The Strained State Cosmology Angelo Tartaglia Politecnico di

The Strained State Cosmology Angelo Tartaglia Politecnico di Torino and INFN

“Elastic” continua N+n N ξa r xμ Xa April 19 2011 r’ PONT-2011 Avignon N 2

Space-time defect Flat reference frame Curved natural frame April 19 2011 PONT-2011 Avignon 3

Strained space-time dr 0 unstrained Strain tensor g dr strained April 19 2011 PONT-2011 Avignon 4

Physical relevance of the strain • In a continuum, strain is associated with stress • Strain and stress correspond to a deformation energy • Defects can fix the global symmetry • Strain is originated by the presence of matter/energy or by defects April 19 2011 PONT-2011 Avignon 5

Isotropic medium Lamé coefficients Elastic energy April 19 2011 PONT-2011 Avignon 6

The Lagrangian density Potential term “Kinetic” term Geometry April 19 2011 PONT-2011 Avignon 7

Robertson-Walker symmetry l r z r l =f(r) April 19 2011 PONT-2011 Avignon 8

The Hubble parameter A. Tartaglia and N. Radicella, CQG, 27, 035001 (2010) September 6, 2010 ERE 2010 - Granada 9

Fitting the data (307 Sn. Ia) April 19 2011 PONT-2011 Avignon 10 10

Other cosmological tests • Primordial nucleosynthesis (correct proportion between He, D and hydrogen) • CMB spectrum • Structure formation after the recombination era. September 6, 2010 ERE 2010 - Granada 11

Bayesian posterior probability April 19 2011 PONT-2011 Avignon 12

Optimal value of the parameters N. Radicella, M. Sereno, A. Tartaglia, IJMPD, 20, n. 3 (2011) April 19 2011 PONT-2011 Avignon 13

Schwarzschild symmetry Natural frame Reference frame (Minkowski) Gauge function April 19 2011 PONT-2011 Avignon 14

The strain tensor 15

Weak strain April 19 2011 PONT-2011 Avignon 16

Approximate solutions , = functions of , ~ , April 19 2011 PONT-2011 Avignon 17

Post-Keplerian circular orbits Looks like the effect of dark matter Light rays April 19 2011 PONT-2011 Avignon 18

Conclusion • The strained space-time theory introduces a strain energy of vacuum depending on curvature • The theory accounts for the accelerated expansion of the universe and is consistent with BBN, structure formation and Sn. Ia’s • The strain affects free fall also in spherically symmetric stationary spacetimes April 19 2011 PONT-2011 Avignon 19

References • • A. Tartaglia and N. Radicella, CQG, 27, 035001 (2010) N. Radicella, M. Sereno, A. Tartaglia, IJMPD, 20, n. 3 (in press) 2011