1. What is in the black box of dark energy: variable cosmological parameters or multiple (interacting) components? Hrvoje Štefančić Universitat de Barcelona IRGAC 2006, Barcelona July 14, 2006

2. Accelerating universe ● accelerating universe – observationally established ● mechanism behind the acceleration? ● dark energy ● alternative mechanisms: modified gravity, braneworlds,... ● dark energy – single component which encodes all our ignorance – efficient effective description - “a black box”

3. Cosmic coincidences ● w presently close to -1 ● possible CC boundary crossing at small redshift ● the ratio of dark energy density and matter energy density presently of order 1 ● Variable cosmological parameters (phenomenology, RGE approaches, holographic DE, 4D effective description of the dynamics in higher dimensions) ● composite dark energy (multiple dark energy components) observational features proposed approaches S. Hannestad, E. Mortsell, JCAP 0409 (2004) 001 A. Upadhye, M. Ishak, P.J. Steinhardt, Phys. Rev. D 72 (2005) 063501 H.K. Jassal, J.S. Bagla, T. Padmanabhan, astro-ph/0601389 G-B. Zhao, J-Q. Xia, B. Feng, X. Zhang, astro-ph/0603621

4. Formalism – variable cosmological parameters ● modification of GR at the level of Einstein equation ● Generalized Bianchi identity ● GR as a limit (for nonvariable parameters)

5. Cosmology – variable cosmological term picture ● FRW metrics – generalized Bianchi identity gives 1) 2) 3) 4) variable CC energy densitymatter density (possibly interacting)

6. Variable cosmological term picture ● variability of parameters with redshift ● Hubble parameter

7. Cosmology – dark energy picture ● standard formalism dark energy matter (noninteracting)

8. Matching of pictures ● Effective dark energy behaviour – matching of pictures ● general results J. Solà, H. Š., Mod. Phys. Lett. A 21 (2006) 479 + + Generalized Bianchi identity

9. Matching of pictures (2) ● redshift dependence of the efective dark energy EOS existence of z* close to z=0

10. Effective dark energy EOS ● slope of the effective dark energy monotonously growing with redshift phantom-like quintessence-like monotonously falling with redshift quintessence-like phantom-like

11. Dark energy effective EOS ● noninteracting (conserved – standard scaling)

12. An example – RG motivated model ● Hubble parameter as a RG scale J. Solà, H. Š., Phys. Lett. B 624 (2005) 147

13. Redshift dependence of the effective EOS (1)

14. Redshift dependence of the effective EOS (2)

15. Explanation of w(z) “coincidence” ● If it exists (to be hopefuly resolved by the upcoming observational data), the CC boundary transition – should happen at small redshift – is allowed for a wide range of parameters (no special values need to be chosen) ● The parameter of effective dark energy EOS is at present close to w(0)=-1 (general result) ● w(z) may exibit substantial variation with the redshift

16. Composite dark energy ● matter component (noninteracting) ● two (interacting) dark energy components: (variable) cosmological term + additional dynamical component J. Grande, J. Solà, H. Š., gr-qc/0604057 interaction dynamics

17. Evolution of analytical (closed form) solution – simple expressions for =const stopping of the expansion: H(z)=0 r has a maximum! How high is it? the redshift dependence of (z)?

18. Parameter constraints ● nucleosynthesis bound: ● existence of the expansion stopping ● height of the maximum of r :

19. Parametric dependence ● dependence

20. Time evolution ● The peak of r(z) is less pronounced

21. Special cases and extensions ● The effect persists for. r is not bounded from below ● Variable cosmological term Lambda and variable Newton coupling G – similar results J. Grande, J. Solà, H. Š., in preparation

22. Conclusions ● effective dark energy picture for the cosmological models with variable parameters ● general and simple analitic results - “RG like” relation between and ● counterintuitive behaviour of the effective dark energy density ● explanation of w(z) “coincidences” ● composite dark energy – solution of the r(z) coincidence problem – when the expansion of the universe stops, r(z) is bounded from above – r(z) may stay close to r(0) for a nonnegligible volume of the parametric space

23. Auxilliary slides

24. Observational evidence ● Dark energy EOS w(z) – various parametrizations used – variability with the redshift – w(z) close to -1 – indication of CC boundary crossing S. Hannestad and E. Mortsell, JCAP 0409 (2004) 001 w(a)=w 0 w 1 (a q + a s q )/(a q w 1 +a s q w 0 )

25. Variable cosmological parameters – motivation (1) ● Phenomenological approaches – “relaxation” of CC – solution of the CC problem – Dirac – big number hypothesis – variable G – cosmology with a decaying vacuum -K. Freese, F.C. Adams, J.A. Frieman, E. Mottola, Nucl. Phys. B 287 (1987) 797 – variable CC interacting with matter - J.M. Overduin, F.I. Cooperstock, Phys. Rev. D 58 (1998) 043506 – variable G and CC - A. Beesham, Nuovo Cim. B 96 (1986) 17

26. Variable cosmological parameters – motivation (2) ● RG cosmology – quantum field theory in curved space-time ● soft decoupling -importance of the most massive fields – scale dependent effective quantum gravity action (Einstein-Hilbert truncation) ● RG flow - IR fixed point hypothesis I.L. Shapiro, J. Solà, Phys. Lett. B 475 (2000) 236 I.L. Shapiro, J. Solà, JHEP 0202 (2002) 006 A. Babić, B. Guberina, R. Horvat, H. Š., Phys. Rev. D 65 (2002) 085002 I.L. Shapiro, J. Solà, C España-Bonet, P. Ruiz-Lapuente, Phys. Lett. B 574 (2003) 149 A. Bonnano, M. Reuter, Phys. Rev. D 65 (2002) 043508 A. Bonnano, M. Reuter, Phys. Lett. B 527 (2000) 9

27. Variable cosmological parameters – motivation (3) ● A.G. Cohen, D.B. Kaplan, A.E. Nelson, Phys. Rev. Lett. 82 (1999) 4971 ● Effective field theory + entropy constraint = relation between UV( ) and IR (1/L) cutoffs ● excluding all states that lie within their Schwarzschield radius ● Holographic dark energy – M. Li, Phys. Lett. B 603 (2004) ● Variable cosmological term - R. Horvat, Phys. Rev. D 70 (2004) 087301

28. Variable cosmological parameters – motivation (4) ● Higher-dimensional models (e.g. GR in 4+N dimensions) ● Variability of e.g. G due to dynamics of extra (compactified) dimensions

29. Effective dark energy EOS

30. Redshift dependence of the effective EOS (3)