1. Renormalization group scale-setting in astrophysical systems Silvije Domazet Ru đ er Bošković Institute,Zagreb Theoretical Physics Division 02.12.2012.9th Vienna Seminar1

2. Overview of presentation Observations Possible explanations Scale-dependent couplings RGGR approach to galactic rotation curves Scale-setting procedure Astrophysical example Summary 02.12.2012.9th Vienna Seminar2 S.D., H. Stefancic-‘Renormalization group scale-setting in astrophysical systems’- PLB 703 1

3. Observations Our galaxy (Oort, 1930’s) Galaxy clusters (Zwicky, 1930’s) Gravitational lensing (galaxy clusters) Rotation of galaxies (Rubin, 1970’s) 02.12.2012.9th Vienna Seminar3

4. Possible explanations MACHO’s WIMP’s MOND (Milgrom) TeVeS (Bekenstein) STVG (Moffat) RGGR (RG corrections of GR) 02.12.2012.9th Vienna Seminar4

5. Scale-dependent coupling constants QFT in curved space-time Fields are quantum Background is classical 02.12.2012.9th Vienna Seminar5

6. 02.12.2012.9th Vienna Seminar6 Effective action

7. It can be calculated from the propagator (using RNC and local momentum representation) Or using Schwinger-DeWitt expansion 02.12.2012.9th Vienna Seminar7

8. 02.12.2012.9th Vienna Seminar8 For example, using S scal, from the propagator (background field method) We can obtain β functions and the running laws for gravitational parameters L.Parker, D.Toms -‘Explicit curvature dependence of coupling constants’- PRD 31 2424

9. Scale dependent coupling constants M.Niedermaier, M.Reuter-‘The Asymptotic Safety Scenario in Quantum Gravity’- Living Reviews in Relativity 9 (2006) Effective action Parameter k is a cut-off (all momenta higher than k are integrated out; those smaller are not) 02.12.2012.9th Vienna Seminar9

10. ERGE Allows for non-perturbative approach Allows investigation of possible fixed point regimes for gravity Non-gaussian IR fixed point 02.12.2012.9th Vienna Seminar10

11. Rotation of galaxies in RGGR approach Rodrigues, Letelier, Shapiro-‘Galaxy rotation curves from General Relativity with Renormalization Group corrections’- JCAP 1004 020 Effective action and it’s low energy behaviour 02.12.2012.9th Vienna Seminar11 Shapiro, Sola, Stefancic- ‘Running G and Lambda at low energies from physics at M(X): Possible cosmological and astrophysical implications’- JCAP 0501 012

12. Variable G, non relativistic approximation of Einstein equations 02.12.2012.9th Vienna Seminar12

13. An Ansatz for the scale: 02.12.2012.9th Vienna Seminar13

14. Galaxy rotation curves Rodrigues, Letelier, Shapiro-‘Galaxy rotation curves from General Relativity with Renormalization Group corrections’- JCAP 1004 020 02.12.2012.9th Vienna Seminar14

15. Scale-setting procedure What have we seen so far: Parameters of gravitational action become scale dependent QFT in CS introduces dependence on the scale μ through regularization and renormalization Asymptotic safety scenario in Qunatum Gravity has a scale k which serves as a cut-off RGGR approach (QFT in CS) using a certain Ansatz for the scale provides good results for rotation of galaxies 02.12.2012.9th Vienna Seminar15

16. Goals of the procedure 02.12.2012.9th Vienna Seminar16 We want to find physical quantities related to scales μ and k (as for instance in QED the μ dependence relates to q dependence of running charge) Can we justify the Ansatz used in RGGR approach to rotation of galaxies?

17. Scale-setting procedure Scale dependent couplings At the level of solutions of Einstein’s equations At the level of Einstein’s equations At the level of the action 02.12.2012.9th Vienna Seminar17

18. Scale-setting procedure Remark: from here on μ represents the physical scale we are looking for Einstein tensor covariantly conserved Assumption: matter energy-momentum tensor is covariantly conserved 02.12.2012.9th Vienna Seminar18

19. μ is a scalar If matter is described as an ideal fluid 02.12.2012.9th Vienna Seminar19

20. Running models used QFT in curved space-time Non-trivial IR fixed point 02.12.2012.9th Vienna Seminar20 At this point we need running laws which are provided by the two theoretical approaches already mentioned

21. Scale-setting condition:Vacuum No space-time dependence of μ Parameters in the action can be considered constant 02.12.2012.9th Vienna Seminar21

22. Scale-setting condition:Isotropic and homogeneous 3D space-’cosmology’ 02.12.2012.9th Vienna Seminar22 A.Babic, B.Guberina, R.Horvat, H.Stefancic-‘Renormalization-group running cosmologies. A Scale-setting procedure’- PRD 71 124041

23. Scale-setting condition:spherically symmetric, static 3D space-’star’ 02.12.2012.9th Vienna Seminar23

24. Scale-setting condition:axisymmetric stationary 3D space-’rotating galaxy’ 02.12.2012.9th Vienna Seminar24

25. Scale identification In both astrophysical situations we ended up with the same scale setting condition, which can be written this way So for both running laws chosen the important physical quantity is pressure 02.12.2012.9th Vienna Seminar25

26. Spherically symmetric system TOV relation For many astrophysical systems Relativistic effects are not so important 02.12.2012.9th Vienna Seminar26

27. Spherically symmetric system We can also take Equation of statepolytropic 02.12.2012.9th Vienna Seminar27

28. Spherically symmetric system Finally So, generally 02.12.2012.9th Vienna Seminar28

29. Summary Gravitational couplings become scale-dependent (running laws provided by two theoretical approaches are used in our work) Scale-dependent couplings are introduced at the level of EOM We assume: Physical scale is a scalar Matter energy-momentum tensor is covariantly conserved 02.12.2012.9th Vienna Seminar29

30. Summary Results: A consistency condition for the choice of relevant physical scale When used in astrophysical situation the scale-setting procedure gives RGGR approach provides good results for rotation of galaxies when compared to other models (DM and modified theory models) using the above relation as an Ansatz 02.12.2012.9th Vienna Seminar30

31. Thank you for your attention! Silvije Domazet Ru đ er Bošković Institute,Zagreb Theoretical Physics Division 02.12.2012.9th Vienna Seminar31

32. 02.12.2012.9th Vienna Seminar32

33. Observations Our galaxy Oort Early 1930’s Studies stellar motions in local neighbourhood Galactic plain contains more mass than is visible Clusters of galaxies Fritz Zwicky Early 1930’s Motion of galaxies on the edge of cluster Virial theorem is used to make a mass estimate More mass than can be deduced from visible matter alone 02.12.2012.9th Vienna Seminar33

34. Observations Rotation of galaxies Vera Rubin 1970’s Measures rotation velocity of galaxies Gravitational lensing Bending of light by galaxy clusters Provides mass estimates They are in disagreement with mass estimates from visible components 02.12.2012.9th Vienna Seminar34

35. Explanations (dark matter) MACHO Dwarf stars Neutron stars Black holes Observations via gravitational lensing Can not account for large amounts of dark matter WIMP Neutrino LSP Axion Kaluza-Klein excitations Can not account for the observed quantity of missing matter Or have not been detected 02.12.2012.9th Vienna Seminar35

36. Explanations (modify theory) MOND Milgrom Modify Newton laws for low accelerations Far from galaxy center TeVeS Bekenstein Relativistic theory yielding MOND phenomenology Multi-field theory Introduces several new parameters and functions Rather complicated 02.12.2012.9th Vienna Seminar36

37. Explanations (modify theory) STVG John Moffat Relativistic theory Postulates the existence of additional vector field Uses additional scalar fields Rather successful 02.12.2012.9th Vienna Seminar37