Steffen Hagstotz

Hunting Modified Gravity
and Neutrinos with
Clusters of Galaxies
Steffen Hagstotz
LMU Munich / Excellence Cluster Universe
with Matteo Costanzi, Marco Baldi and Jochen Weller
Overview
•
Modified Gravity. Why? And What?
•
Neutrinos in Cosmology
•
Constraining new physics with clusters of galaxies
Steffen Hagstotz
Modified Gravity
General Relativity is not well tested on cosmological
scales.
•
Revisit Einstein-Hilbert action:
!
•
S=
Generalise
!
Steffen Hagstotz
S=
Z
Z
dx
dx
4p
4p
g
✓
g
✓
R 2⇤
+ Lm
16⇡G
◆
R + f (R)
+ Lm
16⇡G
◆
Phenomenology I
Modified gravity wish list:
•
should be free of ghosts
•
should allow cosmological solutions
•
shouldn’t mess with the solar system
Steffen Hagstotz
Phenomenology II
•
Consistent and viable extensions of GR are hard!
•
Modified gravity in general leads to fifth forces
Viable theories require screening mechanisms
•
Growth will be scale dependant
Steffen Hagstotz
Hu-Sawicki Gravity
f (R) ⇡
2⇤
R̄02
fR0
R
cosmological for fR0 ⌧ 1
constant background expansion
unchanged
df
New degree of freedom: scalar field fR =
dR
!
enhances gravity on perturbative level by 4/3
Steffen Hagstotz
Where to look for f(R)?
Boost of linear structure growth above screening scale
Cluster
scales!
Steffen Hagstotz
Where to look for f(R)?
Boost of linear structure growth above screening scale
S
S
A
L
C
!
n
G
M g soo
n
i
m
co
Steffen Hagstotz
Cluster
scales!
Neutrinos in cosmology
Neutrinos are massive:
0.06 eV <
from
oscillations
!
X
m⌫ < 6 eV
from direct
measurements
•
At least one additional cosmological fluid:
P
mi
⌦⌫ =
!
93.14 h2 eV
•
Background evolution almost identical, but growth
of structures changed
Steffen Hagstotz
Where to look for neutrinos?
Suppression of linear structure growth below knr where
neutrinos become non-relativistic
Cluster
scales!
Steffen Hagstotz
Neutrinos vs. f(R)
Tug of war with the power spectrum:
Nonlinear dynamics and combination of probes breaks
degeneracy, but requires careful modelling
Steffen Hagstotz
Cosmology with Clusters
Prediction of cluster counts:
Z
Z
Z
dV
dM n(M, z) d⌘P (⌘|M )
N = dz
dz
geometry
growth
astrophysics
with halo mass function
1
d ln
n(M, z) = ⇢¯m
f( )
d ln M
Z
1
2
2
2
(M, z) =
dk k P (k, z) W (kR)
2
2⇡
Steffen Hagstotz
Chameleon Screening
Recover GR limit for
2
fR0 
N
3
Infer mass via
hydrostatic
equilibrium:
d
dP
= ⇢gas
dr
dr
Bias in X-ray mass
estimates by ~10%
Steffen Hagstotz
rscreen
Excursion Set Theory
•
•
The smoothed density
field performs random
walks as function of the
smoothing scale
Collapsed objects form
as soon as a critical
threshold is crossed
c
M
2
Steffen Hagstotz
Cluster abundance in f(R)
•
Kopp et al (1306.3233): obtain numerical solutions
for c (M, fR0 , z)
•
Collaps is ellipsoidal: stochastic, drifting barrier:
!
•
c (M, fR0 , z)
+
2
Mass function involves two free parameters
Steffen Hagstotz
Cluster abundance in f(R)
fR0 = 10
5
Preliminary
fit barrier parameters
once to N-body
simulations
~10% agreement
possible
Steffen Hagstotz
Joint cluster abundance
fR0 = 10
5
+
X
m⌫ = 0.3 eV
Preliminary
Theory captures
neutrino effects without
refitting
Steffen Hagstotz
Current constraints
State of the art from Clusters (+ Planck + BAO):
X
log10 fR0 < 4.5
m⌫ = 0.2 0.3eV
Costanzi et al 1407.8338
Steffen Hagstotz
Cataneo et al 1412.0133
FIG. 1. Constraints on the HS model with n = 1. Dark and light shadings indic
regions (accounting for systematic uncertainties) from the following data sets: cl
SNIa+BAO (blue), and the combination of all these (gold). In the left panel, we u
Planck+WP+lensing+ACT+SPT in the right panel.
Summary
•
Degeneracy of modified gravity and neutrino
effects on LSS: Joint constraints necessary for
realistic limits on new physics
•
New tests combine astrophysics (to infer cluster
masses) and cosmology
Steffen Hagstotz
Cluster abundance in f(R)
fR0 = 10
Steffen Hagstotz
5
Effect largest for
massive, nearby
clusters