CONSTRAINTS ON DARK ENERGY AND MODIFIED GRAVITY
Richard Battye Jodrell Bank Centre for Astrophysics University of Manchester
Collaborators : Adam Moss (University of Nottingham ) Jonathan Pearson (Durham University) Beyond the standard model cosmology
Perturbation Ionization sector sector
Eg r, n_run Isocurvature Defects, .. Standard cosmological model - 6 parameters
Matter sector Modified gravity sector
Eg neutrinos, WDM Eg. Dark energy,massive gravity, F(R), .. Beyond the standard model cosmology
Perturbation Ionization sector NON-COSMOLOGICAL sector CONSTRAINTS Eg r, n_run Isocurvature Defects, .. Standard cosmological model - 6 parameters
Matter sector NON-COSMOLOGICAL Modified CONSTRAINTS gravity sector
Eg neutrinos, WDM Eg. Dark energy,massive gravity, F(R), .. Beyond the standard model cosmology
Perturbation Ionization sector NON-COSMOLOGICAL sector CONSTRAINTS Eg r, n_run Isocurvature Defects, .. Standard cosmological model - 6 parameters
Matter sector NON-COSMOLOGICAL Modified CONSTRAINTS gravity sector
Eg neutrinos, WDM Eg. Dark energy,massive gravity, F(R), .. Eg Quintessence, k-essence, Fundamental models Horndeski, KGB, F(R), ..
OBJECTIVE OF THIS TALK Eg. At background IN THE Phenomenology PERTURBATION order w = P/ρ SECTOR
Observations Eg. CMB, SNe, BAO, Lensing, RSD, ISW
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 Need phenomenology - ISW } for perturbations - RSD Background & perturbations
Background: P=wρ
Perturbations: What is it ?
Must satisfy perturbed conservation equation - if standard energy momentum tensor is conserved Scalar equations of motion
Perturbed conservation equation (Battye & Pearson, 2013) Equation of state approach
Scalar sector ΠS
Vector sector ΠV NB: all gauge invariant !!!!
Tensor sector ΠT
Eliminate all internal degrees of freedom Tensor Sector - easy
B=0
Simplest model is a massive graviton ! Basic idea in the scalar sector
- using synchronous gauge perts h & η
In general functions of space (ie. k) and time Simple models
• Elastic dark energy (EDE) or Lorentz violating massive gravity (Battye & Moss, 2007 & Battye & Pearson 2013)
L=L(gµν)
& time translational invariance -> extra vector field ξi • General k-essence (Weller & Lewis, 2003; Bean & Dore 2003)
L=L(φ,χ)
Non-adiabatic !!
(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 NB gauge invariant are zero ! Data used
• TT likelihood from Planck • WMAP polarization • BAO – 6DF, SDSS, BOSS, WiggleZ
already constrains w approx -1
• CMB lensing from Planck Constrains the • CFHTLenS (exclude } perturbations ! nonlinear scales) EDE model constraints
0.8 Planck+WP+CMB Lensing+CFHTLS+BAO 1.0 0.9 0.8 1.0
max 0.6 P w /
1.1 P 0.4 If |1+w|>0.05
1.2 0.2 TDI (g) Planck+WP+CFHTLS+BAO L Planck+WP+CMB Lensing+CFHTLS+BAO 1.3 0.0 5 4 3 2 1 0 5 4 3 2 1 0 2 2 log10 cs log10 cs
-1 Preference for cs > 0.01 -> Jeans length > 30 h Mpc GSF Model
Planck+WP+CMB Lensing +BAO Planck+WP+CFHTLS +BAO
1.6
1.2 1 0.8
0.4
12
9 2 6
3
4 3 2 1 0.4 0.8 1.2 1.6 3 6 9 12 log10 ↵ 1 2 Constraints on GSF models
15 15 1.8
1.6
1.4 10 10 1.2 2 1 2 1 β β β 0.8
5 5 0.6
0.4
0.2
0 0 0 0 0.5 1 1.5 −5 −4 −3 −2 −1 0 −5 −4 −3 −2 −1 0 β 1 log10α log10α Conclusions
• Equation of state approach to dark energy perts
• Specific cases : EDE & GSF
• Constraints from CMB+lensing presented - NB marginalized w will be model dependent!
• EDE (ie anisotropic stress) impacts on observations more strongly than GSF (isotropic pressure)