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A Stringy Proposal Early Time Thefor Cosmological Cosmology: Slingshot
Scenario
Germani, NEG, Kehagias, hepth/0611246 Germani, NEG, Kehagias, arXiv:0706.0023 Germani, Ligouri, arXiv:0706.0025
Standard cosmology It is nearly homogeneous
The vacuum energy density is very small
4d metric
What do we know about the universe?
It is expanding
It is nearly isotropic
The space is almost flat
It is accelerating
The perturbations around homogeneity have a flat (slightly red) spectrum
WMAP collaboration astro-ph/0603449
Standard cosmology It is nearly homogeneous
The vacuum energy density is very small
It is expanding
4d metric
Einstein equations Hubble equation
Energy Curvature density term
The perturbations around homogeneity have a flat (slightly red) spectrum
It is nearly isotropic
The space is almost flat
It is accelerating
Standard cosmology It is nearly homogeneous
Solution 4d metric
ρ Plank
a
The vacuum energy density is very small
The space is almost flat
Hubble equation Big Bang
It is expanding
It is nearly isotropic
ρ tPlank The perturbations around homogeneity have a flat (slightly red) spectrum
to
t
It is accelerating
Standard cosmology It is nearly homogeneous
The vacuum energy density is very small
It is expanding
It is nearly isotropic
ρ is constant in the observable region of 1028 cm
The space is almost flat
Causally disconnected regions are in equilibrium! tPlank The perturbations around homogeneity have a flat (slightly red) spectrum
to
t
It is accelerating
Standard cosmology It is nearly homogeneous
The vacuum energy density is very small
It is expanding
Belinsky, Khalatnikov, Lifshitz, Adv. Phys. 19, 525
It is nearly isotropic
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!
The perturbations around homogeneity have a flat (slightly red) spectrum
The space is almost flat
It is accelerating
Collins, Hawking Astr.Jour.180, (1973)
Standard cosmology It is nearly homogeneous
It is nearly isotropic
(10-8 at Nuc.) The space is almost flat
The vacuum energy density is very small It is a growing function It is expanding
Since it is small today, it was even smaller at earlier time!
The perturbations around homogeneity have a flat (slightly red) spectrum
It is accelerating
Standard cosmology It is nearly homogeneous
It is nearly isotropic What created perturbations?
The vacuum energy density is very small
It is expanding
If they were created by primordial quantum fluctuations, its resulting spectrum for normal matter is not flat Their existence is necessary for the formation of structure (clusters, galaxies)
The perturbations around homogeneity have a flat (slightly red) spectrum
The space is almost flat
It is accelerating
Guth, PRD 23, 347 (1981) Linde, PLB 108, 389 (1982)
Standard cosmology It is nearly homogeneous
It is nearly isotropic
Inflation Solving to the problems
ρ Plank
a
The vacuum energy density is very small Big Bang
It is expanding
The space is almost flat
ρ tPlank
tearlier < tNuc
to
The perturbations around homogeneity have a flat (slightly red) spectrum
t
It is accelerating
Standard cosmology It is nearly homogeneous
It is nearly isotropic
Bounce
ρ Plank
It is expanding
Quantum regime
The vacuum energy density is very small
a The space is almost flat
ρ tearlier< tNuc
to
The perturbations around homogeneity have a flat (slightly red) spectrum
t
It is accelerating
Standard cosmology It is nearly homogeneous
It is expanding
CanQuantum the bounce regime be classical?
Bounce Inflation
ρ Plank The vacuum energy density is very small
It is nearly isotropic a The space is almost flat
ρ tearlier< tNuc
to
The perturbations around homogeneity have a flat (slightly red) spectrum
t
It is accelerating
Kehagias, Kiritsis hepth/9910174
Mirage cosmology ρ Plank
a
ρ
aBtr l f 3 4d
e ice l n s a
Higher dimensional bulk Warping factor
r
te at
M
v
i Un
e
s er
Cosmological evolution
tearlier
to
t
Mirage cosmology Monotonous motion
Expanding Universe
a
Big Bang
Increasin g warping
ρ Plank
tPlank
ρ tearlier
How can we obtain a bounce?
A turning point in the motion Solve equations of
to
A minimum in the warping Solve factor Einstein equations
t
Slingshot cosmology
Germani, NEG, Kehagias hep-th/0611246
ρ Plank
a
ρ xµ|| te lfr an S d-B BP 4 3 D ice sl
10d bulk IIB SUGRA solution
Cosmological expansion
Warping factor
Xaü
tearlier
to
t
Slingshot cosmology ρ Plank
RR field
Dilaton field
a
Induced metric
ρ X
a ü
xµ||
Bounce Turning point
Xaü
tearlier
to
Burgess, Quevedo, Rabadan, Tasinato, Zavala, hep-th/0310122
t
Slingshot cosmology Transverse 6d flat euclidean metric metric Free particle
ρ Plank
a
AdS5xS5 space
ρ X
a ü
Turning point
Bounce
tearlier
to
Warping factor
Non-vanishing Non-vanishing impact angular momentum parameter
l Xaü
Heavy source Stack of branes
Burgess, Martineau , Quevedo, Rabadan, hepth/0303170 Burgess, NEG, F. Quevedo,
t
Slingshot cosmology 6d flat Euclidean metric There is no Free particle
ρ Plank
a
space curvature AdS5xS5 space
ρ X
tearlier
a ü
Non-vanishing angular momentum
l Xaü
Heavy source Stack of branes
to
t
Slingshot cosmology ρ Plank
a
There is no space curvature
ρ Flatness Can we solve problem the flatness problem? is solved
tearlier
Constraint in parameter space
to
t
Slingshot cosmology All the higher orders in r´
What about Isotropy isotropy? problem is solved
ρ Plank
a
ρ tearlier
to
Dominates at early time, avoiding chaotic behaviour
t
Slingshot cosmology ρ Plank
a
And about perturbations?
ρ tearlier
to
t
Slingshot cosmology ρ Plank
Germani, NEG, Kehagias arXiv:0706.0023 Boehm, Steer, hep-th/0206147
a
Induced scalar Bardeen Scalar field And about Harmonic oscillator potential perturbations? Growing Frozen modes modes Oscilating modes Decaying modes
Frozen modes survive up to late times Decaying modes do not survive
ρ tearlier
to
t
Slingshot cosmology ρ Plank
a
ρ tearlier
Frozen modes
Power spectrum
Created by quantum perturbations
η*
=<
>
to
t
Slingshot cosmology λ > lc
Classical mode
λ < lc
Quantum
ρ Plank
a
mode
r ∗= λ = lkL / lc c
Creation of the mode
ρ
λ = k /a = kL / r
tearlier
We get a flat spectrum
Power spectrum
η*
Hollands, Wald grqc/0205058
to
t
Slingshot cosmology ρ Plank Compactificatio Gravity is ten dimensional n
a
time cosmology AdS Late throat in a CY space Formation of structure
Mirage domination in the throat
Kepler laws Local gravity domination in Real life! the top
tearlier
The transition is out of our control
AdS throat
ρ to
Local 4d Mirage gravity dominate dominated era d era backreaction
Top of the CY
t
Slingshot cosmology It is nearly homogeneous
The vacuum energy density is very small
It is expanding
Nice OpenResults Points Klevanov-Strassler The price we paidgeometry is an gives unknown a slightly transition red spectral region between index, inlocal agreement and mirage with gravityWMAP (reheating) Problems with Hollands and There is no effective 4D theory Wald proposal are avoided in the Slingshot scenario Back-reaction effects should be 4D studied An effective action can be found
The perturbations around homogeneity have a flat spectrum
It is nearly isotropic
The space is almost flat
It is accelerating
Scenario
Germani, NEG, Kehagias, hepth/0611246 Germani, NEG, Kehagias, arXiv:0706.0023 Germani, Ligouri, arXiv:0706.0025
Standard cosmology It is nearly homogeneous
The vacuum energy density is very small
4d metric
What do we know about the universe?
It is expanding
It is nearly isotropic
The space is almost flat
It is accelerating
The perturbations around homogeneity have a flat (slightly red) spectrum
WMAP collaboration astro-ph/0603449
Standard cosmology It is nearly homogeneous
The vacuum energy density is very small
It is expanding
4d metric
Einstein equations Hubble equation
Energy Curvature density term
The perturbations around homogeneity have a flat (slightly red) spectrum
It is nearly isotropic
The space is almost flat
It is accelerating
Standard cosmology It is nearly homogeneous
Solution 4d metric
ρ Plank
a
The vacuum energy density is very small
The space is almost flat
Hubble equation Big Bang
It is expanding
It is nearly isotropic
ρ tPlank The perturbations around homogeneity have a flat (slightly red) spectrum
to
t
It is accelerating
Standard cosmology It is nearly homogeneous
The vacuum energy density is very small
It is expanding
It is nearly isotropic
ρ is constant in the observable region of 1028 cm
The space is almost flat
Causally disconnected regions are in equilibrium! tPlank The perturbations around homogeneity have a flat (slightly red) spectrum
to
t
It is accelerating
Standard cosmology It is nearly homogeneous
The vacuum energy density is very small
It is expanding
Belinsky, Khalatnikov, Lifshitz, Adv. Phys. 19, 525
It is nearly isotropic
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!
The perturbations around homogeneity have a flat (slightly red) spectrum
The space is almost flat
It is accelerating
Collins, Hawking Astr.Jour.180, (1973)
Standard cosmology It is nearly homogeneous
It is nearly isotropic
(10-8 at Nuc.) The space is almost flat
The vacuum energy density is very small It is a growing function It is expanding
Since it is small today, it was even smaller at earlier time!
The perturbations around homogeneity have a flat (slightly red) spectrum
It is accelerating
Standard cosmology It is nearly homogeneous
It is nearly isotropic What created perturbations?
The vacuum energy density is very small
It is expanding
If they were created by primordial quantum fluctuations, its resulting spectrum for normal matter is not flat Their existence is necessary for the formation of structure (clusters, galaxies)
The perturbations around homogeneity have a flat (slightly red) spectrum
The space is almost flat
It is accelerating
Guth, PRD 23, 347 (1981) Linde, PLB 108, 389 (1982)
Standard cosmology It is nearly homogeneous
It is nearly isotropic
Inflation Solving to the problems
ρ Plank
a
The vacuum energy density is very small Big Bang
It is expanding
The space is almost flat
ρ tPlank
tearlier < tNuc
to
The perturbations around homogeneity have a flat (slightly red) spectrum
t
It is accelerating
Standard cosmology It is nearly homogeneous
It is nearly isotropic
Bounce
ρ Plank
It is expanding
Quantum regime
The vacuum energy density is very small
a The space is almost flat
ρ tearlier< tNuc
to
The perturbations around homogeneity have a flat (slightly red) spectrum
t
It is accelerating
Standard cosmology It is nearly homogeneous
It is expanding
CanQuantum the bounce regime be classical?
Bounce Inflation
ρ Plank The vacuum energy density is very small
It is nearly isotropic a The space is almost flat
ρ tearlier< tNuc
to
The perturbations around homogeneity have a flat (slightly red) spectrum
t
It is accelerating
Kehagias, Kiritsis hepth/9910174
Mirage cosmology ρ Plank
a
ρ
aBtr l f 3 4d
e ice l n s a
Higher dimensional bulk Warping factor
r
te at
M
v
i Un
e
s er
Cosmological evolution
tearlier
to
t
Mirage cosmology Monotonous motion
Expanding Universe
a
Big Bang
Increasin g warping
ρ Plank
tPlank
ρ tearlier
How can we obtain a bounce?
A turning point in the motion Solve equations of
to
A minimum in the warping Solve factor Einstein equations
t
Slingshot cosmology
Germani, NEG, Kehagias hep-th/0611246
ρ Plank
a
ρ xµ|| te lfr an S d-B BP 4 3 D ice sl
10d bulk IIB SUGRA solution
Cosmological expansion
Warping factor
Xaü
tearlier
to
t
Slingshot cosmology ρ Plank
RR field
Dilaton field
a
Induced metric
ρ X
a ü
xµ||
Bounce Turning point
Xaü
tearlier
to
Burgess, Quevedo, Rabadan, Tasinato, Zavala, hep-th/0310122
t
Slingshot cosmology Transverse 6d flat euclidean metric metric Free particle
ρ Plank
a
AdS5xS5 space
ρ X
a ü
Turning point
Bounce
tearlier
to
Warping factor
Non-vanishing Non-vanishing impact angular momentum parameter
l Xaü
Heavy source Stack of branes
Burgess, Martineau , Quevedo, Rabadan, hepth/0303170 Burgess, NEG, F. Quevedo,
t
Slingshot cosmology 6d flat Euclidean metric There is no Free particle
ρ Plank
a
space curvature AdS5xS5 space
ρ X
tearlier
a ü
Non-vanishing angular momentum
l Xaü
Heavy source Stack of branes
to
t
Slingshot cosmology ρ Plank
a
There is no space curvature
ρ Flatness Can we solve problem the flatness problem? is solved
tearlier
Constraint in parameter space
to
t
Slingshot cosmology All the higher orders in r´
What about Isotropy isotropy? problem is solved
ρ Plank
a
ρ tearlier
to
Dominates at early time, avoiding chaotic behaviour
t
Slingshot cosmology ρ Plank
a
And about perturbations?
ρ tearlier
to
t
Slingshot cosmology ρ Plank
Germani, NEG, Kehagias arXiv:0706.0023 Boehm, Steer, hep-th/0206147
a
Induced scalar Bardeen Scalar field And about Harmonic oscillator potential perturbations? Growing Frozen modes modes Oscilating modes Decaying modes
Frozen modes survive up to late times Decaying modes do not survive
ρ tearlier
to
t
Slingshot cosmology ρ Plank
a
ρ tearlier
Frozen modes
Power spectrum
Created by quantum perturbations
η*
=<
>
to
t
Slingshot cosmology λ > lc
Classical mode
λ < lc
Quantum
ρ Plank
a
mode
r ∗= λ = lkL / lc c
Creation of the mode
ρ
λ = k /a = kL / r
tearlier
We get a flat spectrum
Power spectrum
η*
Hollands, Wald grqc/0205058
to
t
Slingshot cosmology ρ Plank Compactificatio Gravity is ten dimensional n
a
time cosmology AdS Late throat in a CY space Formation of structure
Mirage domination in the throat
Kepler laws Local gravity domination in Real life! the top
tearlier
The transition is out of our control
AdS throat
ρ to
Local 4d Mirage gravity dominate dominated era d era backreaction
Top of the CY
t
Slingshot cosmology It is nearly homogeneous
The vacuum energy density is very small
It is expanding
Nice OpenResults Points Klevanov-Strassler The price we paidgeometry is an gives unknown a slightly transition red spectral region between index, inlocal agreement and mirage with gravityWMAP (reheating) Problems with Hollands and There is no effective 4D theory Wald proposal are avoided in the Slingshot scenario Back-reaction effects should be 4D studied An effective action can be found
The perturbations around homogeneity have a flat spectrum
It is nearly isotropic
The space is almost flat
It is accelerating
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