COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY
description
Transcript of COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY
![Page 1: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/1.jpg)
COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY
JANILO SANTOS (UFRN) JAILSON S. ALCANIZ (ON) FÁBIO C. CARVALHO (INPE)
![Page 2: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/2.jpg)
THE ACTION IN f(R) GRAVITY
VARYING THE ACTION WITH RESPECT TO THE METRIC WE OBTAIN THE FIELD EQUATIONS:
![Page 3: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/3.jpg)
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
![Page 4: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/4.jpg)
ARE THE LEVI-CIVITA CONNECTIONS
WE CONSIDER MATTER FIELDS SUCH THAT
IN THIS CASE THE SECOND EQUATION REDUCES TO
FROM THIS EQUATION WE OBTAIN THE INDEPENDENT CONNECTIONS AS
![Page 5: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/5.jpg)
THE GENERALIZED FRIEDMANN EQUATION IN THIS FORMULATION IS GIVEN BY
CONSTRAINED BY(TRACE CONSTRAINT)
( WE ARE CONSIDERING ϸᵐ = 0 )
![Page 6: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/6.jpg)
WE CONSIDER THE FUNCTION
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)].
COSMOLOGICAL TESTS
EVALUATED AT Z = 0 THE TRACE CONSTRAINT GIVES
1) CONSTRAINTS FROM HUBBLE PARAMETER
![Page 7: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/7.jpg)
USING H(Z) DETERMINATIONS ONLY H(Z) + BAO + CMB
FOR THE JOINT ANALYSIS ( H(Z) + BAO + CMB ) :
BEST FIT VALUES :
![Page 8: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/8.jpg)
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. SANTOSJCAP 09 (2008) 008
![Page 9: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/9.jpg)
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 )
![Page 10: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/10.jpg)
CONFIDENCE INTERVALS AT 68.3%, 95.4%, 99.73%
FOR THE JOINT ANALYSIS ( SNe Ia + BAO + CMB ):
BEST FIT VALUES:
![Page 11: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/11.jpg)
EFFECTIVE EQUATION OF STATE:
![Page 12: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/12.jpg)
HUBBLE DIAGRAM FOR THE 307 SNe Ia FROM THE “UNION SAMPLE”
![Page 13: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/13.jpg)
[ 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 )
![Page 14: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/14.jpg)
FOR MORE DETAILS SEE: “LATEST SUPERNOVAE CONSTRAINTS ON f (R) COSMOLOGIES”J.SANTOS, J.S. ALCANIZ, F.C. CARVALHO, N. PIRESPHYS. 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 THECONTRIBUTION OF NON-RELATIVISTIC MATTER.
III ) THE UNIVERSE CORRESPONDING TO THE BEST FIT SOLUTION
SHOWS ALL THREE LAST PHASES OF THE COSMOLOGICALEVOLUTION: RADIATION ERA, MATTER AND A LATE TIME COSMIC ACCELERATION WITHAOUT NEED OF DARK ENERGY.
![Page 15: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/15.jpg)
THANK YOU
![Page 16: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/16.jpg)
F.C. CARVALHO, E.M. SANTOS, J.S. ALCANIZ, J. SANTOS (SUBMITTED)
![Page 17: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/17.jpg)
GENERALISED FRIEDMANN EQUATIONS
![Page 18: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/18.jpg)
THE EASIEST WAY TO SEE HOW f (R) – GRAVITYEXPLAIN THE LATE TIME ACCELERATED EXPANSIONIS TO DEFINE THE QUANTITIES:
![Page 19: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/19.jpg)
EXAMPLES AND APLICATIONS
Problems: Solar System Tests, Stability
![Page 20: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/20.jpg)
COSMOLOGICAL CONSTRAINTS
182 Sne Ia (Riess et al.) + SDSS galaxy survey + CMB shift parameter
( M. Fairbairn & S. Rydbeck, JCAP 12 (2007) 005 )
![Page 21: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/21.jpg)
Luca Amendola et al. [PLB 660, 125 (2008); PRD 75, 083504 (2007)]examined the case
and find it cosmologically viable. However, if local gravityexperiments are included they find that
thus this model is very close to the LCDM model.
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)
![Page 22: COSMOLOGICAL TESTS FOR PALATINI f(R) THEORY](https://reader036.fdocuments.in/reader036/viewer/2022062301/56815949550346895dc68417/html5/thumbnails/22.jpg)
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.