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

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

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