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Chaplygin gas in decelerating DGP gravity Matts Roos University of Helsinki Department of Physics and Department of Astronomy 43rd Rencontres de Moriond, Cosmology La Thuile (Val d'Aosta, Italy) March 15 - 22, 2008 Contents Introduction The DGP model The Chaplygin gas model

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chaplygin gas in decelerating dgp gravity

Chaplygin gas in decelerating DGP gravity

Matts Roos

University of Helsinki

Department of Physics

and

Department of Astronomy

43rd Rencontres de Moriond, Cosmology

La Thuile (Val d'Aosta, Italy) March 15 - 22, 2008

contents
Contents
  • Introduction
  • The DGP model
  • The Chaplygin gas model
  • A combined model
  • Observational constraints
  • Conclusions

Matts Roos at 43rd Rencontres de Moriond, 2008

i introduction
I.Introduction

The Universe exhibits accelerating expansion sincez ~ 0.5 .

One has tried to explain it by

  • simple changes to the spacetime geometry on the lefthand side

of Einstein’s equation (e.g. L or self-accelerating DGP)

  • or simplyby some new energy density on the righthand side

in Tmn (a negative pressure scalar field, Chaplygin gas)

(Other viable explanations are not explored here.)

  • LCDM works, but is not understood theoretically.
  • Less simple modelswould be
  • modified self-accelerating DGP (has LCDM as a limit)
  • modified Chaplygin gas (has LCDM as a limit)
  • self-decelerating DGP and Chaplygin gas combined

Matts Roos at 43rd Rencontres de Moriond, 2008

ii the dgp model
II The DGP* model
  • A simple modification of gravity is the braneworld

DGP model.The action of gravity can be written

  • The mass scale on our 4-dim. brane isMPl,

the corresponding scale in the 5-dim. bulk isM5 .

  • Matter fields act on the brane only, gravity through- out the bulk.
  • Define a cross-over length scale

* Dvali-Gabadadze-Porrati

Matts Roos at 43rd Rencontres de Moriond, 2008

slide5
The Friedmann-Lemaître equation (FL) is (k=8pG/3)

On the self-accelerating branch e =+1gravity leaks out from the

brane to the bulk, thus getting weaker on the brane (at late time,

i.e. now). This branch has a ghost.

On the self-decelerating branch e =-1gravity leaks in from the bulk

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

no ghosts.

WhenH << rc )the standard FL equation (for flat space k=0)

When H ~ rc the H /rc term causes deceleration or acceleration.

At late times

Matts Roos at 43rd Rencontres de Moriond, 2008

slide6

Replace rmby , rj by

and rc by

then the FL equation becomes

DGP self-acceleration fits SNeIa data

less well than LCDM, it is too simple.

Modified DGP requires higher-dimensional bulk space

and one parameter more. Not much better!

Matts Roos at 43rd Rencontres de Moriond, 2008

iii the chaplygin gas model
III The Chaplygin gas model
  • A simple addition toTmnis Chaplygin gas, a dark

energy fluid with density rj and pressure pj and an

Equation of State

  • The continuity equation is then

which can be integrated to give

where B is an integration constant.

  • Thus this model has two parameters, Aand B, in

addition to Wm . It has no ghosts.

Matts Roos at 43rd Rencontres de Moriond, 2008

iii the chaplygin gas model8
III The Chaplygin gas model
  • At early times this gas behaves like pressureless dust
  • at late times the negative pressurecauses acceleration:
  • Chaplygin gas then has a ”cross-over length scale”
  • This model is too simple, it does not fit data well, unless one

modifies it and dilutes it with extra parameters.

Matts Roos at 43rd Rencontres de Moriond, 2008

iv a combined chaplygin dgp model
IV A combined Chaplygin-DGP model

Since both models have the same asymptotic behavior

@ H/ rc-> 0 , r -> constant (like LCDM) ;

@ H/ rc > 1 , r -> 1 / r3

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

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

Matts Roos at 43rd Rencontres de Moriond, 2008

iv a combined model
IV A combined model
  • The effective energy density is then

where we have defined

  • The FL equation becomes
  • For the self-decelerating branch e = -1 .

At the present time (a=1) the parameters are related by

  • This does not reduce to LCDM for any choice of parameters.

Matts Roos at 43rd Rencontres de Moriond, 2008

iv a combined model11
IV A combined model

We fit supernova data, redshifts and magnitudes, to H(z)

using the 192 SNeIa in the compilation of Davis & al.*

Magnitudes:

Luminosity distance:

Additional constraints:

  • Wm0 = 0.24 +- 0.09 from CMB data
  • Distance to Last Scattering Surface = 1.70 § 0.03 from CMB data
  • Lower limit to Universe age > 12 Gyr, from the oldest star HE 1523-0901

*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.

Matts Roos at 43rd Rencontres de Moriond, 2008

iv a combined model12
IV A combined model

The best fit has c2 = 195.5 for 190 degrees of freedom (LCDM scores c2 = 195.6 ).

The parameter values are

The 1s errors correspond to c2best + 3.54.

Matts Roos at 43rd Rencontres de Moriond, 2008

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

Wm=0.36+0.12-0.14 , Wrc=0.93 , WA=2.22+0.94-1.20 , F=0.90+0.61-0.71

  • Moreover, the parameters are strongly correlated
  • This confirms that the data contain no information on F ,

Fcan be chosen constant without loss of generality.

Matts Roos at 43rd Rencontres de Moriond, 2008

slide14

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

slide16

Constraints from SNeIaand 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

slide17
One may define an

effective dynamics by

Note thatreffcan be negative for some z

in some part of the parameter space.

Then

the Universe undergoes an anti-deSitter evolution

the weak energy condition is violated

weffis singular at the pointsreff = 0.

This shows that the definition of weff is not very useful

Matts Roos at 43rd Rencontres de Moriond, 2008

w eff z for a selection of points along the 1 s contour in the w rc w a plane
weff (z)for a selection of points along the 1scontour in the (Wrc , WA) -plane

Matts Roos at 43rd Rencontres de Moriond, 2008

the deceleration parameter q z along the 1 s contour in the w rc w a plane
The deceleration parameter q (z) along the 1s contour in the (Wrc , WA) -plane

Matts Roos at 43rd Rencontres de Moriond, 2008

v conclusions
V. Conclusions
  • StandardChaplygin gas embedded in self-decelerated

DGP geometry with the condition of equal cross-over scales

fits supernova data as well as does LCDM.

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

3. The model needs only 3 parameters, Wm, Wrc, W A ,

while LCDM has 2: Wm, WL

4. The model has no ghosts.

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

Matts Roos at 43rd Rencontres de Moriond, 2008

v conclusions21
V. Conclusions

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

7. weffchanged from super-acceleration to

acceleration sometime in the range 0 < z < 1.

In the future it approaches weff = -1.

8. The ”coincidence problem” is a consequence of

the time-independent value of rc , a braneworld property.

Matts Roos at 43rd Rencontres de Moriond, 2008