Chaplygin gas in decelerating DGP gravity Matts Roos University of Helsinki Department of Physics...

Chaplygin gas in decelerating DGP Chaplygin gas in decelerating DGP gravitygravity

Matts RoosMatts Roos

University of HelsinkiUniversity of Helsinki

Department of PhysicsDepartment of Physics

andand

Department of AstronomyDepartment of Astronomy

43rd Rencontres de Moriond, CosmologyLa Thuile (Val d'Aosta, Italy)

March 15 - 22, 2008

ContentsContents

I.I. IntroductionIntroduction

II.II. The DGP modelThe DGP model

III.III. The Chaplygin gas modelThe Chaplygin gas model

IV.IV. A combined modelA combined model

V.V. Observational constraintsObservational constraints

VI.VI. ConclusionsConclusions

Matts Roos at Matts Roos at 43rd Rencontres de Moriond, 2008

I.I. IntroductionIntroductionThe Universe The Universe exhibits accelerating expansion sinceexhibits accelerating expansion since z ~ z ~ 0.50.5 . .One has tried to explain it byOne has tried to explain it by simplesimple changes to the spacetime geometry on the lefthand changes to the spacetime geometry on the lefthand

sideside of Einstein’s equation (e.g. of Einstein’s equation (e.g. or self-accelerating or self-accelerating DGPDGP))

or or simplysimply by some new energy density on the righthand side by some new energy density on the righthand side in in TT(a negative pressure scalar field, Chaplygin gas)(a negative pressure scalar field, Chaplygin gas) (Other viable explanations are not explored here.)(Other viable explanations are not explored here.)

CDMCDM works, but is not understood theoretically. works, but is not understood theoretically.

Less simple modelsLess simple models would bewould be modified self-accelerating DGP (has modified self-accelerating DGP (has CDM as a limit)CDM as a limit) modified Chaplygin gas (has modified Chaplygin gas (has CDM as a limit)CDM as a limit) self-decelerating DGP and Chaplygin gas combinedself-decelerating DGP and Chaplygin gas combined


II The DGPII The DGP** model model

A simple modification of gravity is the braneworld A simple modification of gravity is the braneworld DGP model.DGP model. The action of gravityThe action of gravity can be written can be written

The mass scale on our 4-dim. brane isThe mass scale on our 4-dim. brane is MMPlPl , , the corresponding scalethe corresponding scale in the 5-dim. bulk is in the 5-dim. bulk is MM5 5 .. Matter fields act on the brane only, gravity Matter fields act on the brane only, gravity

through- out the bulk. through- out the bulk. Define a Define a cross-over length scalecross-over length scale

* * Dvali-Gabadadze-PorratiDvali-Gabadadze-Porrati


► The Friedmann-Lemaître equation (FL) is The Friedmann-Lemaître equation (FL) is GG/3)/3)

► On the On the self-accelerating branch self-accelerating branch =+1 =+1 gravity gravity leaks outleaks out from the from the brane to the bulk, thus getting weaker on the brane (at late time, brane to the bulk, thus getting weaker on the brane (at late time, i.e. now). This branch has i.e. now). This branch has a ghosta ghost..

► On the On the self-decelerating branch self-decelerating branch =-1 =-1 gravity gravity leaks inleaks in from the from the bulkbulk

onto the brane, thus getting stronger on the brane. This branch onto the brane, thus getting stronger on the brane. This branch hashas

no ghosts.no ghosts.

WhenWhen H H <<<< r rc c )) the standard FL equation (for flat space k=0)the standard FL equation (for flat space k=0) When When H H ~ ~ rrcc the the H /rH /rcc term term causes deceleration or accelerationcauses deceleration or acceleration.. At late times At late times


Replace Replace mmby , by , by by

and and rrc c by by

then the FL equation becomesthen the FL equation becomes

DGP self-acceleration fits SNeIa dataDGP self-acceleration fits SNeIa data less well than less well than CDM, it isCDM, it is too simple. too simple.

Modified DGP requires Modified DGP requires higher-dimensional bulk spacehigher-dimensional bulk space and one parameter more. and one parameter more. Not much better!Not much better!


III The Chaplygin gas modelIII The Chaplygin gas model A simple addition toA simple addition to TT is is Chaplygin gasChaplygin gas, , a dark a dark energy fluid with density energy fluid with density and pressure and pressure pp and an and an Equation of State Equation of State The continuity equation is thenThe continuity equation is then

which can be integrated to givewhich can be integrated to give

where where B B is an integration constant.is an integration constant.

Thus this model has two parameters, Thus this model has two parameters, AA and and BB, , in in addition to addition to m m . It has no ghosts.. It has no ghosts.


III The Chaplygin gas modelIII The Chaplygin gas model

► At early times this gas behaves like pressureless dustAt early times this gas behaves like pressureless dust

► at late times the negative pressureat late times the negative pressure causes acceleration: causes acceleration:

► Chaplygin gas then has a Chaplygin gas then has a ”cross-over length scale””cross-over length scale”

• This model is This model is too simple, too simple, it does not fit data well, unless oneit does not fit data well, unless one modifies it and dilutes it with modifies it and dilutes it with extra parametersextra parameters..


IV A combined IV A combined Chaplygin-DGPChaplygin-DGP modelmodel

Since both models have the same asymptotic behaviorSince both models have the same asymptotic behavior

@@ H/ r H/ rcc constantconstantlike like

CDM) ;CDM) ;

@ @ H/ rH/ rcc > > 1 , 1 , 1 / 1 / rr33

we shall studywe shall study a model a model combining standard combining standard Chaplygin Chaplygin gas acceleration gas acceleration with with DGP self-deceleration,DGP self-deceleration, in which the in which the two cross-over lengths are assumed proportional with a two cross-over lengths are assumed proportional with a

factor factor FF

Actually we can choose Actually we can choose FF = 1 = 1 and motivate it later.and motivate it later.


IV A combined modelIV A combined model

The effective energy density is thenThe effective energy density is then

where we have definedwhere we have defined The FL equation becomesThe FL equation becomes

For the self-decelerating branch For the self-decelerating branch At the present time (At the present time (a=1a=1) the parameters are related by) the parameters are related by

► This does not reduce to This does not reduce to CDM for any choice of CDM for any choice of parameters.parameters.


IV A combined IV A combined modelmodel

We fit supernova data, redshifts and magnitudes, to We fit supernova data, redshifts and magnitudes, to H(z)H(z) using the 192 SNeIa in the compilation of Davis & al.using the 192 SNeIa in the compilation of Davis & al.**

Magnitudes:Magnitudes:

Luminosity distance:Luminosity distance:

Additional constraints: Additional constraints:

mm00 = 0.24 +- 0.09 = 0.24 +- 0.09 from CMB data from CMB data

Distance to Last Scattering Surface = 1.70 Distance to Last Scattering Surface = 1.70 § § 0.03 0.03 from CMB data from CMB data Lower limit to Universe age > 12 GyrLower limit to Universe age > 12 Gyr, from , from the oldest star HE 1523-0901the oldest star HE 1523-0901

**arXiv:astro-ph/ 0701510 which includes the ”passed” set in Wood-Vasey & al.,arXiv:astro-ph/ 0701510 which includes the ”passed” set in Wood-Vasey & al., arXiv: astro-ph/ 0701041 and the ”Gold” set in Riess & al., Ap.J. 659 (2007)98.arXiv: astro-ph/ 0701041 and the ”Gold” set in Riess & al., Ap.J. 659 (2007)98.


IV A combined modelIV A combined model

The best fit has The best fit has = 195.5 = 195.5 for 190 degrees of freedom for 190 degrees of freedom ((CDM scores CDM scores = 195.6 ). = 195.6 ).

The parameter values are The parameter values are

The 1The 1 errors correspond to errors correspond to bestbest + 3.54. + 3.54.


Are the two Are the two cross-over scales identical? scales identical? We already fixed them to be so, by choosing We already fixed them to be so, by choosing FF =1.=1. Check this by keeping Check this by keeping FF free. Then we findfree. Then we find

mm=0.36=0.36+0.12 -0.14 , , rcrc=0.93 , =0.93 , AA=2.22=2.22+0.94 -1.20 , , FF =0.90=0.90+0.61 -0.71

Moreover, the parameters are strongly correlated

This confirms that the data contain no information on FF , , FF can be chosen constant without loss of generality.


Banana: best fit to SNeIa data and weak CMB m constraint (at +), and 1 contour in 3-dim. space. Ellipse: best fit to SNeIa data and distance to last scattering. Lines: the relation in (m, rc, A)-space at A values +1 (1), central (2), and -1 (3).

Best fit (at +) and 1 contour in 3-dim. space.

Constraints from SNeIa and the Universe age U / r chronometry of the age of the oldest star HE 1523-0901 yields

t * = 13.4 § 0.8stat § 1.8 U production ratio ) tUniv > 12 Gyr (68%C.L.).

The blue range is forbidden

Matts Roos at 43rd Rencontres de Moriond, 2008

► One may define an One may define an effective dynamicseffective dynamics by by

► Note thatNote that effeff can be negative for some can be negative for some zz in some part of the parameter space. in some part of the parameter space. ThenThen the Universe undergoes an anti-deSitter the Universe undergoes an anti-deSitter

evolutionevolution the weak energy condition is violatedthe weak energy condition is violated wweffeff is singular at the pointsis singular at the points effeff = 0. = 0. This shows that the definition of This shows that the definition of wweff eff is not very usefulis not very useful


weff (z) for a selection of points along the

1contour in the rc ,A-plane


The deceleration parameter The deceleration parameter q q ((zz) along the 1) along the 1 contour in the (contour in the (rcrc , , AA) -plane) -plane


V. ConclusionsV. Conclusions 1.1. StandardStandardChaplygin gas embedded in self-decelerated Chaplygin gas embedded in self-decelerated DGP geometry with the condition of equal cross-over scalesDGP geometry with the condition of equal cross-over scales

fits supernova data as well as does fits supernova data as well as does CDM. CDM.

2. It also fits the distance to LSS, and the age of the oldest star.2. It also fits the distance to LSS, and the age of the oldest star.

3. The model needs only 3 parameters, 3. The model needs only 3 parameters, mm, , rcrc, , A A ,, while while CDM has 2: CDM has 2: mm, ,

4. The model has no ghosts.4. The model has no ghosts.

5. The model cannot be reduced to 5. The model cannot be reduced to CDM, it is unique.CDM, it is unique.


V. Conclusions V. Conclusions

6. The conflict between the value of 6. The conflict between the value of and theoretical and theoretical calculations of the vacuum energy is absent.calculations of the vacuum energy is absent.

7. w7. weffeff changed from super-acceleration to changed from super-acceleration to acceleration sometime in the range 0 < acceleration sometime in the range 0 < z < z < 1. 1.

In the future it approaches wIn the future it approaches weffeff = -1. = -1.

8. The ”coincidence problem” is a consequence of8. The ”coincidence problem” is a consequence of

the time-independent value of the time-independent value of rrc c , a braneworld , a braneworld property.property.


Chaplygin gas in decelerating DGP gravity Matts Roos University of Helsinki Department of Physics...

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