Chaplygin gas in decelerating DGP gravity

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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

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Contents

• Introduction
• The DGP model
• The Chaplygin gas model
• A combined model
• Observational constraints
• Conclusions
• Matts Roos at 43rd Rencontres de Moriond, 2008

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I. Introduction

• The Universe exhibits accelerating expansion
  since z 0.5 .
• One has tried to explain it by
• simple changes to the spacetime geometry on the
  lefthand side
• of Einsteins equation (e.g. L or
  self-accelerating DGP)
• or simply by 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 models would 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

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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 is MPl ,
• the corresponding scale in the 5-dim. bulk
  is M5 .
• 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

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• The Friedmann-Lemaître equation (FL) is
  (k8pG/3)
• On the self-accelerating branch e 1 gravity
  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 -1 gravity
  leaks in from the bulk
• onto the brane, thus getting stronger on the
  brane. This branch has
• no ghosts.
• When H ltlt rc ) the standard FL equation (for
  flat space k0)
• When H rc the H /rc term causes deceleration or
  acceleration.
• At late times
• Matts Roos at 43rd Rencontres de Moriond, 2008

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• 
  
  
  
  
  
• Replace rm by , 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

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III The Chaplygin gas model

• A simple addition to Tmn is 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, A and B, in
• addition to Wm . It has no ghosts.
• Matts Roos at 43rd Rencontres de Moriond, 2008

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III The Chaplygin gas model

• At early times this gas behaves like pressureless
  dust
• at late times the negative pressure causes
  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

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IV A combined Chaplygin-DGP model

• Since both models have the same asymptotic
  behavior
• _at_ H/ rc -gt 0 , r -gt constant (like
  LCDM)
• _at_ H/ rc gt 1 , r -gt 1 / r3
• we shall study a model combining 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

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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 (a1) the parameters are
  related by
• This does not reduce to LCDM for any choice of
  parameters.
• Matts Roos at 43rd Rencontres de Moriond, 2008

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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 gt 12 Gyr, from the
  oldest star HE 1523-0901
• arXivastro-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.

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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

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Are the two cross-over scales identical?

• We already fixed them to be so, by choosing F 1.
• Check this by keeping F free. Then we find
• Wm0.360.12 -0.14 , Wrc0.93 ,
  WA2.220.94 -1.20 , F 0.900.61 -0.71
• Moreover, the parameters are strongly correlated
• This confirms that the data contain no
  information on F ,
• F can be chosen constant without loss of
  generality.
• Matts Roos at 43rd Rencontres de Moriond, 2008

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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)-space at WA values 1s (1),
central (2), and -1s (3).
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Best fit (at ) and 1s contour in 3-dim. space.
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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 gt 12 Gyr (68C.L.).
• The blue range is forbidden
• Matts Roos at 43rd Rencontres de Moriond, 2008

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• One may define an
• effective dynamics by
• Note that reff can 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
• weff is singular at the points reff 0.
• This shows that the definition of weff is not
  very useful
• Matts Roos at 43rd Rencontres de Moriond, 2008

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weff (z) for a selection of points along the 1s
contour in the (Wrc , WA) -plane
Matts Roos at 43rd Rencontres de Moriond, 2008
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The deceleration parameter q (z) along the 1s
contour in the (Wrc , WA) -plane
Matts Roos at 43rd Rencontres de Moriond, 2008
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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

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V. Conclusions

• 6. The conflict between the value of L and
  theoretical calculations of the vacuum energy is
  absent.
• 7. weff changed from super-acceleration to
• acceleration sometime in the range 0 lt z lt
  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