renormalization group scale-setting in astrophysical systems silvije domazet ru đ er bošković...
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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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