Outline Outline - The gravitational - The gravitational - The - PDF document

Modern cosmology Modern cosmology Outline Outline - The gravitational - The gravitational - The gravitational perspective perspective perspective • Motivation / Theoretical options Motivation / Theoretical options • • Metric Metric- -affine gravity (MAG) affine gravity (MAG) • • Non • Non- -Riemannian cosmology (NRC) Riemannian cosmology (NRC) Dirk Puetzfeld Dirk Puetzfeld Dirk Puetzfeld • How to test and compare? How to test and compare? • (Iowa State University) (Iowa State University) (Iowa State University) • Summary & Outlook Summary & Outlook • Dark side of the Universe Dark side of the Universe Dark side of the Universe KIAS, Seoul KIAS, Seoul KIAS, Seoul 24 24 - 24 - 26 May 2005 - 26 May 2005 26 May 2005 Cosmological tests and approximation Cosmological tests and approximation What are our What are our methods methods options in options in BBN Expansion rate Expansion rate solving the DM / BBN solving the DM / parametrization parametrization CMB CMB DE problem? DE problem? LSS LSS SNIa / SNIa / Linearized field equations Linearized field equations FRIIb FRIIb I am a detective in the I am a detective in the search for a criminal – search for a criminal – the the Rotation Rotation cosmological constant. I cosmological constant. I curves curves Newtonian limit Newtonian limit know he exists, but I do know he exists, but I do / numerical simulations / numerical simulations not know his appearance, not know his appearance, for instance I do not know for instance I do not know Expansion rate Expansion rate if he is a little man or a tall if he is a little man or a tall parametrization parametrization man. man. Weak field approximation Weak field approximation / Newtonian limit / Newtonian limit Eddington, Proc. Phys. Soc. Eddington , Proc. Phys. Soc. 44 44 (1932) 87 (1932) 87 Theoretical options Strategy (so far) Theoretical options Strategy (so far) Scalar Scalar- -tensor tensor f(R) - - models models f(R) • Examine problem at given length scale Examine problem at given length scale • Higher dimensions Higher dimensions add new sources, i.e. modify RHS add new sources, i.e. modify RHS Topological models Topological models • Strategy works for DM (since we have • Strategy works for DM (since we have Non- -symmetric gravity symmetric gravity Non no a priori estimate for this component) no a priori estimate for this component) but not not for DE (simple estimate from for DE (simple estimate from but Tensor Tensor- -vector vector- -scalar theory scalar theory QFT is too high) modify LHS QFT is too high) modify LHS Non- Non -Riemannian models Riemannian models 1

General idea behind alternative General idea behind alternative The non-Riemannian The non-Riemannian cosmological models cosmological models approach approach • The hope is to eliminate / The hope is to eliminate / • explain Dark Energy Dark Energy by a by a explain “...the essential achievement of general “ ...the essential achievement of general change of the expansion change of the expansion relativity, namely to overcome the 'rigid' relativity, namely to overcome the 'rigid' history history space (i.e. the inertial frame), is space (i.e. the inertial frame), is only only indirectly indirectly connected with the introduction connected with the introduction of a Riemannian metric. The directly of a Riemannian metric. The directly relevant conceptual element is the relevant conceptual element is the 'displacement field 'displacement field‘ ‘ , which , which • Eliminate Eliminate Dark Matter Dark Matter in in • expresses the infinitesimal displacement expresses the infinitesimal displacement of vectors…” of vectors …” condensed structures by condensed structures by corrections to the usual corrections to the usual New New GR GR “ … “ … it seems to be of it seems to be of secondary secondary gravitational law on scales gravitational law on scales theory theory importance importance in some sense that some in some sense that some greater than the solar greater than the solar particular field can be deduced from a particular field can be deduced from a system system Riemannian metric... Riemannian metric...” ” Einstein (1955) Einstein (1955) Why non- -Riemannian gravity ? Riemannian gravity ? Why non A more general connection A more general connection Classify elementary particles by Poincaré Classify elementary particles by Poincar é group group Spin Mass Mass Spin Translational part Translational part Rotational part Rotational part Introduce field theoretical notions Introduce field theoretical notions Energy- Energy -momentum tensor momentum tensor Spin angular momentum tensor Spin angular momentum tensor Torsion Torsion Nonmetricity Nonmetricity Metric Metric Torsion Torsion Schouten (1955) Schouten (1955) Riemann- Riemann -Cartan spacetime Cartan spacetime Analogy with elasticity theory Analogy with elasticity theory and theory of dislocations and theory of dislocations Torsion ~ Dislocations Torsion ~ Dislocations Classification of Classification of non-Riemmanian non-Riemmanian theories theories In some cases torsion can be interpreted In some cases torsion can be interpreted as the surface density of the Burgers vector, as the surface density of the Burgers vector, i.e. it is proportional to the dislocation i.e. it is proportional to the dislocation density of an elastic medium density of an elastic medium Krö Kr öner (1958), Hehl (1967) ner (1958), Hehl (1967) 2

Spacetime types Spacetime types Non- -Riemannian theories Riemannian theories Non (two examples) (two examples) Metric Metric- -affine affine Einstein Einstein- -Cartan (EC) Cartan (EC) theory theory Poincaré Poincar é gauge theory (PGT) gauge theory (PGT) Weyl- Weyl -Cartan Cartan • FEQs: • • Make contact interaction Make contact interaction • FEQs: propagating propagating Riemann- Riemann -Cartan Cartan Weyl Weyl • • PGT has the geometric PGT has the geometric • • Spin- Spin -spin contact interaction spin contact interaction structure of Riemann- -Cartan Cartan structure of Riemann spacetime spacetime • For vanishing spin: EC GR For vanishing spin: EC GR • Riemann Riemann Lagrangian and field equations Lagrangian and field equations Metric-Affine Metric-Affine Momentum Momentum- -current current Metric Metric Gravity (MAG) Gravity (MAG) Hypermomentum Hypermomentum- -current current Affine- Affine -connection connection Metric-affine gravity (MAG) Metric-affine gravity (MAG) Field equations Field equations Potentials Field strengths Gauge currents Excitations Matter currents Nonmetricity Nonmetricity Torsion Torsion 0 I Curvature Curvature I I 3