Download Nicolás Grandi

A Stringy Proposal for Early Time Cosmology:
The Cosmological
Slingshot Scenario
Germani, NEG, Kehagias, hep-th/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
It is nearly
isotropic
4d metric
The space is
almost flat
Einstein
equations
Hubble equation
Energy
density
Curvature
term
The perturbations around
homogeneity have a flat
(slightly red) spectrum
It is accelerating
Standard cosmology
It is nearly
homogeneous
Solution
4d metric
It is nearly
isotropic
Plank
a
The vacuum
energy density is
very small
Big Bang
It is expanding
The space is
almost flat
Hubble equation

tPlank
The perturbations around
homogeneity have a flat
(slightly red) spectrum
to
It is accelerating
t
Standard cosmology
It is nearly
homogeneous
The vacuum
energy density is
very small
It is expanding
It is nearly
isotropic
 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
It is accelerating
t
Standard cosmology
It is nearly
homogeneous
The vacuum
energy density is
very small
It is expanding
Belinsky, Khalatnikov, Lifshitz,
Adv. Phys. 19, 525 (1970)
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 vacuum
energy density is
very small
The space is
almost flat
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
SolvingInflation
to the problems
Plank
a
The vacuum
energy density is
very small
Big Bang
It is expanding
The space is
almost flat

tPlank
tearlier < tNuc
The perturbations around
homogeneity have a flat
(slightly red) spectrum
to
It is accelerating
t
Standard cosmology
It is nearly
homogeneous
It is nearly
isotropic
Bounce
Plank
It is expanding
The space is
almost flat
Quantum regime
The vacuum
energy density is
very small
a

tearlier< tNuc
The perturbations around
homogeneity have a flat
(slightly red) spectrum
to
It is accelerating
t
Standard cosmology
It is nearly
homogeneous
It is expanding
be classical?
the bounceregime
Can Quantum
Bounce
Inflation
Plank
The vacuum
energy density is
very small
It is nearly
isotropic
a
The space is
almost flat

tearlier< tNuc
The perturbations around
homogeneity have a flat
(slightly red) spectrum
to
It is accelerating
t
Kehagias, Kiritsis
hep-th/9910174
Mirage cosmology
Plank
a

Higher dimensional
bulk
Warping factor
Cosmological
evolution
tearlier
to
t
Mirage cosmology
Monotonous
motion
Expanding
Universe
a
Big Bang
Increasing
warping
Plank
tPlank

tearlier
to
t
How can we
obtain a bounce?
A minimum in the
warping factor
A turning point
in the motion
Solve equations
of motion
Solve Einstein
equations
Germani, NEG, Kehagias
Slingshot cosmology
hep-th/0611246
Plank
a

x||
10d bulk
IIB SUGRA solution
Cosmological
expansion
Warping factor
Xaü
tearlier
to
t
Slingshot cosmology
RR field
Dilaton field
Plank
a
Induced metric

Xaü
x||
Bounce
Turning
point
Xaü
tearlier
to
Burgess, Quevedo, Rabadan,
Tasinato, Zavala, hep-th/0310122
t
Slingshot cosmology
Plank
6d
Transverse
flat euclidean
metricmetric
a
Free particle
AdS5xS5 space

Xa
ü
Turning
point
Bounce
to
Warping
factor
Non-vanishing angular
impact
momentum
parameter l
Heavy source
Stack of branes
tearlier
Xaü
Burgess, Martineau , Quevedo,
Rabadan, hep-th/0303170
Burgess, NEG, F. Quevedo,
Rabadan, hep-th/0310010
t
Slingshot cosmology
Plank
6d flat Euclidean metric
a
There is no space
Free particle
curvature
AdS5xS5 space

tearlier
Xaü
Non-vanishing angular
momentum l
Heavy source
Stack of branes
Xaü
to
t
Slingshot cosmology
Plank
a
There is no space
curvature

Flatness
problem
Can
we solve
the
flatness
problem?
is solved
tearlier
Constraint in
parameter space
to
t
Slingshot cosmology
All the higher orders in r´
Plank
a
What problem
about
Isotropy
isotropy?
is
solved

tearlier
to
Dominates at early time,
avoiding chaotic behaviour
t
Slingshot cosmology
Plank
a
And about
perturbations?

tearlier
to
t
Slingshot cosmology
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

tearlier
to
t
Slingshot cosmology
Plank
a

tearlier
Frozen modes
to
Power spectrum
Created by quantum perturbations
h*
=<
>
t
Slingshot cosmology
Plank
l > lc
Classical mode
l < lc
Quantum mode
r *=
l
= lkL
c / lc
Creation
Creation of
of the
the mode
mode
a

l = k /a = kL / r
tearlier
We get a flat
spectrum
Power spectrum
h*
Hollands, Wald
gr-qc/0205058
to
t
Slingshot cosmology
Plank
a
time
Gravity is ten dimensionalAdS Late
Compactification
throat
in acosmology
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

to
Local 4d gravity
Mirage
dominated dominated era
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
The
Klevanov-Strassler
price we paid isgeometry
an unknown
gives
transition
a slightly
region
red spectral
betweenindex,
local and
in
mirage
agreement
gravitywith
(reheating)
WMAP
Problems with Hollands and Wald
There is no effective 4D theory
proposal are avoided in the
Slingshot scenario
Back-reaction effects should be
An effectivestudied
4D action can be
found
The perturbations around
homogeneity have a flat
spectrum
It is nearly
isotropic
The space is
almost flat
It is accelerating