Cosmological Perturbative formalism Numerical method Quasistatic - - PowerPoint PPT Presentation

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Cosmological Perturbative formalism Numerical method Quasistatic - - PowerPoint PPT Presentation

Jul 22, 2023 229 likes •1.14k views

Braneworld models DGP background geometry DGP and the ISW effect Cosmological Perturbative formalism Numerical method Quasistatic approximation perturbationsinthe SA results NB results DGPscenario

slide-1
SLIDE 1
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 1/11

Cosmological perturbationsinthe DGPscenario

SanjeevS.Seahra

Departmentof Mathematics&Statistics Universityof NewBrunswick,Canada incollaborationwith:Antonio Cardoso,KazuyaKoyamaand FabioPSilva

arXiv:0711.2563[astro-ph]

slide-2
SLIDE 2
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 2/11

Braneworld models

  • bservable

universe

slide-3
SLIDE 3
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 2/11

Braneworld models

slide-4
SLIDE 4
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 2/11

Braneworld models

slide-5
SLIDE 5
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 2/11

Braneworld models

slide-6
SLIDE 6
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 2/11

Braneworld models

slide-7
SLIDE 7
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 2/11

Braneworld models

slide-8
SLIDE 8
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 2/11

Braneworld models

Randall-Sundrum model

(AdSbulk)

slide-9
SLIDE 9
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 2/11

Braneworld models

(Minkowskibulk)

Dvali-Gabadadze- Porratimodel

slide-10
SLIDE 10
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 2/11

Braneworld models

Randall-Sundrum model

(Minkowskibulk) (AdSbulk)

Dvali-Gabadadze- Porratimodel

slide-11
SLIDE 11
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 2/11

Braneworld models

Randall-Sundrum model

(Minkowskibulk) (AdSbulk)

Dvali-Gabadadze- Porratimodel

eachmodelspecifiedbyasinglelengthparameter

slide-12
SLIDE 12
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 2/11

Braneworld models

Randall-Sundrum model

(Minkowskibulk) (AdSbulk)

Dvali-Gabadadze- Porratimodel

eachmodelspecifiedbyasinglelengthparameter

slide-13
SLIDE 13
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

slide-14
SLIDE 14
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

future past

slide-15
SLIDE 15
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

b r a n e

future past

slide-16
SLIDE 16
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

b r a n e

braneworldsymmetry: weneedtoexciseone half of thebulkand replaceitwiththemirror imageof theotherhalf

future past

slide-17
SLIDE 17
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

branchambiguity:whichhalfofbulkdowekeep?

b r a n e

braneworldsymmetry: weneedtoexciseone half of thebulkand replaceitwiththemirror imageof theotherhalf

future past

slide-18
SLIDE 18
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

branchambiguity:whichhalfofbulkdowekeep?

b r a n e normal branch self- accelerating branch

braneworldsymmetry: weneedtoexciseone half of thebulkand replaceitwiththemirror imageof theotherhalf

future past

slide-19
SLIDE 19
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

branchambiguity:whichhalfofbulkdowekeep?

b r a n e normal branch self- accelerating branch branetrajectoryfixed byFriedmanneq:

future past

slide-20
SLIDE 20
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

branchambiguity:whichhalfofbulkdowekeep?

b r a n e normal branch self- accelerating branch branetrajectoryfixed byFriedmanneq:

future past

slide-21
SLIDE 21
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

branchambiguity:whichhalfofbulkdowekeep?

b r a n e normal branch self- accelerating branch

self-acceleratingbranch canhavelatetime accelerationwithouta cosmologicalconstant

branetrajectoryfixed byFriedmanneq:

future past

slide-22
SLIDE 22
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

branchambiguity:whichhalfofbulkdowekeep?

b r a n e normal branch self- accelerating branch

self-acceleratingbranch canhavelatetime accelerationwithouta cosmologicalconstant bigcatch:self- acceleratingbranchhas aperturbativeghost

future past

slide-23
SLIDE 23
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

branchambiguity:whichhalfofbulkdowekeep?

b r a n e normal branch self- accelerating branch

self-acceleratingbranch canhavelatetime accelerationwithouta cosmologicalconstant bigcatch:self- acceleratingbranchhas aperturbativeghost

Ignore

future past

slide-24
SLIDE 24
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

bigcatch:self- acceleratingbranchhas aperturbativeghost

b r a n e normal branch self- accelerating branch

bestfittogeometric tests(SAbranch): branchambiguity:whichhalfofbulkdowekeep? self-acceleratingbranch canhavelatetime accelerationwithouta cosmologicalconstant

Ignore

[Lazkoz&Majerotto2007] past

slide-25
SLIDE 25
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

b r a n e normal branch self- accelerating branch

branchambiguity:whichhalfofbulkdowekeep?

future past

slide-26
SLIDE 26
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

b r a n e normal branch self- accelerating branch

branchambiguity:whichhalfofbulkdowekeep?

future past

slide-27
SLIDE 27
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 3/11

DGP background geometry

b r a n e normal branch self- accelerating branch

branchambiguity:whichhalfofbulkdowekeep?

future past [Lazkoz&Majerotto2007]

geometrictestsrequire:

slide-28
SLIDE 28
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 4/11

DGP and the late time ISW effect

furtherconstrainDGPby lookingatperturbations

slide-29
SLIDE 29
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 4/11

DGP and the late time ISW effect

bestdonewiththe integratedSachs-Wolfe (ISW)effect furtherconstrainDGPby lookingatperturbations

slide-30
SLIDE 30
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 4/11

DGP and the late time ISW effect

CMB photon

Earth bestdonewiththe integratedSachs-Wolfe (ISW)effect furtherconstrainDGPby lookingatperturbations

  • verdensity
slide-31
SLIDE 31
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 4/11

DGP and the late time ISW effect

Earth photonblueshiftedby potentialwell

CMB photon

  • verdensity

bestdonewiththe integratedSachs-Wolfe (ISW)effect furtherconstrainDGPby lookingatperturbations

slide-32
SLIDE 32
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 4/11

DGP and the late time ISW effect

Earth photonblueshiftedby potentialwell

CMB photon

bestdonewiththe integratedSachs-Wolfe (ISW)effect furtherconstrainDGPby lookingatperturbations

  • verdensity

densitycontrast changesasphoton crossesit

slide-33
SLIDE 33
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 4/11

DGP and the late time ISW effect

bestdonewiththe integratedSachs-Wolfe (ISW)effect Earth photonemerges withdifferent colour photonblueshiftedby potentialwell

CMB photon

densitycontrast changesasphoton crossesit furtherconstrainDGPby lookingatperturbations

  • verdensity
slide-34
SLIDE 34
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 4/11

DGP and the late time ISW effect

DGPmodifieslatestructuregrowth,whichmodifies ISWeffectandleadstochangesin...

slide-35
SLIDE 35
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 4/11

DGP and the late time ISW effect

DGPmodifieslatestructuregrowth,whichmodifies ISWeffectandleadstochangesin...

CMBpowerspectra

WMAPscienceteam

slide-36
SLIDE 36
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 4/11

DGP and the late time ISW effect

DGPmodifieslatestructuregrowth,whichmodifies ISWeffectandleadstochangesin...

CMBpowerspectra CMB-LSScross correlation

WMAPscienceteam

slide-37
SLIDE 37
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 4/11

DGP and the late time ISW effect

DGPmodifieslatestructuregrowth,whichmodifies ISWeffectandleadstochangesin...

CMBpowerspectra CMB-LSScross correlation

toquantifytheseeffects weneedtoknowhow perturbationsevolvein DGPmodels

slide-38
SLIDE 38
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 5/11

Perturbative formalism

b r a n e

future past

Remove

focusonnormalbranch:

slide-39
SLIDE 39
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 5/11

Perturbative formalism

b r a n e

future past

Remove

slide-40
SLIDE 40
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 5/11

Perturbative formalism

b r a n e

future past

Remove

slide-41
SLIDE 41
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 5/11

Perturbative formalism

b r a n e

future past

Remove

slide-42
SLIDE 42
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 5/11

Perturbative formalism

b r a n e

future past

Remove solveusing numerical simulations

slide-43
SLIDE 43
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 6/11

Numerical method

future past

Remove solveusing numerical simulations null computational domain

slide-44
SLIDE 44
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 6/11

Numerical method

future past

Remove solveusing numerical simulations null computational domain initialdata

slide-45
SLIDE 45
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 6/11

Numerical method

future past

Remove solveusing numerical simulations null computational domain initialdata coupledbrane ODEandbulk PDEsolved usingnullfinite elements

slide-46
SLIDE 46
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 6/11

Numerical method

future past

Remove solveusing numerical simulations null computational domain initialdata coupledbrane ODEandbulk PDEsolved usingnullfinite elements

thereisanattractorsolution: initialfieldconfiguration unimportantif initialsurface farenoughinthepast

slide-47
SLIDE 47
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 6/11

Numerical method

future past

Remove solveusing numerical simulations null computational domain initialdata coupledbrane ODEandbulk PDEsolved usingnullfinite elements

thereisanattractorsolution: initialfieldconfiguration unimportantif initialsurface farenoughinthepast

alternateapproach: directscalingsol’nof Sawickietal(2007)...get sameanswer

slide-48
SLIDE 48
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 7/11

Quasistatic approximation

{

equationstosolve

slide-49
SLIDE 49
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 7/11

Quasistatic approximation

Koyama&Maartens(2006) havedevolopeda “quasistaticapproximation” tosolvethissystem

{

equationstosolve

slide-50
SLIDE 50
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 7/11

Quasistatic approximation

QSapprox

{

equationstosolve

Koyama&Maartens(2006) havedevolopeda “quasistaticapproximation” tosolvethissystem

slide-51
SLIDE 51
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 7/11

Quasistatic approximation

QSapprox QSapprox

Koyama&Maartens(2006) havedevolopeda “quasistaticapproximation” tosolvethissystem

{

equationstosolve

slide-52
SLIDE 52
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 7/11

Quasistatic approximation

QSapprox QSapprox

ADVANTAGE:needto solveODEsnotPDEs Koyama&Maartens(2006) havedevolopeda “quasistaticapproximation” tosolvethissystem

{

equationstosolve

slide-53
SLIDE 53
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 7/11

Quasistatic approximation

QSapprox QSapprox

QUESTION:onwhich scalescanwetrustthe QSapproximation? ADVANTAGE:needto solveODEsnotPDEs Koyama&Maartens(2006) havedevolopeda “quasistaticapproximation” tosolvethissystem

{

equationstosolve

slide-54
SLIDE 54
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-55
SLIDE 55
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-56
SLIDE 56
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-57
SLIDE 57
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-58
SLIDE 58
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-59
SLIDE 59
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-60
SLIDE 60
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-61
SLIDE 61
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-62
SLIDE 62
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-63
SLIDE 63
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-64
SLIDE 64
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-65
SLIDE 65
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-66
SLIDE 66
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-67
SLIDE 67
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 8/11

Self-accelerating branch results

slide-68
SLIDE 68
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 9/11

Normal branch results

■ Ωrc = 1/4H2 0r2 c → 0 corresponds to ΛCDM limit ■ unlike SA branch, Φ− is larger than ΛCDM ■ curves are close to QS (not shown) for k 0.01 h Mpc−1

slide-69
SLIDE 69
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 9/11

Normal branch results

slide-70
SLIDE 70
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 10/11

Comparison to observations

■ direct solution for 5D perturbations too expensive for

Boltzmann codes/Monte Carlo methods, instead:

slide-71
SLIDE 71
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 10/11

Comparison to observations

■ direct solution for 5D perturbations too expensive for

Boltzmann codes/Monte Carlo methods, instead:

◆ concentrate on QS regime

slide-72
SLIDE 72
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 10/11

Comparison to observations

■ direct solution for 5D perturbations too expensive for

Boltzmann codes/Monte Carlo methods, instead:

◆ concentrate on QS regime ◆ use fitting functions in place of simulation results (PPF

formalism)

slide-73
SLIDE 73
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 10/11

Comparison to observations

■ direct solution for 5D perturbations too expensive for

Boltzmann codes/Monte Carlo methods, instead:

◆ concentrate on QS regime ◆ use fitting functions in place of simulation results (PPF

formalism)

■ Giannantonio et al (2008):

slide-74
SLIDE 74
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 10/11

Comparison to observations

■ direct solution for 5D perturbations too expensive for

Boltzmann codes/Monte Carlo methods, instead:

◆ concentrate on QS regime ◆ use fitting functions in place of simulation results (PPF

formalism)

■ Giannantonio et al (2008): ◆ considered normal branch in QS regime

slide-75
SLIDE 75
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 10/11

Comparison to observations

■ direct solution for 5D perturbations too expensive for

Boltzmann codes/Monte Carlo methods, instead:

◆ concentrate on QS regime ◆ use fitting functions in place of simulation results (PPF

formalism)

■ Giannantonio et al (2008): ◆ considered normal branch in QS regime ◆ current measurements cannot rule model out

slide-76
SLIDE 76
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 10/11

Comparison to observations

■ direct solution for 5D perturbations too expensive for

Boltzmann codes/Monte Carlo methods, instead:

◆ concentrate on QS regime ◆ use fitting functions in place of simulation results (PPF

formalism)

■ Giannantonio et al (2008): ◆ considered normal branch in QS regime ◆ current measurements cannot rule model out

■ improve observations of CMB-LSS cross-correlation

applies more pressure

slide-77
SLIDE 77
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 10/11

Comparison to observations

■ direct solution for 5D perturbations too expensive for

Boltzmann codes/Monte Carlo methods, instead:

◆ concentrate on QS regime ◆ use fitting functions in place of simulation results (PPF

formalism)

■ Giannantonio et al (2008): ◆ considered normal branch in QS regime ◆ current measurements cannot rule model out

■ improve observations of CMB-LSS cross-correlation

applies more pressure

◆ curvature helps fit

slide-78
SLIDE 78
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 10/11

Comparison to observations

■ direct solution for 5D perturbations too expensive for

Boltzmann codes/Monte Carlo methods, instead:

◆ concentrate on QS regime ◆ use fitting functions in place of simulation results (PPF

formalism)

■ Giannantonio et al (2008): ◆ considered normal branch in QS regime ◆ current measurements cannot rule model out

■ improve observations of CMB-LSS cross-correlation

applies more pressure

◆ curvature helps fit ■ Fang et al (2008):

slide-79
SLIDE 79
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 10/11

Comparison to observations

■ direct solution for 5D perturbations too expensive for

Boltzmann codes/Monte Carlo methods, instead:

◆ concentrate on QS regime ◆ use fitting functions in place of simulation results (PPF

formalism)

■ Giannantonio et al (2008): ◆ considered normal branch in QS regime ◆ current measurements cannot rule model out

■ improve observations of CMB-LSS cross-correlation

applies more pressure

◆ curvature helps fit ■ Fang et al (2008): ◆ concentrated on SA branch using PPF framework

slide-80
SLIDE 80
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 10/11

Comparison to observations

■ direct solution for 5D perturbations too expensive for

Boltzmann codes/Monte Carlo methods, instead:

◆ concentrate on QS regime ◆ use fitting functions in place of simulation results (PPF

formalism)

■ Giannantonio et al (2008): ◆ considered normal branch in QS regime ◆ current measurements cannot rule model out

■ improve observations of CMB-LSS cross-correlation

applies more pressure

◆ curvature helps fit ■ Fang et al (2008): ◆ concentrated on SA branch using PPF framework ◆ k 0.01 h Mpc−1 DGP modes give rise to too much

power in l 10 CMB

slide-81
SLIDE 81
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 10/11

Comparison to observations

■ direct solution for 5D perturbations too expensive for

Boltzmann codes/Monte Carlo methods, instead:

◆ concentrate on QS regime ◆ use fitting functions in place of simulation results (PPF

formalism)

■ Giannantonio et al (2008): ◆ considered normal branch in QS regime ◆ current measurements cannot rule model out

■ improve observations of CMB-LSS cross-correlation

applies more pressure

◆ curvature helps fit ■ Fang et al (2008): ◆ concentrated on SA branch using PPF framework ◆ k 0.01 h Mpc−1 DGP modes give rise to too much

power in l 10 CMB

◆ self-acceleration is in trouble

slide-82
SLIDE 82
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 11/11

Summary

■ we have solved the bulk/brane linear perturbations

equations in the DGP model

slide-83
SLIDE 83
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 11/11

Summary

■ we have solved the bulk/brane linear perturbations

equations in the DGP model

◆ no additional approximations

slide-84
SLIDE 84
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 11/11

Summary

■ we have solved the bulk/brane linear perturbations

equations in the DGP model

◆ no additional approximations ◆ results independent of bulk initial conditions

slide-85
SLIDE 85
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 11/11

Summary

■ we have solved the bulk/brane linear perturbations

equations in the DGP model

◆ no additional approximations ◆ results independent of bulk initial conditions ◆ tested other approximations in the literature

slide-86
SLIDE 86
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 11/11

Summary

■ we have solved the bulk/brane linear perturbations

equations in the DGP model

◆ no additional approximations ◆ results independent of bulk initial conditions ◆ tested other approximations in the literature

■ quasistatic approximation valid on scales 100 Mpc

slide-87
SLIDE 87
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 11/11

Summary

■ we have solved the bulk/brane linear perturbations

equations in the DGP model

◆ no additional approximations ◆ results independent of bulk initial conditions ◆ tested other approximations in the literature

■ quasistatic approximation valid on scales 100 Mpc ■ direct scaling solution gives sufficiently accurate results

  • n all interesting scales
slide-88
SLIDE 88
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 11/11

Summary

■ we have solved the bulk/brane linear perturbations

equations in the DGP model

◆ no additional approximations ◆ results independent of bulk initial conditions ◆ tested other approximations in the literature

■ quasistatic approximation valid on scales 100 Mpc ■ direct scaling solution gives sufficiently accurate results

  • n all interesting scales

■ perturbation results have been compared to observations

slide-89
SLIDE 89
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 11/11

Summary

■ we have solved the bulk/brane linear perturbations

equations in the DGP model

◆ no additional approximations ◆ results independent of bulk initial conditions ◆ tested other approximations in the literature

■ quasistatic approximation valid on scales 100 Mpc ■ direct scaling solution gives sufficiently accurate results

  • n all interesting scales

■ perturbation results have been compared to observations ◆ self-accelerating DGP is in trouble due to excess large

scale power in CMB

slide-90
SLIDE 90
  • Braneworld models
  • DGP background geometry
  • DGP and the ISW effect
  • Perturbative formalism
  • Numerical method
  • Quasistatic approximation
  • SA results
  • NB results
  • Comparison to observations
  • Summary

Sanjeev S. Seahra; 26 August, 2008 Cosmological perturbations in the DGP scenario - p. 11/11

Summary

■ we have solved the bulk/brane linear perturbations

equations in the DGP model

◆ no additional approximations ◆ results independent of bulk initial conditions ◆ tested other approximations in the literature

■ quasistatic approximation valid on scales 100 Mpc ■ direct scaling solution gives sufficiently accurate results

  • n all interesting scales

■ perturbation results have been compared to observations ◆ self-accelerating DGP is in trouble due to excess large

scale power in CMB

◆ normal branch still alive but future measures of ISW-LSS

cross correlation will be more definitive