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

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

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

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

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

th Vienna Seminar6 Effective action

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

th 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

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) th Vienna Seminar9

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

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

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

An Ansatz for the scale: th Vienna Seminar13

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

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 th Vienna Seminar15

Goals of the procedure th 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?

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 th Vienna Seminar17

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 th Vienna Seminar18

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

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

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

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

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

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

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 th Vienna Seminar25

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

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

Spherically symmetric system Finally So, generally th Vienna Seminar28

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 th Vienna Seminar29

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 th Vienna Seminar30

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

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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 th Vienna Seminar33

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 th Vienna Seminar34

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 th Vienna Seminar35

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 th Vienna Seminar36

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