Perturbative formalism Quasistatic approximation ...seahra/resources/slides/DGP_perts.pdf ·...
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. 1/11 Cosmological perturbations in the DGP scenario Sanjeev S. Seahra Department of Mathematics & Statistics University of New Brunswick, Canada in collaboration with: Antonio Cardoso, Kazuya Koyama and Fabio P Silva arXiv: 0711.2563 [astro-ph]
Transcript of Perturbative formalism Quasistatic approximation ...seahra/resources/slides/DGP_perts.pdf ·...
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
perturbations in the
DGP scenario
Sanjeev S. SeahraDepartment of Mathematics & Statistics
University of New Brunswick, Canada
in collaboration with: AntonioCardoso, Kazuya Koyama and
Fabio P Silva
arXiv: 0711.2563 [astro-ph]
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
observableuniverse
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
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
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
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
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
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-Sundrummodel
(AdS bulk)
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
(Minkowski bulk)
Dvali-Gabadadze-Porrati model
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-Sundrummodel
(Minkowski bulk)
(AdS bulk)
Dvali-Gabadadze-Porrati model
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-Sundrummodel
(Minkowski bulk)
(AdS bulk)
Dvali-Gabadadze-Porrati model
each model specified by a single length parameter
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-Sundrummodel
(Minkowski bulk)
(AdS bulk)
Dvali-Gabadadze-Porrati model
each model specified by a single length parameter
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
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
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
bra
ne
future
past
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
bra
ne
braneworld symmetry:we need to excise one
half of the bulk andreplace it with the mirrorimage of the other half
future
past
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
branch ambiguity: which half of bulk do we keep?
bra
ne
braneworld symmetry:we need to excise one
half of the bulk andreplace it with the mirrorimage of the other half
future
past
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
branch ambiguity: which half of bulk do we keep?
bra
nenormal
branchself-
acceleratingbranch
braneworld symmetry:we need to excise one
half of the bulk andreplace it with the mirrorimage of the other half
future
past
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
branch ambiguity: which half of bulk do we keep?
bra
nenormal
branchself-
acceleratingbranch
brane trajectory fixedby Friedmann eq:
future
past
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
branch ambiguity: which half of bulk do we keep?
bra
nenormal
branchself-
acceleratingbranch
brane trajectory fixedby Friedmann eq:
future
past
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
branch ambiguity: which half of bulk do we keep?
bra
nenormal
branchself-
acceleratingbranch
self-accelerating branchcan have late time
acceleration without acosmological constant
brane trajectory fixedby Friedmann eq:
future
past
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
branch ambiguity: which half of bulk do we keep?
bra
nenormal
branchself-
acceleratingbranch
self-accelerating branchcan have late time
acceleration without acosmological constant
big catch: self-accelerating branch has
a perturbative ghost
future
past
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
branch ambiguity: which half of bulk do we keep?
bra
nenormal
branchself-
acceleratingbranch
self-accelerating branchcan have late time
acceleration without acosmological constant
big catch: self-accelerating branch has
a perturbative ghost
Ignore
future
past
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
big catch: self-accelerating branch has
a perturbative ghost
bra
nenormal
branchself-
acceleratingbranch
best fit to geometrictests (SA branch):
branch ambiguity: which half of bulk do we keep?
self-accelerating branchcan have late time
acceleration without acosmological constant
Ignore
[Lazkoz & Majerotto 2007]
past
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
bra
nenormal
branchself-
acceleratingbranch
branch ambiguity: which half of bulk do we keep?
future
past
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
bra
nenormal
branchself-
acceleratingbranch
branch ambiguity: which half of bulk do we keep?
future
past
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
bra
nenormal
branchself-
acceleratingbranch
branch ambiguity: which half of bulk do we keep?
future
past
[Lazkoz & Majerotto 2007]
geometric tests require:
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
further constrain DGP bylooking at perturbations
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
best done with theintegrated Sachs-Wolfe
(ISW) effect
further constrain DGP bylooking at perturbations
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
CMBphoton
Earth
best done with theintegrated Sachs-Wolfe
(ISW) effect
further constrain DGP bylooking at perturbations
overdensity
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
photon blueshifted bypotential well
CMBphoton
overdensity
best done with theintegrated Sachs-Wolfe
(ISW) effect
further constrain DGP bylooking at perturbations
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
photon blueshifted bypotential well
CMBphoton
best done with theintegrated Sachs-Wolfe
(ISW) effect
further constrain DGP bylooking at perturbations
overdensity density contrastchanges as photon
crosses it
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
best done with theintegrated Sachs-Wolfe
(ISW) effect
Earth
photon emergeswith different
colour
photon blueshifted bypotential well
CMBphoton
density contrastchanges as photon
crosses it
further constrain DGP bylooking at perturbations
overdensity
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
DGP modifies late structure growth, which modifiesISW effect and leads to changes in...
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
DGP modifies late structure growth, which modifiesISW effect and leads to changes in...
CMB power spectra
WM
AP
sc
ien
ce
tea
m
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
DGP modifies late structure growth, which modifiesISW effect and leads to changes in...
CMB power spectraCMB-LSS cross
correlation
WM
AP
sc
ien
ce
tea
m
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
DGP modifies late structure growth, which modifiesISW effect and leads to changes in...
CMB power spectraCMB-LSS cross
correlation
to quantify these effectswe need to know how
perturbations evolve inDGP models
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
bra
ne
future
past
Remove
focus on normal branch:
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
bra
ne
future
past
Remove
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
bra
ne
future
past
Remove
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
bra
ne
future
past
Remove
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
bra
ne
future
past
Remove
solve usingnumerical
simulations
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
solve usingnumerical
simulations
nullcomputational
domain
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
solve usingnumerical
simulations
nullcomputational
domain
initial data
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
solve usingnumerical
simulations
nullcomputational
domain
initial data
coupled braneODE and bulk
PDE solvedusing null finite
elements
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
solve usingnumerical
simulations
nullcomputational
domain
initial data
coupled braneODE and bulk
PDE solvedusing null finite
elements
there is an attractor solution:initial field configuration
unimportant if initial surfacefar enough in the past
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
solve usingnumerical
simulations
nullcomputational
domain
initial data
coupled braneODE and bulk
PDE solvedusing null finite
elements
there is an attractor solution:initial field configuration
unimportant if initial surfacefar enough in the past
alternate approach:direct scaling sol’n of
Sawicki et al (2007)... getsame answer
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 approximationequations to solve
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)have devoloped a
“quasistatic approximation”to solve this system
equations to solve
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
QS approx
e
qu
ati
on
s t
o s
olv
e Koyama & Maartens (2006)have devoloped a
“quasistatic approximation”to solve this system
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
QS
ap
pro
x
QS approx
Koyama & Maartens (2006)have devoloped a
“quasistatic approximation”to solve this system
eq
ua
tio
ns
to
so
lve
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
QS
ap
pro
x
QS approx
ADVANTAGE: need tosolve ODEs not PDEs
Koyama & Maartens (2006)have devoloped a
“quasistatic approximation”to solve this system
eq
ua
tio
ns
to
so
lve
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
QS
ap
pro
x
QS approx
QUESTION: on whichscales can we trust the
QS approximation?
ADVANTAGE: need tosolve ODEs not PDEs
Koyama & Maartens (2006)have devoloped a
“quasistatic approximation”to solve this system
eq
ua
tio
ns
to
so
lve
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 forBoltzmann codes/Monte Carlo methods, instead:
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 forBoltzmann codes/Monte Carlo methods, instead: concentrate on QS regime
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 forBoltzmann codes/Monte Carlo methods, instead: concentrate on QS regime use fitting functions in place of simulation results (PPF
formalism)
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 forBoltzmann codes/Monte Carlo methods, instead: concentrate on QS regime use fitting functions in place of simulation results (PPF
formalism) Giannantonio et al (2008):
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 forBoltzmann 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
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 forBoltzmann 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
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 forBoltzmann 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-correlationapplies more pressure
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 forBoltzmann 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-correlationapplies more pressure
curvature helps fit
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 forBoltzmann 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-correlationapplies more pressure
curvature helps fit Fang et al (2008):
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 forBoltzmann 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-correlationapplies more pressure
curvature helps fit Fang et al (2008):
concentrated on SA branch using PPF framework
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 forBoltzmann 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-correlationapplies 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
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 forBoltzmann 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-correlationapplies 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
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 perturbationsequations in the DGP model
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 perturbationsequations in the DGP model no additional approximations
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 perturbationsequations in the DGP model no additional approximations results independent of bulk initial conditions
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 perturbationsequations in the DGP model no additional approximations results independent of bulk initial conditions tested other approximations in the literature
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 perturbationsequations 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
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 perturbationsequations 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
on all interesting scales
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 perturbationsequations 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
on all interesting scales perturbation results have been compared to observations
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 perturbationsequations 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
on all interesting scales perturbation results have been compared to observations
self-accelerating DGP is in trouble due to excess largescale power in CMB
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 perturbationsequations 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
on all interesting scales perturbation results have been compared to observations
self-accelerating DGP is in trouble due to excess largescale power in CMB
normal branch still alive but future measures of ISW-LSScross correlation will be more definitive
![Linear Momentum Density in Quasistatic Electromagnetic Systems · arXiv:physics/0404139v1 [physics.ed-ph] 29 Apr 2004 Linear Momentum Density in Quasistatic Electromagnetic Systems](https://static.fdocuments.in/doc/165x107/5e00efafeeb98575462d5f23/linear-momentum-density-in-quasistatic-electromagnetic-systems-arxivphysics0404139v1.jpg)
