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 ?

Perturbed conservation equation

Scalar equations of motion

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)

Tensor Sector - easy

B=0

Simplest model is a massive graviton !

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

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)