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.