CONSTRAINTS ON DARK ENERGY AND MODIFIED GRAVITY

Richard Battye Jodrell Bank Centre for Astrophysics

Collaborators : Adam Moss (University of Nottingham ) Jonathan Pearson (Durham University) Beyond the standard model

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 • 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)