1. Constraining Dark Energy with Double Source Plane Strong Lenses Thomas Collett With: Matt Auger, Vasily Belokurov, Phil Marshall and Alex Hall ArXiv:1203.2758

2. Constraining Dark Energy with Double Source Plane Strong Lenses 2 ● How do we probe dark energy? ● How do we know it exists? ● What are double source plane strong lenses? ● How can we do cosmology with double source plane lenses? ● What are the best double source plane systems for cosmology? ● How well can the dark energy equation of state be constrained with double source plane lenses? Outline

3. Constraining Dark Energy with Double Source Plane Strong Lenses 3 Our universe is expanding. And that expansion appears to be accelerating. But gravity pulls masses together. It doesn't push them apart! What's causing the acceleration? How do we probe dark energy? (and how do we know it exists?)

4. Constraining Dark Energy with Double Source Plane Strong Lenses 4 Dark energy as an additional cosmological fluid w ~ –1 (but it could easily be –1.1 or –0.9. )* Results are from several different cosmological probes. All look at different quantities that change depending on w: ● Angular diameter distances, ● Luminosity distances, ● Growth of large scale structure in the universe. Are there other observables that can teach us about dark energy? w is not necessarily a constant, but I'll spend most of this talk assuming that it is. We can define a new fluid, that exerts a negative pressure on the universe, and give it an equation of state relating the pressure to the density:

5. Constraining Dark Energy with Double Source Plane Strong Lenses 5 What is double source plane strong lensing? A gravitational lens system with two background sources, each at a different redshift.

6. Gravitational lensing is like an optical bench. Image configurations depend on the underlying cosmology. Constraining Dark Energy with Double Source Plane Strong Lenses 6 What is double source plane strong lensing?

7. Constraining Dark Energy with Double Source Plane Strong Lenses 7 A gravitational lens system with two background sources, each at a different redshift. What is double source plane strong lensing? SLACS J0946+1006

8. Constraining Dark Energy with Double Source Plane Strong Lenses 8 A gravitational lens system with two background sources, each at a different redshift. What is double source plane strong lensing? SLACS J0946+1006 Lens Galaxy

9. Constraining Dark Energy with Double Source Plane Strong Lenses 9 A gravitational lens system with two background sources, each at a different redshift. What is double source plane strong lensing? SLACS J0946+1006 Images of the intermediate source

10. Constraining Dark Energy with Double Source Plane Strong Lenses 10 A gravitational lens system with two background sources, each at a different redshift. What is double source plane strong lensing? SLACS J0946+1006 Images of the background source

11. Constraining Dark Energy with Double Source Plane Strong Lenses 11 Galaxy scale lenses: Gavazzi et al. (2008), J0946: No redshift for the second source, so no cosmology. Cluster scale lenses: Soucail et al. (2004): 4 sources behind Abel 2218. 0.7 < z < 5.5. Jullo et al (2010): 12 sources behind Abel 1689. 1 < z < 5. ● But clusters are complicated! ● Images are far apart, so feel the different parts of the cluster ● Need to assume a lens model. ● Jullo et al. threw away images for 22 more sources Previous Results:

12. Constraining Dark Energy with Double Source Plane Strong Lenses 12 Jullo et al. Results: Ω M = 0.25 ± 0.05, w DE = −0.97 ± 0.07 (Abel 1689 + WMAP5 + X-ray cluster constraints)

13. Constraining Dark Energy with Double Source Plane Strong Lenses 13 Jullo et al. Results: Ω M = 0.25 ± 0.05, w DE = −0.97 ± 0.07 (Abel 1689 + WMAP5 + X-ray cluster constraints)

14. Constraining Dark Energy with Double Source Plane Strong Lenses 14 Jullo et al. Results: Ω M = 0.25 ± 0.05, w DE = −0.97 ± 0.07 (Abel 1689 + WMAP5 + X-ray cluster constraints)

15. Constraining Dark Energy with Double Source Plane Strong Lenses 15 Two important quantities: The Einstein Radius: Angular diameter distances (flat universe, w constant): So why do I need a second source to do cosmology? ● We can't reliably infer the mass of the lens.

16. Constraining Dark Energy with Double Source Plane Strong Lenses 16 The Ratio of Einstein Radii. The observable: Independent of the Hubble constant.

17. Constraining Dark Energy with Double Source Plane Strong Lenses 17 The observable: Independent of the Hubble constant. The Ratio of Einstein Radii.

18. Constraining Dark Energy with Double Source Plane Strong Lenses 18 Two cosmological parameters: Ω M and w DE If I observed a double source plane lens system, how well could I constrain Ω M and w DE ? Let's assume some redshifts, and a 1% uncertainty on η. Constraining Cosmology. (J0946: 0.22 0.61 ~ 2)

19. Constraining Dark Energy with Double Source Plane Strong Lenses 19 Constraining Cosmology. z l =0.35 z s1 = 0.6 z s2 = 1.5

20. Constraining Dark Energy with Double Source Plane Strong Lenses 20 Constraining Cosmology. z l =0.35 z s1 = 0.6 z s2 = 1.5 WMAP

21. Constraining Dark Energy with Double Source Plane Strong Lenses 21 Constraining Cosmology. z l =0.35 z s1 = 0.6 z s2 = 1.5 WMAP Combination

22. Constraining Dark Energy with Double Source Plane Strong Lenses 22 What if we'd picked different redshifts? 2.0 Intuition: The light from the background source probes a longer epoch of expansion, so deviations from w = -1 sh ould be more pronounced ● Expect more constraining power.

23. Constraining Dark Energy with Double Source Plane Strong Lenses 23 What if we'd picked different redshifts? Far source further away → More constraining power z l =0.35 z s1 = 0.6 z s2 = 1.5 z l =0.35 z s1 = 0.6 z s2 = 2.0

24. Constraining Dark Energy with Double Source Plane Strong Lenses 24 What if we'd picked different redshifts? 0.45 Intuition: Less of D s2 forms part of D s1 so deviations from the D s2 / D s1 ( w = -1 ) would be more pronounced ● Expect more constraining power.

25. Constraining Dark Energy with Double Source Plane Strong Lenses 25 What if we'd picked different redshifts? Near source closer to lens → More constraining power z l =0.35 z s1 = 0.6 z s2 = 1.5 z l =0.35 z s1 = 0.45 z s2 = 1.5

26. Constraining Dark Energy with Double Source Plane Strong Lenses 26 What if we'd picked different redshifts? 0.8 Intuition: Altered the ratios of D s / D ls ● Might be helpful, but might not! ● (Although if we moved the lens too close to the observer, the rings will lie on top of each other, regardless of the cosmology – which would make constraining cosmology much harder) 0.55

27. Constraining Dark Energy with Double Source Plane Strong Lenses 27 What if we'd picked different redshifts? Move lens, and first source further away. → Tilts the allowed region z l =0.35 z s1 = 0.6 z s2 = 1.5 z l =0.55 z s1 = 0.8 z s2 = 1.5

28. Constraining Dark Energy with Double Source Plane Strong Lenses 28 What if we'd picked different redshifts? Move lens, and first source further away. → Tilts the allowed region Doesn't help much when combined with WMAP. ☹ z l =0.35 z s1 = 0.6 z s2 = 1.5 z l =0.55 z s1 = 0.8 z s2 = 1.5

29. Constraining Dark Energy with Double Source Plane Strong Lenses 29 The best systems for cosmology: 1. High redshift background source 2. Close lens–source pair 3. Lens redshift > 0.2 But we really want a population of systems.

30. Constraining Dark Energy with Double Source Plane Strong Lenses 30 The best systems for cosmology: 1. High redshift background source 2. Close lens–source pair 3. Lens redshift > 0.2 But we really want a population of systems. Where's the best place to look?.... Known lenses! 1. Massive lens 2. Small separation between lens and source Ideally also: 3. Simple lens geometry (easier to model) 4. Low mass source (less secondary lensing)

31. Constraining Dark Energy with Double Source Plane Strong Lenses 31 How can we forecast a population of systems? We have to assume an observing strategy. Objective: Find the best double source plane systems for cosmology Lens and first source are known, but we have to find the second source. 1) Want to maximise the number of double source plane systems. 2) Want to maximise the redshift of second sources. 3) Want to find them efficiently. 4) Would be nice to do ancillary science with the known source and lens. Millimetre Observations? If anyone has any other ideas, please talk to me afterwards!

32. Constraining Dark Energy with Double Source Plane Strong Lenses 32 What can we do with a population of systems? 1.1mm, S > 1 mJy. z l = 0.2, σ V = 350 km s -1 P(Source) = 6% Source model from Bethermin et al. 2011

33. Constraining Dark Energy with Double Source Plane Strong Lenses 33 SLACS: 1.1mm, S > 1 mJy → ~1.5 double source plane systems (1.5 in 78) 1.1mm, S > 0.3 mJy → ~3 double source plane systems (3 in 78) Cosmology with a population of systems. But can be more efficient if you focus only on the most massive lenses.

34. Constraining Dark Energy with Double Source Plane Strong Lenses 34 Constraints with 6 systems. Pick the set of systems that provided the median constraints on w. WMAP+6 systems is ~2.5 times better than WMAP+1. WMAP+ 1 system w DE = −0.99 ± 0.27 6 systems w DE = −1.01 ± 0.11

35. Constraining Dark Energy with Double Source Plane Strong Lenses 35 Beyond wCDM Evolving models of dark energy: Not very informative without a prior on Ω M. But combined with simulated Planck forecasts, these constraints are almost as powerful for constraining dark energy as Planck+SNe

36. Constraining Dark Energy with Double Source Plane Strong Lenses 36 Summary ● Double source plane lenses provide another way to probe dark energy. ● The best double source systems for cosmography have a close lens–source pair and a high redshift background source. ● A population of systems is much better than one ● A handful of double source plane systems have the potential to be competitive with more mature cosmic probes Future work Conduct detailed analysis of biases and uncertainties. Make forecasts for upcoming surveys. If you look LSST deep there should be hundreds of double source plane systems!

37. Spare Slides Constraining Dark Energy with Double Source Plane Strong Lenses 37

38. Constraining Dark Energy with Double Source Plane Strong Lenses 38 Constraining Dark Energy with Double Source Plane Strong Lenses 38 What about the assumption of flatness? Constraining Dark Energy with Double Source Plane Strong Lenses Ω k ≡ 0 Ω k ≠ 0

39. Constraining Dark Energy with Double Source Plane Strong Lenses 39 What if we can't measure the ratio of Einstein radii to 1%? 1. Compound lensing – the intermediate source has mass 2. The lens is an astrophysical object – they aren't perfectly isothermal or perfectly spherical

40. Constraining Dark Energy with Double Source Plane Strong Lenses 40 Constraining Dark Energy with Double Source Plane Strong Lenses 40 Planck+6 Constraining Dark Energy with Double Source Plane Strong Lenses

41. 41 Constraints with 6 systems. Pick the set of systems that provided the median constraints on w. WMAP+6 systems is ~2.5 times better than WMAP+1. WMAP+ 1 system w DE = −0.99 ± 0.27 6 systems w DE = −1.01 ± 0.11 WMAP+BAO+Time Delay+ 6 systems w DE = −1.04 ± 0.09

42. Constraining Dark Energy with Double Source Plane Strong Lenses 42 We observe dark energy's effect on the universe's expansion. How do we probe dark energy? (and how do we know it exists?) Our universe is expanding. And that expansion appears to be accelerating! Riess et al. (1998) & Perlmutter et al. (1999) found evidence that type Ia supernovae were dimmer than predicted by models of a universe made entirely from baryonic matter.

43. Constraining Dark Energy with Double Source Plane Strong Lenses 43 On cosmic scales, the baryonic matter in our universe only interacts via gravity. Gravity pulls masses together. It doesn't push them apart! So we need to add something to the universe (or change the equations governing gravity), that can cause accelerated expansion. What is it? Dark Energy * * This is perhaps the most unsatisfactory answer possible. Knowing that I'm called Tom, doesn't tell you much about me. Nor does giving dark energy a name give us any physical insights. How do we probe dark energy? (and how do we know it exists?)

44. Constraining Dark Energy with Double Source Plane Strong Lenses 44 We can define a new fluid, that exerts a negative pressure on the universe, and give it an equation of state relating the pressure to the density: Perhaps an easier way to visualise w, is how the fluid's energy density scales with cosmic expansion. ● Non-relativistic matter: w = 0,ρ ~ a -3 ● Relativistic Matter: w = 1/3, ρ ~ a -4 ● Dark energy: w < -1/3, ρ ~ a -3(1+w) ➢ Cosmological Constant: w = -1,ρ ~ Constant How do we probe dark energy? (and how do we know it exists?)

45. Constraining Dark Energy with Double Source Plane Strong Lenses 45 Current constraints w ~ –1 But it could easily be –1.1 or –0.9. Results from Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations (BAO), Supernovae (SNe) and others. All look at different quantities that change depending on w: ● Angular diameter distances, ● Luminosity distances, ● Growth of large scale structure in the universe. w is not necessarily a constant, but I'll spend most of this talk assuming that it is.