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COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY

COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY. JANILO SANTOS (UFRN) JAILSON S. ALCANIZ (ON) FÁBIO C. CARVALHO (INPE). THE ACTION IN f(R) GRAVITY. VARYING THE ACTION WITH RESPECT TO THE METRIC WE OBTAIN THE FIELD EQUATIONS:.

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COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY

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  1. COSMOLOGICAL TESTS FORPALATINI f(R) THEORY JANILO SANTOS (UFRN) JAILSON S. ALCANIZ (ON) FÁBIO C. CARVALHO (INPE)

  2. THE ACTION IN f(R) GRAVITY VARYING THE ACTION WITH RESPECT TO THE METRIC WE OBTAIN THE FIELD EQUATIONS:

  3. IN PALATINI FORMALISM THE METRIC AND THE CONECTIONS ARE TREATED AS INDEPENDENT VARIABLES WITH RESPECT TO WICH THE GENERALIZED ACTION IS VARIED. THE EQUATIONS OF MOTION ARE WHERE

  4. WE CONSIDER MATTER FIELDS SUCH THAT IN THIS CASE THE SECOND EQUATION REDUCES TO FROM THIS EQUATION WE OBTAIN THE INDEPENDENT CONNECTIONS AS ARE THE LEVI-CIVITA CONNECTIONS

  5. THE GENERALIZEDFRIEDMANN EQUATIONIN THIS FORMULATION ISGIVEN BY CONSTRAINED BY (TRACE CONSTRAINT) ( WE ARE CONSIDERING ϸᵐ = 0 )

  6. COSMOLOGICAL TESTS WE CONSIDER THE FUNCTION EVALUATED AT Z = 0 THE TRACE CONSTRAINT GIVES 1) CONSTRAINTS FROM HUBBLE PARAMETER WE TEST THIS MODEL USING THE HUBBLE PARAMETER DETERMINATIONS AT DIFFERENT REDSHIFTS OBTAINED FROM DIFFERENTIAL AGE TECHNIQUES: J. SIMON et al. [ PRD 71, 123001 (2005); R. JIMENEZ and A. LOEB, ApJ 573, 37 (2002)].

  7. USING H(Z) DETERMINATIONS ONLY H(Z) + BAO + CMB FOR THE JOINT ANALYSIS ( H(Z) + BAO + CMB ) : BEST FIT VALUES :

  8. EFFECTIVE EQUATION OF STATE : FOR MORE DETAILS SEE : “COSMOLOGICAL CONSTRAINTS FROM HUBBLE PARAMETER ON f (R ) COSMOLOGIES “ F.C. CARVALHO, E.M. SANTOS, J.S. ALCANIZ, J. SANTOS JCAP 09 (2008) 008

  9. 2) CONSTRAINTS FROM SUPERNOVAE WE ALSO TEST THIS MODEL WITH THE 307 SUPERNOVAE FROM THE “UNION SAMPLE” (M. KOWALSKI et al., arXiv: 0804.4142 [astro-ph] ) THE PREDICTED DISTANCE MODULUS FOR A SUPERNOVA AT REDSHIFT Z, IS WHERE m AND M ARE THE APPARENT AND ABSOLUTE MAGNITUDES, AND ( LUMINOSITY DISTANCE )

  10. CONFIDENCE INTERVALS AT 68.3%, 95.4%, 99.73% FOR THE JOINT ANALYSIS ( SNe Ia + BAO + CMB ): BEST FIT VALUES:

  11. EFFECTIVE EQUATION OF STATE:

  12. HUBBLE DIAGRAM FOR THE 307 SNe Ia FROM THE “UNION SAMPLE”

  13. [ 6 ] M. AMARZGUIOUI et al., ( A & A 454, (2006) 707 ) [ 7 ] S. FAY & R. TAVAKOL, ( PRD 75, (2007) 063509 ) [ 10 ] F.C. CARVALHO et al., (JCAP 0809 (2008) 008 ) [ 11 ] T. KOIVISTO, ( PRD 76 (2007) 043527 ) [ This Letter ] J. SANTOS et al., ( PLB 669 (2008) 14 )

  14. FOR MORE DETAILS SEE: • “LATEST SUPERNOVAE CONSTRAINTS ON f (R) COSMOLOGIES” • SANTOS, J.S. ALCANIZ, F.C. CARVALHO, N. PIRES • PHYS. LETT. B 669 (2008) 14 CONCLUSIONS I ) DIFFERENTIAL AGE METHOD DETERMINATIONS OF H(Z), WHEN COMBINED WITH BAO AND CMB, LEAD TO CONSTRAINTS ON f(R) COMPETITIVE WITH THOSE ACHIEVED WITH SNe Ia ; II ) THE BEST FIT VALUE FOR THE DENSITY PARAMETER ( Ωо = 0.26 ) IS CONSISTENT WITH CURRENT ESTIMATES OF THE CONTRIBUTION OF NON-RELATIVISTIC MATTER. III ) THE UNIVERSE CORRESPONDING TO THE BEST FIT SOLUTION SHOWS ALL THREE LAST PHASES OF THE COSMOLOGICAL EVOLUTION: RADIATION ERA, MATTER AND A LATE TIME COSMIC ACCELERATION WITHAOUT NEED OF DARK ENERGY.

  15. THANK YOU

  16. F.C. CARVALHO, E.M. SANTOS, J.S. ALCANIZ, J. SANTOS (SUBMITTED)

  17. GENERALISED FRIEDMANN EQUATIONS

  18. THE EASIEST WAY TO SEE HOW f (R) – GRAVITY EXPLAIN THE LATE TIME ACCELERATED EXPANSION IS TO DEFINE THE QUANTITIES:

  19. EXAMPLES AND APLICATIONS Problems: Solar System Tests, Stability

  20. COSMOLOGICAL CONSTRAINTS 182 Sne Ia (Riess et al.) + SDSS galaxy survey + CMB shift parameter ( M. Fairbairn & S. Rydbeck, JCAP 12 (2007) 005 )

  21. ENERGY CONDITIONS in f(R) – GRAVITY (for FLRW metric with a perfect fluid) see J. Santos, J.S. Alcaniz, F.C. Carvalho and M.J. Reboucas, Phys. Rev. D, 083513 (2007) Luca Amendola et al. [PLB 660, 125 (2008); PRD 75, 083504 (2007)] examined the case and find it cosmologically viable. However, if local gravity experiments are included they find that thus this model is very close to the LCDM model.

  22. W. Hu & I. Sawicki [PRD 76, 064004 (2007)] proposed the model Can be consistent with both cosmological and local gravity constraints for n ≥ 2 A. A. Starobinsky [JETP Lett. 86, 157 (2007)] proposed the model SPIRES (search author): S. Capozziello, S.D. Odintsov, A. Troisi, S. Tsujikawa, J.D. Barrow.

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