Renormalization group scale-setting in astrophysical systems

Silvije Domazet

Ruđer Bošković Institute,ZagrebTheoretical Physics Division

02.12.2012. 9th Vienna Seminar 1

Overview of presentationObservationsPossible explanationsScale-dependent couplingsRGGR approach to galactic rotation curvesScale-setting procedureAstrophysical exampleSummary

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S.D., H. Stefancic-‘Renormalization group scale-setting in astrophysical systems’- PLB 703 1

ObservationsOur galaxy (Oort, 1930’s)Galaxy clusters (Zwicky, 1930’s)Gravitational lensing (galaxy clusters)Rotation of galaxies (Rubin, 1970’s)

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Possible explanationsMACHO’sWIMP’sMOND (Milgrom)TeVeS (Bekenstein)STVG (Moffat)RGGR (RG corrections of GR)

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Scale-dependent coupling constantsQFT in curved space-time

Fields are quantum

Background is classical

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Effective action

It can be calculated from the propagator(using RNC and local momentum representation)

Or using Schwinger-DeWitt expansion

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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

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)

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ERGE

Allows for non-perturbative approachAllows investigation of possible fixed point

regimes for gravityNon-gaussian IR fixed point

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Rotation of galaxies in RGGR approachRodrigues, Letelier, Shapiro-‘Galaxy rotation curves from General Relativity with Renormalization Group corrections’- JCAP 1004 020

Effective action and it’s low energy behaviour

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Shapiro, Sola, Stefancic-‘Running G and Lambda at low energies from physics at M(X): Possible cosmological and astrophysical implications’- JCAP 0501 012

Variable G, non relativistic approximation of Einstein equations

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An Ansatz for the scale:

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Galaxy rotation curves

Rodrigues, Letelier, Shapiro-‘Galaxy rotation curves from General Relativity with Renormalization Group corrections’- JCAP 1004 020

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Scale-setting procedureWhat 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

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Goals of the procedure

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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 couplingsAt the level of solutions of Einstein’s equationsAt the level of Einstein’s equationsAt the level of the action

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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

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μ is a scalar

If matter is described as an ideal fluid

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Running models used

QFT in curved space-time

Non-trivial IR fixed point

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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 μParameters in the action can be considered

constant

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Scale-setting condition:Isotropic and homogeneous 3D space-’cosmology’

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A.Babic, B.Guberina, R.Horvat, H.Stefancic-‘Renormalization-group running cosmologies. A Scale-setting procedure’- PRD 71 124041

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

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

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Scale identificationIn 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

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Spherically symmetric systemTOV relation

For many astrophysical systemsRelativistic effects are not so important

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Spherically symmetric systemWe can also take

Equation of state polytropic

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Spherically symmetric systemFinally

So, generally

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SummaryGravitational 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 scalarMatter energy-momentum tensor is covariantly

conserved02.12.2012. 9th Vienna Seminar 29

SummaryResults:

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

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Thank you for your attention!

Silvije Domazet

Ruđer Bošković Institute,ZagrebTheoretical Physics Division

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ObservationsOur galaxy

Oort Early 1930’s Studies stellar

motions in local neighbourhood

Galactic plain contains more mass than is visible

Clusters of galaxiesFritz ZwickyEarly 1930’sMotion of galaxies on

the edge of clusterVirial theorem is

used to make a mass estimate

More mass than can be deduced from visible matter alone

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ObservationsRotation of galaxies

Vera Rubin1970’sMeasures rotation

velocity of galaxies

Gravitational lensingBending of light by

galaxy clustersProvides mass

estimatesThey are in

disagreement with mass estimates from visible components

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Explanations (dark matter)MACHO

Dwarf starsNeutron starsBlack holes

Observations viagravitational lensing

Can not account forlarge amounts of dark matter

WIMPNeutrinoLSP

AxionKaluza-Klein

excitationsCan not account for

the observed quantity of missing matter

Or have not been detected

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Explanations (modify theory)MOND

MilgromModify Newton laws

for low accelerations

Far from galaxy center

TeVeSBekensteinRelativistic theory

yielding MOND phenomenology

Multi-field theoryIntroduces several

new parameters and functions

Rather complicated

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Explanations (modify theory) STVG

John Moffat Relativistic theory Postulates the existence of additional vector

field Uses additional scalar fields Rather successful

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