Testing Modified Gravity using WiggleZ David Parkinson

Transcription

1 Testing Modified Gravity using WiggleZ David Parkinson 1

2 Outline Introduction Modified Gravity models Structure Formation WiggleZ Dark Energy Survey Results Conclusions Testing Modified Gravity with WiggleZ / David Parkinson 2/22

3 Dark Fluids General Relativity (Einsteinian gravity) is broken It requires either the existence Dark Fluids or modification of the Einstein equations to explain the rotation and motions of galaxies Instead of Dark Energy, maybe the law of gravity is wrong c.f. perihelion of Mercury - Vulcan vs. Einstein Models of Modified Gravity require more than distance data to test, as they behave differently on different Testing Modified Gravity with WiggleZ / David Parkinson 3/22

4 Dark Fluids General Relativity (Einsteinian gravity) is broken It requires either the existence Dark Fluids or modification of the Einstein equations to explain the rotation and motions of galaxies Instead of Dark Energy, maybe the law of gravity is wrong c.f. perihelion of Mercury - Vulcan vs. Einstein Models of Modified Gravity require more than distance data to test, as they behave differently on different Testing Modified Gravity with WiggleZ / David Parkinson 3/22

5 Dark Fluids General Relativity (Einsteinian gravity) is broken It requires either the existence Dark Fluids or modification of the Einstein equations to explain the rotation and motions of galaxies Instead of Dark Energy, maybe the law of gravity is wrong c.f. perihelion of Mercury - Vulcan vs. Einstein Models of Modified Gravity require more than distance data to test, as they behave differently on different Testing Modified Gravity with WiggleZ / David Parkinson 3/22

6 Models Testing Modified Gravity 4with WiggleZ / David Parkinson 4/22

7 Models Growth index (γ) as a free parameter Testing Modified Gravity 4with WiggleZ / David Parkinson 4/22

8 Models Growth index (γ) as a free parameter Testing Modified Gravity 4with WiggleZ / David Parkinson 4/22

9 Models Growth index (γ) as a free parameter Two faces of Ωm - decouple matter density that contributes to expansion history and growth history Testing Modified Gravity 4with WiggleZ / David Parkinson 4/22

10 Models Growth index (γ) as a free parameter Two faces of Ωm - decouple matter density that contributes to expansion history and growth history f(r) - Modified Einstein-Hilbert action Testing Modified Gravity 4with WiggleZ / David Parkinson 4/22

11 Models Growth index (γ) as a free parameter Two faces of Ωm - decouple matter density that contributes to expansion history and growth history f(r) - Modified Einstein-Hilbert action DGP - Davli-Gabadadze-Porrati model Testing Modified Gravity 4with WiggleZ / David Parkinson 4/22

12 Models Growth index (γ) as a free parameter Two faces of Ωm - decouple matter density that contributes to expansion history and growth history f(r) - Modified Einstein-Hilbert action DGP - Davli-Gabadadze-Porrati model Massive Gravity - where the graviton has some inherent or induced mass Testing Modified Gravity 4with WiggleZ / David Parkinson 4/22

13 Models Growth index (γ) as a free parameter Two faces of Ωm - decouple matter density that contributes to expansion history and growth history f(r) - Modified Einstein-Hilbert action DGP - Davli-Gabadadze-Porrati model Massive Gravity - where the graviton has some inherent or induced mass Galileon models - the scalar brane-bending term in 5D gravity obeys Galileon symmetry Testing Modified Gravity 4with WiggleZ / David Parkinson 4/22

14 Models Growth index (γ) as a free parameter Two faces of Ωm - decouple matter density that contributes to expansion history and growth history f(r) - Modified Einstein-Hilbert action DGP - Davli-Gabadadze-Porrati model Massive Gravity - where the graviton has some inherent or induced mass Galileon models - the scalar brane-bending term in 5D gravity obeys Galileon symmetry TeVeS - the relativistic successor to MOND Testing Modified Gravity 4with WiggleZ / David Parkinson 4/22

15 Models Growth index (γ) as a free parameter Two faces of Ωm - decouple matter density that contributes to expansion history and growth history f(r) - Modified Einstein-Hilbert action DGP - Davli-Gabadadze-Porrati model Massive Gravity - where the graviton has some inherent or induced mass Galileon models - the scalar brane-bending term in 5D gravity obeys Galileon symmetry TeVeS - the relativistic successor to MOND Testing Modified Gravity 5with WiggleZ / David Parkinson 5/22

16 f(r) gravity We can replace the Ricci scalar in Einstein-Hilbert action with more complex function, f(r) If so if f(r)->0, then we recover ordinary GR. If we vary this action with respect to the metric, we produce the modified Einstein equations If f(r) is a constant, you recover the standard Λ term (the cosmological constant) If f(r) is linear with R, all you achieve is a rescaling of Newton s constant G Testing Modified Gravity 6with WiggleZ / David Parkinson 6/22

17 Equations of motion By inserting the definition of R from the homogeneous FRW metric into the Einstein equation, we produce a modified Hubble law Song, Hu & Sawicki (2007) showed how to create models that have the same expansion history as ordinary DE, but make different LSS predictions. We assume H given by (Note that ρ DE is not the Dark Energy density, merely an effective density induced in the Hubble law by the modification of gravity) We can now reconstruct f(r) from the expansion history using Testing Modified Gravity 7with WiggleZ / David Parkinson 7/22

18 Reconstructed f(r) Testing Modified Gravity 8with WiggleZ / David Parkinson 8/22

19 Testing gravity through Structure Formation How do we test gravity on Earth watching particles fall towards each other Structure forms in the universe under gravity Small perturbations in matter density (δ) grow by attracting and accumulating material The rate of growth on large scales (linear physics) is set by the theory of gravity We find rate of growth is a power law of the density of matter Testing Modified Gravity 9with WiggleZ / David Parkinson 9/22

20 f(r) structure formation We perturb the metric, allowing for space and time dependent gravitation potentials GR predicts a relationship between Φ and Ψ, such that Φ=-Ψ. This is broken in f(r) gravity, as Φ evolves as If we know the history for H and B, we can solve for Φ and Ψ The metric ratio (g=(φ+ψ)/(φ-ψ)) enters into the perturbation equation, modifying the growth of structure on different scales Testing Modified Gravity 10with WiggleZ / David Parkinson 10/22

21 f(r) density perturbations Testing Modified Gravity 11with WiggleZ / David Parkinson 11/22

22 f(r) growth Testing Modified Gravity 12with WiggleZ / David Parkinson 12/22

23 f(r) predictions for gamma Image Credit: Chris Blake Testing Modified Gravity 13with WiggleZ / David Parkinson 13/22

24 WiggleZ Survey See also talk by Chris Blake WiggleZ is a spectroscopic galaxy redshift survey conducted on the AAT It covers 1000 square degrees over the southern sky, and has measured the redshift of around 240,000 galaxies It targets bright, star-forming galaxies at high redshift by using the GALEX satellite to generate a source catalogue It started in 2006 and finished in January 2011 (this year!) Testing Modified Gravity 14with WiggleZ / David Parkinson 14/22

25 The WiggleZ Team University of Queensland: Michael Drinkwater, Tamara Davis, David Parkinson, Signe Reimer-Sorensen Swinburne: Chris Blake, Carlos Contreras, Warrick Couch, Darren Croton, Karl Glazebrook, Tornado Li, Felipe Marin, Greg Poole, Emily Wisniowski AAO: Sarah Brough, Matthew Colless, Mike Pracy, Rob Sharp Scott Croom (USyd), Ben Jelliffe (USyd), David Woods (UBC), Kevin Pimblet (Monash), Russell Jurek (ATNF), Rachel Mandelbaum (Princeton) Galex Team: Karl Forster, Barry Madore, Chris Martin, Ted Wyder RCS2 Team: David Gilbank, Mike Gladders, Howard Yee Associate: Berian James (DARK) Testing Modified Gravity 15with WiggleZ / David Parkinson 15/22

26 Redshift-space distortions The motions of galaxies are perturbed by the local gravitational field The Power spectrum/ correlation function in the line of sight is distorted relative to the transverse direction Assuming these motions are generated by matter perturbations, we can measure the growth of structure Credit: Chris Blake Testing Modified Gravity 16with WiggleZ / David Parkinson 16/22

27 2D Power Spectra Testing Modified Gravity 17with WiggleZ / David Parkinson 17/22

28 Growth of structure Credit: Chris Blake Testing Modified Gravity 18with WiggleZ / David Parkinson 18/22

29 AP/Growth measurements Testing Modified Gravity 19with WiggleZ / David Parkinson 19/22

30 Theories of Gravity Testing Modified Gravity 20with WiggleZ / David Parkinson 20/22

31 WMAP only Testing Modified Gravity 21with WiggleZ / David Parkinson 21/22

32 WiggleZ WMAP only Testing Modified Gravity 21with WiggleZ / David Parkinson 21/22

33 WiggleZ WMAP Combined only Testing Modified Gravity 21with WiggleZ / David Parkinson 21/22

34 Conclusions We can use the WiggleZ redshift-space distortion measurements of the growth of structure to probe different models of modified gravity f(r) gravity is a generic way to modify gravity, using only geometric quantities (as in GR), that can reproduce exactly the same expansion history as ΛCDM, but has a very different growth history The WiggleZ growth data, combined with WMAP measurements of the amplitude of perturbations at early times, constrains the Compton Wavelength of the theory B0<10-3 (at 95% conf. limits) Testing Modified Gravity 22with WiggleZ / David Parkinson 22/22