post-newtonian cosmologycosmo05.uni-bonn.de/up/puetzfeld.pdf · post-minkowskian (weak field / fast...

Dirk Puetzfeld(Iowa State University)

COSMO-05, Bonn 28 August - 1 September

2005

Dirk PuetzfeldDirk Puetzfeld(Iowa State University)(Iowa State University)

COSMOCOSMO--05, Bonn 05, Bonn 28 August 28 August -- 1 September 1 September

20052005

cosmologycosmologyPost-NewtonianPost-Newtonian

MotivationMotivationi.i. Is there a Is there a systematicsystematic framework framework

which allows us to which allows us to quantify quantify general general relativistic (GR) effects in relativistic (GR) effects in cosmology?cosmology?

ii.ii. Is there a Is there a systematicsystematic framework framework which allows us to which allows us to testtest and and classifyclassifydifferent gravity theories by using different gravity theories by using cosmological tests?cosmological tests?

D. D. PuetzfeldPuetzfeld, COSMO 05, Bonn, COSMO 05, Bonn


which allows us to which allows us to quantifyquantify general general relativistic (GR) effects in relativistic (GR) effects in cosmology?cosmology?



Approximation schemes (GR)Approximation schemes (GR)

•• Expand metric around Expand metric around Minkowski backgroundMinkowski background

•• Try to mimic Try to mimic electrodynamicselectrodynamics

•• Do Do notnot expand matter expand matter variablesvariables

PostPost--MinkowskianMinkowskian(Weak field / Fast motion)(Weak field / Fast motion)

PostPost--NewtonianNewtonian(Weak field / Slow motion)(Weak field / Slow motion)

•• Start from Newtonian Start from Newtonian limitlimit

•• Expand metric Expand metric and and velocities in powers of cvelocities in powers of c

•• Try mimic Newtonian Try mimic Newtonian gravitygravity

•• Do Do notnot expand other expand other matter variablesmatter variables


Cosmological tests and approximation methods


BBNBBN

CMBCMBLSSLSS

SNIa / SNIa / FRIIbFRIIb

Rotation Rotation curvescurves

Expansion rate Expansion rate parametrizationparametrization

Linearized field equationsLinearized field equations

Newtonian limitNewtonian limit/ numerical simulations/ numerical simulations


Weak field approximation Weak field approximation / Newtonian limit/ Newtonian limit


Approximation schemes (cosmology)

Approximation schemes (cosmology)

•• Expand metric around Expand metric around FLRWFLRW backgroundbackground

•• Try to mimic Try to mimic electrodynamicselectrodynamics

•• Do Do notnot expand matter expand matter variablesvariables

Cosmological PerturbationsCosmological Perturbations(Weak field / Fast motion)(Weak field / Fast motion)

Cosmological PostCosmological Post--NewtonianNewtonian(Weak field / Slow motion)(Weak field / Slow motion)

•• Start from Newtonian Start from Newtonian limit (with additional limit (with additional cosmic cosmic expansionexpansion))

•• Expand metric Expand metric and and velocities in powers of cvelocities in powers of c

•• Try mimic Newtonian Try mimic Newtonian gravitygravity

•• Do Do notnot expand other expand other matter variablesmatter variables




BBNBBN

CMBCMBLSSLSS

SNIa / SNIa / FRIIbFRIIb

Rotation Rotation curvescurves


Linearized field equationsLinearized field equations

Newtonian limitNewtonian limit/ numerical simulations/ numerical simulations


Weak field approximation Weak field approximation / Newtonian limit/ Newtonian limit


The PN philosphy The PN philosphy

Energy densityEnergy density Momentum densityMomentum density

Ener

gy fl

ux

Ener

gy fl

ux

dens

ityde

nsity MomentumMomentum

flux densityflux density

andand expandable in powers of expandable in powers of


PN order schemePN order scheme

Newtonian

0.5PN

1PN

1.5PN

2PN

2.5PN

3PN

3.5PN

2

0

4

5

6

7

...

...

0

0

3

0

5

6

...

...

0

0

2

0

4

5

6

7

MetricOrder

Numbers correspond to order in inverse powersNumbers correspond to order in inverse powersof the speed of lightof the speed of light


CPNA metric ansatz & strategyCPNA metric ansatz & strategy

Velocities / EM tensor

Provide metric ansatz by hand

Connection / Curvature / FEQs

Impose GC / „Solve“ FEQs

Determine form of the metric

EOMs / EMPT

Determine final set FEQs / EOMs

NumericsStart over


Metric & Field equations (1CPNA)Metric & Field equations (1CPNA)

1CPN metric1CPN metric

„„Poisson likePoisson like““ FEQ hierarchyFEQ hierarchy Constraints from GCConstraints from GCD. D. PuetzfeldPuetzfeld, COSMO 05, Bonn, COSMO 05, Bonn

Equations of motion (1CPNA)Equations of motion (1CPNA)1PN form of the metric 1PN form of the metric

(general form)(general form)


Testing gravitational theoriesTesting gravitational theories

f(R)ScalarTensor Brans-DickeNGT

BraneworldMAG Bimetric SGGR

Newtonian

Cosmological tests

Cosmological concordance model

LSSCMB SNIa FRIIbBBN

Weak lensing

Stronglensing

Microlensing

X-ray cluster

Rotationcurves

Gravity theories





Newtonian

Cosmological tests

Post-Newtonian cosmological formulation



Weak lensing

Stronglensing

Microlensing

X-ray cluster

Rotationcurves

Gravity theories



which allows us to which allows us to quantifyquantify general general relativistic (GR) effects in relativistic (GR) effects in cosmology?cosmology?






Newtonian

Cosmological tests

Alternative cosmologicalmodel



Weak lensing

Stronglensing

Microlensing

X-ray cluster

Rotationcurves

Gravity theories





Newtonian

Cosmological tests

(Parametrized) Post-Newtonian

cosmological formulation

Alternative cosmologicalmodels



Weak lensing

Stronglensing

Microlensing

X-ray cluster

Rotationcurves

Gravity theories


Combination of approximation schemes

Combination of approximation schemes

CPMACPMA CPNACPNA


Summary & OutlookSummary & Outlooki.i. We successfully derived the We successfully derived the FEQs / EOMs / FEQs / EOMs /

EMPT to 1EMPT to 1stst CPNA orderCPNA order (following (following ChandrasekharChandrasekhar‘‘s ordering scheme)s ordering scheme)

ii.ii. We are currently searching for a form of the We are currently searching for a form of the FEQs and EOMs which is most suitable for FEQs and EOMs which is most suitable for numerical simulationsnumerical simulations

iii.iii. We implemented and tested a We implemented and tested a CA packageCA packageof routines for Maple of routines for Maple (to be released soon!)(to be released soon!)

iv.iv. We want We want higher ordershigher orders and a and a combinationcombinationof different approximation methodsof different approximation methods


CollaboratorsCollaborators•• JaiJai--chan Hwang chan Hwang

(Kyungpook National Unversity)(Kyungpook National Unversity)

•• Hyerim NohHyerim Noh(Korea Astronomy and Space Science Institute)(Korea Astronomy and Space Science Institute)

Last words...Last words...

1938

Eddington & ClarkEddington & ClarkInfeldInfeldEinstein et al.Einstein et al. HuHuEinstein & InfeldEinstein & InfeldFockFock Infeld & SchildInfeld & Schild

1939 1940 1947 1949

Systematic slow motion Systematic slow motion treatmenttreatment

PublicationsPublications•• Hwang et al. astroHwang et al. astro--ph/0507085ph/0507085•• Puetzfeld et al. (in preparation)Puetzfeld et al. (in preparation)


post-newtonian cosmologycosmo05.uni-bonn.de/up/puetzfeld.pdf · post-minkowskian (weak field / fast...

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