1. Voids of dark energy Irit Maor Case Western Reserve University With Sourish Dutta PRD 75, gr-qc/0612027 Irit Maor Case Western Reserve University With Sourish Dutta PRD 75, gr-qc/0612027 MAY 8, 2007 CCAPP, OSU MAY 8, 2007 CCAPP, OSU

2. A very quick summary: The universe is accelerating. [kinematics] We do not know why.[dynamics] Cosmological constant? 120 orders of magnitude! The universe is accelerating. [kinematics] We do not know why.[dynamics] Cosmological constant? 120 orders of magnitude!

3. wmap3: w = ¡ 1 : 062 + 0 : 128 ¡ 0 : 079 “wmap does not need quintessence ” (Page)

4. Motivation for the cosmological constant Bludman, 0702085

5. But: “CMB needs something else” Many degeneracies for w(z). Maor et al, 0007297 Upadhye et al, 0411803 Which parameters? Liddle, 0401198 Which priors? Maor et al, 0112526 Which data sets? Bridle et al, 0303180 Many degeneracies for w(z). Maor et al, 0007297 Upadhye et al, 0411803 Which parameters? Liddle, 0401198 Which priors? Maor et al, 0112526 Which data sets? Bridle et al, 0303180

6. Motivation for dynamical dark energy A mild generalization of the old standard cosmological model. A mild generalization of the old standard cosmological model. Scalar fields are not a new concept, “inspired” by fundamental theories. Scalar fields are not a new concept, “inspired” by fundamental theories. Hopes for dynamical fine tuning. Hopes for dynamical fine tuning. Probably an ok description of more complicated scenarios. Probably an ok description of more complicated scenarios. A mild generalization of the old standard cosmological model. A mild generalization of the old standard cosmological model. Scalar fields are not a new concept, “inspired” by fundamental theories. Scalar fields are not a new concept, “inspired” by fundamental theories. Hopes for dynamical fine tuning. Hopes for dynamical fine tuning. Probably an ok description of more complicated scenarios. Probably an ok description of more complicated scenarios. w = w ( z ) 6 = ¡ 1

7. ..but:..but: tracker, k-essence, phantom, coupled, …your favourite DDE model fine tuning not solved! tracker, k-essence, phantom, coupled, …your favourite DDE model fine tuning not solved!

8. Other alternatives SN are wrong SN are wrong Xtra dimensions (  effective w(z) or coupled DDE) Xtra dimensions (  effective w(z) or coupled DDE) your favourite theory of gravity (  same as above) your favourite theory of gravity (  same as above) super horizon modes super horizon modes SN are wrong SN are wrong Xtra dimensions (  effective w(z) or coupled DDE) Xtra dimensions (  effective w(z) or coupled DDE) your favourite theory of gravity (  same as above) your favourite theory of gravity (  same as above) super horizon modes super horizon modes

9. The background: BAOClustersCMBISWSNSZWL…BAOClustersCMBISWSNSZWL…  #% for maybe #% for w 0 d w d z Background measurements will have a very hard time differentiating between CC and DDE. All focus on w(z). Null experiments, how far? Background measurements will have a very hard time differentiating between CC and DDE. All focus on w(z). Null experiments, how far?

10. Looking for the dark stuff Solar system Extrapolation from the cosmic to the solar scale. Clear signature of dark gravity! Solar system Extrapolation from the cosmic to the solar scale. Clear signature of dark gravity!

11. Looking for the dark stuff Perturbations Does DDE cluster on scales less than ~100 Mpc? (yes) A thorough understanding of the behaviour of perturbations is needed. If it clusters, it is not the cosmological constant!! Perturbations Does DDE cluster on scales less than ~100 Mpc? (yes) A thorough understanding of the behaviour of perturbations is needed. If it clusters, it is not the cosmological constant!!

12. Looking for the dark stuff Non linear regime how does the DDE behave? model sensitivity vs generality? Non linear regime how does the DDE behave? model sensitivity vs generality? In progress, with Dutta

13. Implications of inhomogeneities?

14. Large Scale, CMB Weller and Lewis, 0307104

15. Smaller scale inhomogeneities Takada, 0606533

16. Maor and Lahav, 0505308

17. Nunes et al, 0506043

18. Calculate, instead of parameterize, the clustering properties of DDE.

19. L = L G + L m + L Á Standard gravitational action Standard pressureless fluid Standard gravitational action Standard pressureless fluid L G L m L Á = 1 2 ( @ ¹ Á ) 2 ¡ V ( Á ) V ( Á ) = 1 2 m 2 Á 2 m H 0 ¼ 1

20. Linear perturbation (Synchronous gauge) d s 2 = d t 2 ¡ a 2 ( t ) £ ( 1 + 2 ³ ( t ; r )) d r 2 + (( 1 + 2 à ( t ; r )) r 2 d ­ 2 ¤ » ´ _ ³ + 2 _ à ½ m ( t ; r ) ! ½ m ( t ) + ± ½ ( t ; r ) Á ( t ; r ) ! Á ( t ) + ±Á ( t ; r ) V ( Á + ±Á ) = V ( Á ) + ± V ( Á ; ±Á )

21. The equations Zeroth order: standard FRW evolution of the background. Zeroth order: standard FRW evolution of the background. First order: equations for the perturbation variables, which after a Fourier transformation are ODE’s. First order: equations for the perturbation variables, which after a Fourier transformation are ODE’s. Zeroth order: standard FRW evolution of the background. Zeroth order: standard FRW evolution of the background. First order: equations for the perturbation variables, which after a Fourier transformation are ODE’s. First order: equations for the perturbation variables, which after a Fourier transformation are ODE’s.

22. Initial conditions Matter: gaussian, with width well within the horizon. Matter: gaussian, with width well within the horizon. Scalar field: homogeneous IC, with no kinetic energy (w=-1). Scalar field: homogeneous IC, with no kinetic energy (w=-1). Metric: by the constraints equations. Metric: by the constraints equations. Results are insensitive to IC Matter: gaussian, with width well within the horizon. Matter: gaussian, with width well within the horizon. Scalar field: homogeneous IC, with no kinetic energy (w=-1). Scalar field: homogeneous IC, with no kinetic energy (w=-1). Metric: by the constraints equations. Metric: by the constraints equations. Results are insensitive to IC

23. ResultsResults Anti-correlation between matter and DE perturbations

24. ResultsResults Amplitude grows fast!

25. ResultsResults “cross-over”

26. Equation of State Background EOS Linear correction to EOS First order corrected EOS ± w = 1 ½ 0 ¡ ± p ¡ w 0 ± ½ ¢ w 0 = p 0 ½ 0 = 1 2 _ Á 2 ¡ V 1 2 _ Á 2 + V w 1 = w 0 + ± w

27. Equation of state Spatial profile of the equation of state

28. Why a void?

29. Void formation Energy density correction: PE correction < 0 KE correction > 0 KE correction quickly dominates void ± ½ Á = m 2 Á ± Á + _ Á ± _ Á

30. Acceleration slows, but doesn’t change sign. Á > 0 _ Á < 0 ±Á < 0 ± KE > 0 ± _ Á < 0 ± PE < 0

31. ConclusionsConclusions DDE develops voids [ripples]. Our results are generic for slow-roll DDE. Possible interesting dynamics in the non-linear regime. Observables? DDE develops voids [ripples]. Our results are generic for slow-roll DDE. Possible interesting dynamics in the non-linear regime. Observables?