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 β 0.8 0.4 12 9 2 β 6 3 4 3 2 1 0.4 0.8 1.2 1.6 3 6 9 12 − − − − log10 ↵ β1 β2 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) .