Post-Newtonian cosmology
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1 Post-Newtonian cosmology Dirk Puetzfeld (Iowa State University) COSMO-05, Bonn 28 August - 1 September 2005
2 Motivation i. Is there a systematic framework which allows us to quantify general relativistic (GR) effects in cosmology? ii. Is there a systematic framework which allows us to test and classify different gravity theories by using cosmological tests?
3 Motivation i. Is there a systematic framework which allows us to quantify general relativistic (GR) effects in cosmology? ii. Is there a systematic framework which allows us to test and classify different gravity theories by using cosmological tests?
4 Approximation schemes (GR) Post-Minkowskian (Weak field / Fast motion) Post-Newtonian (Weak field / Slow motion) Expand metric around Minkowski background Try to mimic electrodynamics Do not expand matter variables Start from Newtonian limit Expand metric and velocities in powers of c Try mimic Newtonian gravity Do not expand other matter variables
5 Cosmological tests and approximation methods BBN CMB LSS Expansion rate parametrization SNIa / FRIIb Rotation curves Linearized field equations Newtonian limit / numerical simulations Expansion rate parametrization Weak field approximation / Newtonian limit
6 Approximation schemes Cosmological Perturbations (Weak field / Fast motion) (cosmology) Cosmological Post-Newtonian (Weak field / Slow motion) Expand metric around FLRW background Try to mimic electrodynamics Do not expand matter variables Start from Newtonian limit (with additional cosmic expansion) Expand metric and velocities in powers of c Try mimic Newtonian gravity Do not expand other matter variables
7 Approximation schemes Cosmological Perturbations (Weak field / Fast motion) (cosmology) Cosmological Post-Newtonian (Weak field / Slow motion) Expand metric around FLRW background Try to mimic electrodynamics Do not expand matter variables Start from Newtonian limit (with additional cosmic expansion) Expand metric and velocities in powers of c Try mimic Newtonian gravity Do not expand other matter variables
8 Cosmological tests and approximation methods BBN CMB LSS Expansion rate parametrization SNIa / FRIIb Rotation curves Linearized field equations Newtonian limit / numerical simulations Expansion rate parametrization Weak field approximation / Newtonian limit
9 The PN philosphy Energy density Momentum density Energy flux density Momentum flux density and expandable in powers of
10 PN order scheme Metric Order Newtonian PN PN PN PN PN PN PN Numbers correspond to order in inverse powers of the speed of light
11 CPNA metric ansatz & strategy Provide metric ansatz by hand Velocities / EM tensor Connection / Curvature / FEQs Impose GC / Solve FEQs Determine final set FEQs / EOMs Determine form of the metric EOMs / EMPT Start over Numerics
12 Metric & Field equations (1CPNA) 1CPN metric Poisson like FEQ hierarchy Constraints from GC
13 Equations of motion (1CPNA) 1PN form of the metric (general form)
14 Testing gravitational theories GR Newtonian MAG Braneworld Bimetric SG Scalar Tensor f(r) NGT Brans-Dicke Gravity theories Cosmological concordance model Cosmological tests BBN Weak CMB LSS SNIa FRIIb Strong Micro X-ray cluster Rotation curves
15 Testing gravitational theories GR Newtonian MAG Braneworld Bimetric SG Scalar Tensor f(r) NGT Brans-Dicke Gravity theories Cosmological concordance model Post-Newtonian cosmological formulation Cosmological tests BBN Weak CMB LSS SNIa FRIIb Strong Micro X-ray cluster Rotation curves
16 Motivation i. Is there a systematic framework which allows us to quantify general relativistic (GR) effects in cosmology? ii. Is there a systematic framework which allows us to test and classify different gravity theories by using cosmological tests?
17 Testing gravitational theories GR Newtonian MAG Braneworld Bimetric SG Scalar Tensor f(r) NGT Brans-Dicke Gravity theories Cosmological concordance model Alternative cosmological model Cosmological tests BBN Weak CMB LSS SNIa FRIIb Strong Micro X-ray cluster Rotation curves
18 Testing gravitational theories GR Newtonian MAG Braneworld Bimetric SG Scalar Tensor f(r) NGT Brans-Dicke Gravity theories Cosmological concordance model (Parametrized) Post-Newtonian cosmological formulation Alternative cosmological models Cosmological tests BBN Weak CMB LSS SNIa FRIIb Strong Micro X-ray cluster Rotation curves
19 Combination of approximation schemes CPMA CPNA
20 Summary & Outlook i. We successfully derived the FEQs / EOMs / EMPT to 1 st CPNA order (following Chandrasekhar s s ordering scheme) ii. We are currently searching for a form of the FEQs and EOMs which is most suitable for numerical simulations iii. We implemented and tested a CA package of routines for Maple (to be released soon!) iv. We want higher orders and a combination of different approximation methods
21 Jai-chan Hwang Collaborators (Kyungpook National Unversity) Hyerim Noh (Korea Astronomy and Space Science Institute) Publications Hwang et al. astro-ph/ Puetzfeld et al. (in preparation) Last words... Eddington & Clark Infeld Einstein et al. Systematic slow motion treatment Fock Einstein & Infeld Hu Infeld & Schild
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