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Презентация была опубликована 2 года назад пользователемГеоргий Мордвинов

1 1 I L Zhogin ISSCM SB RAS, Novosibirsk 6-9 July, PIRT-2009 On relevance of modified gravities

2 2 Riemann-squared modified gravities are not appropriate: either field equations are incompatible and irregular [f(R)-gravities; Gauss- Bonnet (or Lovelock) gravities with extra dimension(s)], or the gravitation polarizations (related to the Weyl tensor) are linearly unstable (R mn G mn ). Most interesting eq-n of Absolute Parallelism (AP) is better: no singularities; no free parameters (D =5 is a must); regime of weak gravity is stable (but not the trivial solution); non-stationary cosmology (looks like FLRW with a(t) = t ); topological (quasi)charges, 4D-phenomenology of topological quanta. Conclusions Appendix (possible question) -What about SNe1a? Simple model a = t gives a good fitting. Plan Plan

3 3 Riemann-squared gravities (a+bR+R 2 /2)gravity (4 th order): new 3 d order eq-ns (irregular): The same is valid for other f (R )gravities (with f (R) R). Eq-ns of Gauss-Bonnet (Lovelock) gravity are irregular too (in second jets).

4 4 Riemann-squared gravities L=R mn G mn RG-gravity: Bianchi identity, prolongation & contractions Linear approximation, and linear instability (related to Weyl tensor): Ricci tensor is a source. Weak gravity is impossible here ! ! homogeneous density of order p :

5 5 High symmetry of equation + irreducibility of frame field : includes symmetries of both SR and GR; metric is a quadratic form Interesting features of Absolute Parallelism Absence of arising singularities and uniqueness: there is one unique variant of AP, with the unique D, D=5, which solutions are free of singularities. No room for changes ! Topological features: field configurations with topological charge and/or quasi-charge (topological quanta) Energy-momentum tensor (positive energy): conservation laws arise in presence of symmetries (Killing vectors), or in weak field; but most `polarizations do not contribute to energy (powerless, intangible waves) Instability of trivial solution (growing intangible waves); non-stationary O 4 -symmetric solution (single wave) as more appropriate expanding cosmological background to be filled with stochastic waves and topological quanta AP First order covariant:

6 6 Linear approximation, and linear instability: AP Gravitation polarizations do not grow (stable) ! But the trivial solution is still linearly unstable ! Tensor f mn is a source of instability. Can there exist some regions of instability ? First order covariant (and its irreducible parts): Tensor f mn (only it carries energy-momentum). Identities: Field eq-ns: unstable, ie growing polarizations, ~ t Linear instability

7 7 Energy-momentum tensor Prolonged equation,, can be written as RG-gravity: only f-component (three transverse polarizations in D=5) carries D-momentum and angular momentum (`powerful' waves); other 12 polarizations are `powerless', or `intangible' (this is a very unusual feature); f-component feels only metric and S-field which has effect only on polarization of f: S does not enter eikonal equation, and f moves along usual Riemannian geodesic (if background has f=0)AP This eq-n can be derived from the (trivial, quasi-) action: Symmetrical equation does not lead to energy-momentum :

8 8 Spherically-symmetrical solutions x (radius) High symmetry: AP Relativistically expanding S 3 -spherical shell serves as a storage for tangible f –waves (noise) which should move very tangentially to the shell (at very-very small angles). Growing intangible waves can scatter and leave the shell (non-linearity and large fluctuations, even with topological charge+anticharge) `photons move along the spirals Scalar responsible for longitudinal wave: Nonuniformity of metric behaves as inhomogeneous refraction

9 9 Topological charges and quasi-charges AP Symmetries and quasi-charges Symmetries of cosmological background Group of topological charge: cylindrical + discrete

10 10 FLRW model and Hilbert-Einstein action AP Lagrangian 4D-phenomenology for topological quanta GR Transition to a proxy- lagrangian for the scale factor a (t ) Projection along the extra dimension on the central layer (surface); high anisotropy of tangent waves (t. noise) enable superposition of proxy-fields (psi-filds) quantum- spaghetti Can we write a 4D proxy- lagrangian (holography) ? Additional (classical) fields and constraints ? Can it looks like a 4D QFT on a classical background ?

11 11 Thank you for your attention ! Several conclusions Riemann-squared modified gravities are not appropriate AP grants remarkable eq-n: no singularities; no free parameters (D =5 is a must); topological quanta with a 4D -phenomenology looking like QFT (on a classical background) Can this mathematical reality coincide with our Universe? – Maybe. Some qualitative predictions are possible: perhaps, seemingly, some modified gravitational phenomenology is necessary GR is not suitable for gravitational waves; short-wave GWs are suppressed; no more than four generations (lepton flavors); neutrinos are true neutral (kinda Majorana; without see-saw mechanism); no spin zero elementary quanta, no room for supersymmetry and DM So, we are still waiting for LHC.

12 12 arXiv: Data from Hicken, et al., arXiv: Looks like FLRW-model with Good fitting

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Готово:

Special relativity. Special relativity (SR, also known as the special theory of relativity or STR) is the physical theory of measurement in an inertial.

Special relativity. Special relativity (SR, also known as the special theory of relativity or STR) is the physical theory of measurement in an inertial.

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