale:
10−26 eV ≲ m ≲ 10−21 eV
c2s =ℏ2k2
4m2a2
kJ = 66.5a1/4( ΩFDMh2
0.12 )1/4
( m10−22 eV )1/2
Mpc−1
Marsh (1510.07633)
CκκlPmatter(k, z)
Cκκl
Nori et al. (1801.08144)
Pmatter(k, z)
N-Body(AX-Gadget,
Modified AREPO, etc.)
N-Body(AX-Gadget,
Modified AREPO, etc.)
Cκκl
LPT (Peak-Patch,
Pinocchio, COLA,etc.)
Pmatter(k, z)
Nori et al. (1801.08144)
Why Modified LPT
1. Non-linear CMB lensing from LSS
2. Low computational cost
3. Large simulation volume
Image: ESA
Peak-Patch Method
Stein et al. (1810.07727)
Peak-Patch Method
Stein et al. (1810.07727)
Peak-Patch Method
Stein et al. (1810.07727)
Peak-Patch Method
Stein et al. (1810.07727)
Peak-Patch Method Modifications
FDM-Modified Steps
A.B.
C.
LPT Step
Stein et al. (1810.07727)
A. Initial Conditions
Heavier Particles
Computed with AxionCAMB (1607.08208)
Lensing ConstraintsC
κκ lΔ
Cκκ l
/Cκκ l
Cψl ≈ ∫χ
0χ′�dχ′�PΨ(l/χ′�; η0 − χ′�)( χ − χ′�χχ′� )
2
l
Lensing Constraints
ACT Limit
Cκκ l
ΔC
κκ l/C
κκ l
l
ConstrainedRegion
ObservationallyUnexplored
ComputationallyAccessible
ΔC
κκ l/C
κκ l
l
log10(m) [eV]
ΩFDMΩDM
C. LPT Displacements
Final PositionInitial Position
∇x ⋅ (d2Ψ
dτ2+ 2
·aa
dΨdτ ) = − 4πGρ̄δ(x) − c
2s
a2∇2xδ(x)
Fuzzy DM Term
x = q + Ψ Displacement Ψ ≈ Ψ(1) + Ψ(2)
Linear Quadratic
Axion Sound Speed
Ove
rden
sity
δ(x)
1 Mpc
CDM
Ove
rden
sity
δ(x)
1 Mpc
FDM
kSZ Contribution
ΔTTCMB
∝ vpec
Future Outlook
✤ Part B. of the modifications: Ellipsoidal Collapse
✤ Further constraints from CMB lensing
✤ Comparison with N-Body/Hydro simulations
Thank you!
Baryon-Dominated Suppression
L ≈ 3000 Nguyễn et al. (1710.03747)
Dynamical Effects (QP)
Both
Adding Pressure
Changing I.C.
m = 10−22 eV
N-Body (AX-GADGET)
z = 3
Nori et al. (2018)
Dynamical Effects (QP)
Both
Adding Pressure
Changing I.C.
m = 10−22 eV
N-Body (AX-GADGET)
z = 3
Nori et al. (2018)
Pressure subdominant compared to change in I.C.
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