1 / 32

Has elasticity anything to do with cosmology?

Has elasticity anything to do with cosmology?. Angelo Tartaglia RELGRAV. r. r’. X a. “Elastic” continua. N+n. N. ξ a. x μ. N. Geometry and elasticity. In a strained medium each point is in one to one correspondence with points in the unstrained state.

mikko
Download Presentation

Has elasticity anything to do with cosmology?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Has elasticity anything to do with cosmology? Angelo Tartaglia RELGRAV

  2. r r’ Xa “Elastic” continua N+n N ξa xμ N RELGRAV

  3. Geometry and elasticity In a strained medium each point is in one to one correspondence with points in the unstrained state u, r and r’ are (N+n)-vectors in the flat embedding space RELGRAV

  4. The strain is described by the differential change of u RELGRAV

  5. Metricity RELGRAV

  6. What about space-time? Space-time/Matter-energy What is this? RELGRAV

  7. What is space-time? • Is it a mathematical artifact to describe the gravitational field and the global properties of the universe? • Is it something real endowed with physical properties? RELGRAV

  8. A four-dimensional manifold Minkowski (flat) space-time General (curved) space-time RELGRAV

  9. Defects in continua Flat reference frame Curved natural frame RELGRAV

  10. What consequences from a defect? • The defect fixes the global symmetry • A spontaneous strain tensor εμν(or displacement vector field ua) appears • All this must show up in the Lagrangian of the strained manifold (space-time) RELGRAV

  11. Strained space-time unstrained dr0  Strain tensor g dr strained RELGRAV

  12. Hooke’s law The “elastic” approach Stress tensor Elastic modulus tensor RELGRAV

  13. Isotropic medium Lamé coefficients Elastic energy RELGRAV

  14. The Lagrangian density Potential term “Kinetic”term Geometry RELGRAV

  15. l r  z l r Robertson-Walker symmetry  =f(r) RELGRAV

  16. Has the universe a R-W symmetry? RELGRAV

  17. The Hubble parameter from the Einstein equations A. Tartaglia and N. Radicella, CQG, 27, 035001 (2010) RELGRAV

  18. The distance modulus of bright objects Observed magnitude Absolute magnitude Hubble parameter Distances in Mpc RELGRAV

  19. Fitting the data (307 SnIa) RELGRAV 19

  20. Other cosmological tests • Primordial nucleosynthesis (correct proportion between He, D and hydrogen) • CMB acoustic horizon • Structure formation after the recombination era. RELGRAV

  21. Nucleosynthesis In the early stages the universe is radiation-dominated XBoost

  22. Large Scale Stractures Particle horizon at the equality epoch (z=3150) Constraint from LSS: Ωm0 : matter density in units of h: Hubble constant in units of km/(sMpc)

  23. Acoustic scale of the CMB The power spectrum of the CMB depends on the expansion rate of the universe zls 1090 last scattering DA:angular diameter distance rs:sound horizon

  24. Bayesian posterior probability RELGRAV

  25. Optimal value of the parameters N. Radicella, M. Sereno, A. Tartaglia RELGRAV

  26. Schwarzschild symmetry Natural frame Reference frame (Minkowski) Gauge function RELGRAV

  27. The strain tensor RELGRAV

  28. Three field equations RELGRAV

  29. Weak strain RELGRAV

  30. Approximate solutions ,  = functions of , ~ , RELGRAV

  31. Post-Keplerian circular orbits Looks like the effect of dark matter Light rays RELGRAV

  32. Conclusion • The strained space-time theory introduces a strain energy of vacuum depending on curvature • The idea of a cosmic defect explains why the symmetry of the universe should be R-W (or anything else) • The theory accounts for the accelerated expansion of the universe and is consistent with BBN, structure formation, acoustic scale of the CMB and SnIa’s luminosity RELGRAV

More Related