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COSMOLOGICAL TESTS FORPALATINI 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:

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

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

THE GENERALIZEDFRIEDMANN EQUATIONIN THIS FORMULATION ISGIVEN BY

CONSTRAINED BY

(TRACE CONSTRAINT)

( WE ARE CONSIDERING ϸᵐ = 0 )

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)].

USING H(Z) DETERMINATIONS ONLY

H(Z) + BAO + CMB

FOR THE JOINT ANALYSIS ( H(Z) + BAO + CMB ) :

BEST FIT VALUES :

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

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 )

CONFIDENCE INTERVALS AT 68.3%, 95.4%, 99.73%

FOR THE JOINT ANALYSIS ( SNe Ia + BAO + CMB ):

BEST FIT VALUES:

EFFECTIVE EQUATION

OF STATE:

[ 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 )

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.

THE EASIEST WAY TO SEE HOW f (R) – GRAVITY

EXPLAIN THE LATE TIME ACCELERATED EXPANSION

IS TO DEFINE THE QUANTITIES:

EXAMPLES AND APLICATIONS

Problems: Solar System Tests, Stability

COSMOLOGICAL CONSTRAINTS

182 Sne Ia (Riess et al.) + SDSS galaxy survey + CMB shift parameter

( M. Fairbairn & S. Rydbeck, JCAP 12 (2007) 005 )

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.

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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