Testing gravity at large scales.

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1 Testing gravity at large scales. Outline: How to test gravity at large scales with Cosmology What can we expect from different experiments in the next decade. F. B. Abdalla

2 Cosmology: Concordance Model Heavy elements 0.03% Neutrinos 0.3% Stars 0.5% H + He gas 4% Dark matter 20% Dark Energy 75% Outstanding questions: initial conditions (inflation?) nature of the dark matter nature of the dark energy value of the neutrino mass Is Einstein s theory right at these scales? 04/01/2011 Filipe B. Abdalla (UCL)

3 Standard model of cosmology: Dark energy & dark matter exists, No budget for neutrino mass: Observational data Type Ia Supernovae Galaxy Clusters Cosmic Microwave Background Large Scale Structure Gravitational Lensing Physical effects: Geometry Growth of Structure

4 Dark Energy: Stress Energy vs. Modified Gravity Stress-Energy: Gravity: G µν = 8πG [T µν (matter) + T µν (dark energy)] G µν + f(g µν ) = 8πG T µν (matter) Key Experimental Questions: 1. Is DE observationally distinguishable from a cosmological constant, for which T µν (vacuum) = Λg µν /8πG? To decide, measure w (ratio of pressure to energy density): what precision is needed? 2. Can we distinguish between gravity and stress-energy? 3. If w -1, it likely evolves: how well can/must we measure dw/da?

5 Different methods

6 Sound waves: After recombination: Universe is neutral. Photons can travel freely past the baryons. Phase of oscillation at t rec affects late-time amplitude. Waves are frozen Wayne Hu Before recombination: Universe is ionized. Photons provide enormous pressure and restoring force. Perturbations oscillate as acoustic waves. Eisenstein

7 BAO in LSS

8 Looking back in time in the Universe CREDIT: WMAP & SDSS websites FLAT GEOMETRY

9 Looking back in time in the Universe CLOSED GEOMETRY

10 Looking back in time in the Universe CREDIT: WMAP & SDSS websites

11 Redsfhit space distortions On large scales velocities towards overdensities relate to derivative of the growth with respect to time On small scales they relate to the circular velocity of collapsed objects.

12 Redshift-space clustering r π σ z-space distortions due to peculiar velocities are quantified by correlation fn ξ(σ,π). Two effects visible: Small separations on sky: Fingerof-God ; Large separations on sky: flattening along line of sight

13 Redshift distortions in the correlation maps : Results The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. 2dFGRS (Colless et al. 00) (Peacock et al. 2001, Nature) <Z>= ,000 galaxies f=0.5±0.1 σ=390±50 km/s VVDS LeFevre et al. 05 <Z>= ,000 galaxies f=0.9±0.4 σ=400±50 km/s (Guzzo et al. 2007)

14 The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The The image image cannot cannot be be displayed. displayed. Your Your computer computer may may not not have have enough enough memory memory to to open open the the image, image, or or the the image image may may have have been been corrupted. corrupted. Restart Restart your your computer, computer, and and then then open open the the file file again. again. If If the the red red x still still appears, appears, you you may may have have to to delete delete the the image image and and then then The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert insert it it again. again. insert it again. Background sources Dark matter halos Observer Statistical measure of shear pattern, ~1% distortion Radial distances depend on geometry of Universe Foreground mass distribution depends on growth of structure

15 Different experiments:

16 21cm: a Hydrogen Detector local hydrogen redshifted galaxy SPECTRAL domain 0.5 to 1.4 GHz An SKA sensitivity (100x current) needed to get from z=0.2 galaxies to z ~ 2 Radio telescopes can have enormous fields of view (cf optical etc) Radio telescopes gain sensitivity on galaxies linearly with A (cf optically ) SKA will quickly pinpoint ~10 9 galaxies in 3D (cf ~10 6 galaxies in Sloan) A

17 Current knowledge:

18 Full SKA Predictions Have to rely on educated guesses H 2 HI Abdalla & Rawlings Obreschkow et al No evolution In ~100 days, phased arrays deliver >10 9 galaxies over ~20,000 deg 2 to z~2 (and multiple P(k) to at least z~1)

19 SKA number density (sparser arrays ): In ~100 days, phased arrays deliver >10 9 galaxies over ~20,000 deg 2 to z~2 (and multiple P(k) to at least z~1) Abdalla, Blake & Rawlings 10

20 Results on w: The DETF advocated using an FOM w0-wa, then advocated using a binning PCA approach. In both SKA does very well, but there are caveats. (Abdalla, Blake & Rawlings 09; Tang, Abdalla & Weller 08)

21 Euclid A geometrical probe of the universe proposed for Cosmic Issue Vision Target = + All-sky optical imaging for gravitational lensing All-sky near- IR spectra to H=22 for BAO

22 BAO Science Requirements Category Item Requirement

23 Comparing Euclid to SKA. Results are competitive, and give similar constraints on the dark energy equation of state. i.e. measuring w to below per cent level or a rate of change to 10% level. This is unsurprising given that both surveys are cosmic variance limited over the same volume. But with a caveat of technology!

24 Phased arrays Galactic HI (1420 MHz) from 4-m 2 THEA prototype built at ASTRON All digital with ~10 8 `omnidirectional elements, some separated by λ/2? Computationally impossible. Need ~ dishes or `stations (beams can be very widely separated); time buffering possible Still `Mapping speed = FoV x (A / T sys ) 2 [x BW] improved by >10 5-7!

25 DMD-based NIR spectra and BAO Moral of the story: IR/space based people had a shot of making a technological breakthrough to improve an order of magnitude Kim et al quote equal FOM for SKA and Euclid with DMD s but a factor of 2 worst without DMD s for BAO s. because of a factor of 100 less galaxies Harder to compare lensing because of number counts and systematics but SKA has a larger potential as Euclid is relativelly shallow

26 For RSD we can use all galaxies! If we take the ratio of the deltas for different galaxy types, the delta from the underlying density drops out. Hence it is not dependent on the previous error Can probably do without bar. (MacDonald & Seljak 08) Hence results are in fact much better than a factor of 2 for SKA compared to Euclid Important region

27 More that w because of redshift space distortions and lensing

28 Growth of structure Two perturbation/metric potentials in the Newtonian Gauge This is the Poisson equation DGP GR Koyama (06) DGP GR gives us linear growth equations

29 N.B - Modified Gravity might break the relationship between potential powerspectrum and the matter powerspectrum Deflection Angle To relate the two powerspectra one must take the powerspectrum of (phi + psi). This can be done by substituting to obtain just (phi) and then taking the powerspectrum of the corresponding Poisson equation. Thomas Abdalla & Weller 09 GR phi = psi MG Generally, however, the two modifications lead to

30 Predictions for the expansion history and growth rate The current measurement of H(z) is from Wang & Mukherjee (2007). The error forecast for Euclid measurement of H(z) is obtained using a fisher matrix code (from Y. Wang) Growth Rate f_g(z) Errors from direct measurement of redshift-space distortions on two-point correlation function (from L. Guzzo). Can constrain Modified gravity as Einstein's Eqns have a one to one relation of geometry and growth

31 Conclusions: Gone through some ways to measure gravity at large scales: Geometry and Baryonic acoustic oscillations. Growth and redshift space distortions Geometry and growth via Weak gravitational lensing There are experiments which will be able to do a very good job: How well some of the long term will do for dark energy will depend on technology used, baring in mind all the uncertainties. For Dark energy, with DMD technology, Euclid could compete with SKA. Without DMD s it will not. The SKA will make a bigger impact if there is a large FOV component (focal plane arrays or phased arrays) These experiments will measure the equation of state of dark energy below the per cent level. These experiments will also provide other ways to probe gravity by comparing the way light and matter operates under Einstein's theory and measure fields phi and psi to 10% measuring the growth history to below per cent level.

Gravity Testing and Interpreting Cosmological Measurement

Gravity Testing and Interpreting Cosmological Measurement Cosmological Scale Tests of Gravity Edmund Bertschinger MIT Department of Physics and Kavli Institute for Astrophysics and Space Research January 2011 References Caldwell & Kamionkowski 0903.0866 Silvestri