slingshot cosmology - porto
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The Cosmological Slingshot The Cosmological Slingshot ScenarioScenario
A New Proposal for Early Time A New Proposal for Early Time CosmologyCosmology
Germani, NEG, Kehagias, hep-th/0611246
Germani, NEG, Kehagias, arXiv:0706.0023
Germani, Ligouri, arXiv:0706.0025
Standard cosmologyStandard cosmologyIt is nearly It is nearly
homogeneous homogeneous It is nearly It is nearly isotropicisotropic
The vacuum The vacuum energy density energy density is very smallis very small
It is expanding It is expanding It is It is acceleratingaccelerating
The space is The space is almost flatalmost flat
The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat (slightly red) spectrum(slightly red) spectrum
Space curvature+1, 0
4d metric
Cosmic time
Scale factor
Space Coordinate
s(polar)
What do we What do we know about know about
the universe?the universe?
WMAP collaboration
astro-ph/0603449
Standard cosmologyStandard cosmologyIt is nearly It is nearly
homogeneous homogeneous It is nearly It is nearly isotropicisotropic
The vacuum The vacuum energy density energy density is very smallis very small
It is expanding It is expanding It is It is acceleratingaccelerating
The space is The space is almost flatalmost flat
4d metric
Einstein equationsHubble equation
Energy density
Curvature term
Equation of state
The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat (slightly red) spectrum(slightly red) spectrum
Energy Conditions
Equation of state
Standard cosmologyStandard cosmologyIt is nearly It is nearly
homogeneous homogeneous It is nearly It is nearly isotropicisotropic
The vacuum The vacuum energy density energy density is very smallis very small
It is expanding It is expanding It is It is acceleratingaccelerating
The space is The space is almost flatalmost flat
4d metric
Hubble equation
to
a
t
Plank
tPlank
Big
Bang
Solution
The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat (slightly red) spectrum(slightly red) spectrum
Standard cosmologyStandard cosmologyIt is nearly It is nearly
homogeneous homogeneous It is nearly It is nearly isotropicisotropic
The vacuum The vacuum energy density energy density is very smallis very small
It is expanding It is expanding It is It is acceleratingaccelerating
The space is The space is almost flatalmost flat
tot
tPlank
The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat (slightly red) spectrum(slightly red) spectrum
is constant in the observable region of 1028 cm
Causally disconnected regions are in equilibrium!
Standard cosmologyStandard cosmologyIt is nearly It is nearly
homogeneous homogeneous It is nearly It is nearly isotropicisotropic
The vacuum The vacuum energy density energy density is very smallis very small
It is expanding It is expanding It is It is acceleratingaccelerating
The space is The space is almost flatalmost flat
The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat (slightly red) spectrum(slightly red) spectrum
Isotropic solutions form a subset of measure zero on the
set of all Bianchi solutions
Perturbations around isotropy dominate at early time, like a -
6 , giving rise to chaotic behavior!
Belinsky, Khalatnikov, Lifshitz, Adv. Phys. 19, 525 (1970)
Collins, HawkingAstr.Jour.180, (1973)
Standard cosmologyStandard cosmologyIt is nearly It is nearly
homogeneous homogeneous It is nearly It is nearly isotropicisotropic
The vacuum The vacuum energy density energy density is very smallis very small
It is expanding It is expanding It is It is acceleratingaccelerating
The space is The space is almost flatalmost flat
The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat (slightly red) spectrum(slightly red) spectrum
It is a growing function
Since it is small today, it was even smaller at earlier time!
(10-8 at Nuc.)
Standard cosmologyStandard cosmologyIt is nearly It is nearly
homogeneous homogeneous It is nearly It is nearly isotropicisotropic
The vacuum The vacuum energy density energy density is very smallis very small
It is expanding It is expanding It is It is acceleratingaccelerating
The space is The space is almost flatalmost flat
The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat (slightly red) spectrum(slightly red) spectrum
What created perturbations?
If they were created by primordial quantum
fluctuations, its resulting spectrum for 2-n < 6 is not flatTheir existence is necessary
for the formation of structure (clusters, galaxies)
The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat (slightly red) spectrum(slightly red) spectrum
The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat (slightly red) spectrum(slightly red) spectrum
Plank
tPlank
Big
Bang
Solving to the problemsInflationPlank
Standard cosmologyStandard cosmologyIt is nearly It is nearly
homogeneous homogeneous It is nearly It is nearly isotropicisotropic
The vacuum The vacuum energy density energy density is very smallis very small
It is expanding It is expanding It is It is acceleratingaccelerating
The space is The space is almost flatalmost flat
tearlier < tNuc
to
a
t
It is nearly It is nearly homogeneous homogeneous
The space is The space is almost flatalmost flat
It is nearly It is nearly isotropicisotropic
Guth, PRD 23, 347 (1981)
Linde, PLB 108, 389 (1982)
The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat (slightly red) spectrum(slightly red) spectrum
It is nearly It is nearly isotropicisotropic
The space is The space is almost flatalmost flat
Plank
Bounce
Standard cosmologyStandard cosmologyIt is nearly It is nearly
homogeneous homogeneous
The vacuum The vacuum energy density energy density is very smallis very small
It is expanding It is expanding It is It is acceleratingaccelerating
The space is The space is almost flatalmost flat
tearlier< tNuc
to
a
t
Quan
tum
regi
me
It is nearly It is nearly homogeneous homogeneous
Lasts enough?
Plank
to
a
t
Plank
to
a
t
BounceInflation
Standard cosmologyStandard cosmologyIt is nearly It is nearly
homogeneous homogeneous It is nearly It is nearly isotropicisotropic
The vacuum The vacuum energy density energy density is very smallis very small
It is expanding It is expanding It is It is acceleratingaccelerating
The space is The space is almost flatalmost flat
The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat (slightly red) spectrum(slightly red) spectrum
tearlier< tNuc
Quan
tum
regi
me
Can
the
boun
ce b
e cla
ssica
l?
Mirage cosmologyMirage cosmology
Higher dimensional
bulk4d flat sl
ice
3-Brane
Warping factor
Matter
Universe
Cosmological evolution
Plank
to
a
ttearlier
Kehagias, Kiritsishep-th/
9910174
PlankPlank
tPlank
Big
Bang
Mirage cosmologyMirage cosmology
to
a
ttearlier
Increasing
warping
Monotonousmotion
Expanding Universe
How can we obtain a bounce? A minimum in
the warping factorA turning point
in the motionSolve
Einstein equations
Solve equations of
motion
Slingshot cosmologySlingshot cosmology
10d bulk IIB SUGRA solution
4d flat
slice BPS
Warping factor
D3-BraneCosmological
expansion
Plank
to
a
ttearlier
XaT
x||
Germani, NEG, Kehagias
hep-th/0611246
Slingshot cosmologySlingshot cosmology
XaT
x||
Plank
to
a
ttearlierXa
T
Dilaton field Induced metric
RR field
Turning point
BounceBurgess, Quevedo, Rabadan, Tasinato, Zavala, hep-th/0310122
6d flat euclidean metric
Warping factor
Slingshot cosmologySlingshot cosmology
XaT
Plank
to
a
ttearlierXa
T
Transverse metric
AdS5xS5 space
Free particle
Turning point
Bounce
Non-vanishing impact parameter
Non-vanishing angular momentum
l
Heavy source Stack of branes
Burgess, Martineau , Quevedo, Rabadan, hep-th/0303170 Burgess, NEG, F. Quevedo, Rabadan, hep-th/0310010
Non-vanishing angular momentum
l
6d flat Euclidean metric
Slingshot cosmologySlingshot cosmology
XaT
Plank
to
a
ttearlierXa
T
AdS5xS5 space
Free particle
Heavy source Stack of branes
There is no space curvature
Can we solve the flatness problem?
Flatness problemis solved
There is no space curvature
Slingshot cosmologySlingshot cosmologyPlank
to
a
ttearlier
Constraint in parameter
space
Slingshot cosmologySlingshot cosmologyPlank
to
a
ttearlier
What about isotropy?
Dominates at early time, avoiding chaotic behaviour
All the higher orders in r´
Isotropy problem is
solved
Slingshot cosmologySlingshot cosmologyPlank
to
a
ttearlier
And about perturbations?
Induced scalar Bardeen potential
Slingshot cosmologySlingshot cosmologyPlank
to
a
ttearlier
And about perturbations?
Scalar fieldHarmonic oscillator
Growing modes
Oscilating modes
Frozen modes
Decaying modes
Frozen modes survive up to late times Decaying modes do not
survive Boehm, Steer,hep-th/0206147
Germani, NEG, Kehagias
arXiv:0706.0023
Frozen modes
Slingshot cosmologySlingshot cosmologyPlank
to
a
ttearlier
Power spectrum
= < >
Created by quantum perturbations
*
= lc Creation of the moder= kL/ lc Creation of the mode
Slingshot cosmologySlingshot cosmologyPlank
to
a
ttearlier
Power spectrum *
> lc Classical mode< lc Quantum mode
Hollands, Waldgr-qc/0205058
= ka= kL / rWe get a flat
spectrum
Slingshot cosmologySlingshot cosmologyPlank
to
a
ttearlier
Gravity is ten dimensional
Late time cosmology
Formation of structureKepler laws
Real life!
Compactification
AdS throat in a CY space
AdS throat
Top of the CY
Mirage dominate
d era
Local 4d gravity
dominated erabackreaction
Mirage domination in
the throat
Local gravity domination in
the top
The transition is out of our
control
Open PointsOpen PointsThe price we paid is an
unknown transition region between local and mirage
gravity (reheating)
It is nearly It is nearly isotropicisotropic
The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat
spectrumspectrum
The space is The space is almost flatalmost flat
Slingshot cosmologySlingshot cosmologyIt is nearly It is nearly
homogeneous homogeneous
The vacuum The vacuum energy density energy density is very smallis very small
It is expanding It is expanding It is It is acceleratingaccelerating
Nice ResultsNice ResultsKlevanov-Strassler geometry gives a slightly red spectral index, in agreement with
WMAPProblems with Hollands and
Wald proposal are avoided in the Slingshot scenario
Einstein frame is also compatible with observations
There is no effective 4D theory
Back-reaction effects should be studied
Thanks!
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