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Richard Battye Jodrell Bank Centre for Astrophysics
University of Manchester
Collaborators : Adam Moss (University of Nottingham ) Jonathan Pearson (Durham University)
CONSTRAINTS ON DARK ENERGY AND MODIFIED GRAVITY
Beyond the standard model cosmology
Standard cosmological model - 6 parameters
Perturbation sector
Modified gravity sector
Matter sector
Ionization sector
Eg r, n_run Isocurvature Defects, ..
Eg neutrinos, WDM Eg. Dark energy,massive gravity, F(R), ..
Beyond the standard model cosmology
Standard cosmological model - 6 parameters
Perturbation sector
Modified gravity sector
Matter sector
Ionization sector
Eg r, n_run Isocurvature Defects, ..
Eg neutrinos, WDM Eg. Dark energy,massive gravity, F(R), ..
NON-COSMOLOGICAL CONSTRAINTS
NON-COSMOLOGICAL CONSTRAINTS
Beyond the standard model cosmology
Standard cosmological model - 6 parameters
Perturbation sector
Modified gravity sector
Matter sector
Ionization sector
Eg r, n_run Isocurvature Defects, ..
Eg neutrinos, WDM Eg. Dark energy,massive gravity, F(R), ..
NON-COSMOLOGICAL CONSTRAINTS
NON-COSMOLOGICAL CONSTRAINTS
Fundamental models
Phenomenology
Observations
Eg Quintessence, k-essence, Horndeski, KGB, F(R), ..
Eg. CMB, SNe, BAO, Lensing, RSD, ISW
Eg. At background order w = P/ρ
OBJECTIVE OF THIS TALK
IN THE PERTURBATION
SECTOR
Make no attempt to connect to solar system and other observations at smaller scales - non-linear & would require the full theory !!!
Observations • Background only
- CMB (medium & high l) - BAO - SNe
• Background and perturbations - CMB (low l) - Lensing - ISW - RSD
} Need phenomenology for perturbations
Background & perturbations
Must satisfy perturbed conservation equation
P=wρ Background:
Perturbations:
- if standard energy momentum tensor is conserved
What is it ?
Equation of state approach
Scalar sector
Vector sector
Tensor sector
Eliminate all internal degrees of freedom
ΠS
ΠT
ΠV
NB: all gauge invariant !!!!
(Battye & Pearson, 2013)
Basic idea in the scalar sector
In general functions of space (ie. k) and time
- using synchronous gauge perts h & η
Simple models • Elastic dark energy (EDE) or Lorentz violating massive gravity
• General k-essence
(Battye & Moss, 2007 & Battye & Pearson 2013)
L=L(gµν)
L=L(φ,χ)
& time translational invariance -> extra vector field ξi
Non-adiabatic !!
(Weller & Lewis, 2003; Bean & Dore 2003)
(NB minimally coupled Quintessence has α=1)
Generalized scalar field (GSF) models
Assume that:
1. At most linear in the last term 2. Second-order field equations 3. Reparametrzation invariant
Anisotropic stresses are zero !
NB gauge invariant
Data used
• TT likelihood from Planck • WMAP polarization • BAO – 6DF, SDSS, BOSS, WiggleZ
already constrains w approx -1
• CMB lensing from Planck • CFHTLenS (exclude
nonlinear scales)
} Constrains the perturbations !
EDE model constraints
�5 �4 �3 �2 �1 0log10 c2
s
0.0
0.2
0.4
0.6
0.8
1.0
P/P
max
Planck+WP+CFHTLS+BAO
Planck+WP+CMB Lensing+CFHTLS+BAO
�5 �4 �3 �2 �1 0
log10 c2s
�1.3
�1.2
�1.1
�1.0
�0.9
�0.8
w
Planck+WP+CMB Lensing+CFHTLS+BAO
TDI L(g)
If |1+w|>0.05
Preference for cs > 0.01 -> Jeans length > 30 h-1Mpc
GSF Model
3 6 9 12�2
0.4
0.8
1.2
1.6
� 1
�4 �3 �2 �1log10 ↵
3
6
9
12
� 2
0.4 0.8 1.2 1.6�1
Planck+WP+CMB Lensing +BAO
Planck+WP+CFHTLS +BAO
Constraints on GSF models
0 0.5 1 1.50
5
10
15
β 1
β2
−5 −4 −3 −2 −1 00
5
10
15
log1 0α
β2
−5 −4 −3 −2 −1 00
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
log1 0α
β1