Renormalization group scale-setting in astrophysical systems

1. Renormalization group scale-setting in astrophysical systems Silvije Domazet Ruđer Bošković Institute,ZagrebTheoretical Physics Division 9th Vienna Seminar

2. Overview of presentation • Observations • Possible explanations • Scale-dependent couplings • RGGR approach to galactic rotation curves • Scale-setting procedure • Astrophysical example • Summary S.D., H. Stefancic-‘Renormalization group scale-setting in astrophysical systems’- PLB 703 1 9th Vienna Seminar

3. Observations • Our galaxy (Oort, 1930’s) • Galaxy clusters (Zwicky, 1930’s) • Gravitational lensing (galaxy clusters) • Rotation of galaxies (Rubin, 1970’s) 9th Vienna Seminar

4. Possible explanations • MACHO’s • WIMP’s • MOND (Milgrom) • TeVeS (Bekenstein) • STVG (Moffat) • RGGR (RG corrections of GR) 9th Vienna Seminar

5. Scale-dependent coupling constants • QFT in curved space-time • Fields are quantum • Background is classical 9th Vienna Seminar

6. Effective action 9th Vienna Seminar

7. It can be calculated from the propagator(using RNC and local momentum representation) • Or using Schwinger-DeWitt expansion 9th Vienna Seminar

8. For example, using Sscal , 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 9th Vienna Seminar

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) 9th Vienna Seminar

10. ERGE • Allows for non-perturbative approach • Allows investigation of possible fixed point regimes for gravity • Non-gaussian IR fixed point 9th Vienna Seminar

11. Rotation of galaxies in RGGR approach Rodrigues, Letelier, Shapiro-‘Galaxy rotation curves from General Relativity with Renormalization Group corrections’- JCAP 1004020 • Effective action and it’s low energy behaviour Shapiro, Sola, Stefancic- ‘Running G and Lambda at low energies from physics atM(X): Possiblecosmological and astrophysicalimplications’- JCAP 0501 012 9th Vienna Seminar

12. Variable G, non relativistic approximation of Einstein equations 9th Vienna Seminar

13. An Ansatz for the scale: 9th Vienna Seminar

14. Galaxy rotation curves Rodrigues, Letelier, Shapiro-‘Galaxy rotation curves from General Relativity with Renormalization Group corrections’- JCAP 1004 020 9th Vienna Seminar

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 9th Vienna Seminar

16. Goals of the procedure • 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? 9th Vienna Seminar

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 9th Vienna Seminar

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 iscovariantly conserved 9th Vienna Seminar

19. μ is a scalar • If matter is described as an ideal fluid 9th Vienna Seminar

20. Running models used QFT in curved space-time Non-trivial IR fixed point At this point we need running laws which are provided by the two theoretical approaches already mentioned 9th Vienna Seminar

21. Scale-setting condition:Vacuum • No space-time dependence of μ • Parameters in the action can be considered constant 9th Vienna Seminar

22. Scale-setting condition:Isotropic and homogeneous 3D space-’cosmology’ A.Babic, B.Guberina, R.Horvat, H.Stefancic-‘Renormalization-group running cosmologies. A Scale-setting procedure’- PRD 71 124041 9th Vienna Seminar

23. Scale-setting condition:spherically symmetric, static 3D space-’star’ 9th Vienna Seminar

24. Scale-setting condition:axisymmetric stationary 3D space-’rotating galaxy’ 9th Vienna Seminar

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 9th Vienna Seminar

26. Spherically symmetric system • TOV relation • For many astrophysical systems • Relativistic effects are not so important 9th Vienna Seminar

27. Spherically symmetric system • We can also take • Equation of state polytropic 9th Vienna Seminar

28. Spherically symmetric system • Finally • So, generally 9th Vienna Seminar

29. Summary • Gravitational couplings become scale-dependent(running laws provided by two theoretical approachesare used in our work) • Scale-dependent couplings are introducedat the level of EOM • We assume: • Physical scale is a scalar • Matter energy-momentum tensor is covariantly conserved 9th Vienna Seminar

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 9th Vienna Seminar

31. Thank you for your attention! Silvije Domazet Ruđer Bošković Institute,ZagrebTheoretical Physics Division 9th Vienna Seminar

32. 9th Vienna Seminar

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 9th Vienna Seminar

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 9th Vienna Seminar

35. Explanations (dark matter) • MACHO • Dwarf stars • Neutron stars • Black holes • Observations viagravitational lensing • Can not account forlarge 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 9th Vienna Seminar

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 9th Vienna Seminar

37. Explanations (modify theory) • STVG • John Moffat • Relativistic theory • Postulates the existence of additional vector field • Uses additional scalar fields • Rather successful 9th Vienna Seminar