The Cosmological Slingshot Scenario

A Stringy Proposal for Early Time Cosmology:

Germani, NEG, Kehagias, hep-th/0611246 Germani, NEG, Kehagias, arXiv:0706.0023

Germani, Ligouri, arXiv:0706.0025

What do we know about

the universe?

Standard cosmologyIt is nearly

homogeneous It is nearly isotropic

The vacuum energy density is very small

It is expanding It is accelerating

The space is almost flat

The perturbations around homogeneity have a flat (slightly red) spectrum

4d metric

WMAP collaboration

astro-ph/0603449

Standard cosmologyIt is nearly

homogeneous It is nearly isotropic

The vacuum energy density is very small

It is expanding It is accelerating

The space is almost flat

4d metric

Einstein equationsHubble equation

Energy density

Curvature term

The perturbations around homogeneity have a flat (slightly red) spectrum

Standard cosmologyIt is nearly

homogeneous It is nearly isotropic

The vacuum energy density is very small

It is expanding It is accelerating

The space is almost flat

4d metric

Hubble equation

to

a

t

Plank

tPlank

Big

Bang

Solution

The perturbations around homogeneity have a flat (slightly red) spectrum

Standard cosmologyIt is nearly

homogeneous It is nearly isotropic

The vacuum energy density is very small

It is expanding It is accelerating

The space is almost flat

to

ttPlank

The perturbations around homogeneity have a flat (slightly red) spectrum

is constant in the observable region of 1028 cm

Causally disconnected regions are in equilibrium!

Standard cosmologyIt is nearly

homogeneous It is nearly isotropic

The vacuum energy density is very small

It is expanding It is accelerating

The space is almost flat

The perturbations around homogeneity have a flat (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 cosmologyIt is nearly

homogeneous It is nearly isotropic

The vacuum energy density is very small

It is expanding It is accelerating

The space is almost flat

The perturbations around homogeneity have a flat (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 cosmologyIt is nearly

homogeneous It is nearly isotropic

The vacuum energy density is very small

It is expanding It is accelerating

The space is almost flat

The perturbations around homogeneity have a flat (slightly red) spectrum

What created perturbations?

If they were created by primordial quantum fluctuations, its resulting spectrum for normal

matter is not flatTheir existence is necessary for the formation of structure

(clusters, galaxies)

The perturbations around homogeneity have a flat (slightly red) spectrum

The perturbations around homogeneity have a flat (slightly red) spectrum

Plank

tPlank

Big

Bang

Solving to the problemsInflation

Plank

Standard cosmologyIt is nearly

homogeneous It is nearly isotropic

The vacuum energy density is very small

It is expanding It is accelerating

The space is almost flat

tearlier < tNuc

to

a

t

It is nearly homogeneous

The space is almost flat

It is nearly isotropic

Guth, PRD 23, 347 (1981) Linde, PLB 108, 389

(1982)

The perturbations around homogeneity have a flat (slightly red) spectrum

It is nearly isotropic

The space is almost flat

Plank

Bounce

Standard cosmologyIt is nearly

homogeneous

The vacuum energy density is very small

It is expanding It is accelerating

The space is almost flat

tearlier< tNuc

to

a

t

Quantu

m r

egim

e

It is nearly homogeneous

Plank

to

a

t

Bounce

Plank

to

a

t

Inflation

Standard cosmologyIt is nearly

homogeneous It is nearly isotropic

The vacuum energy density is very small

It is expanding It is accelerating

The space is almost flat

The perturbations around homogeneity have a flat (slightly red) spectrum

tearlier< tNuc

Quantu

m r

egim

eC

an t

he b

ounce

be c

lass

ical?

Mirage cosmology

Higher dimensional

bulk4d flat s

lice

3-Bra

ne

Warping factor

Matter

Universe

Cosmological evolution

Plank

to

a

ttearlier

Kehagias, Kiritsishep-th/

9910174

PlankPlank

tPlank

Big

B

ang

Mirage 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 motion

Solve Einstein

equationsSolve

equations of motion

Slingshot cosmology

10d bulk IIB SUGRA solution

4d flat

slice

BPS

Warping factor

D3-Bra

neCosmological

expansion

Plank

to

a

ttearlier

Xaü

x||

Germani, NEG, Kehagias

hep-th/0611246

Slingshot cosmology

Xaü

x||

Plank

to

a

ttearlierXa

ü

Dilaton field Induced metric

RR field

Turning point

Bounce

Burgess, Quevedo, Rabadan, Tasinato, Zavala, hep-th/0310122

6d flat euclidean metric

Warping factor

Slingshot cosmology

Xaü

Plank

to

a

ttearlierXa

ü

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 cosmology

Xaü

Plank

to

a

ttearlierXa

ü

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 cosmologyPlank

to

a

ttearlier

Constraint in parameter

space

Slingshot 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 cosmologyPlank

to

a

ttearlier

And about perturbations?

Induced scalar Bardeen potential

Slingshot 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 cosmologyPlank

to

a

ttearlier

Power spectrum

= < >

Created by quantum perturbations

h*

r *= kL / lc Creation of the

mode

l = lc Creation of the mode

Slingshot cosmologyPlank

to

a

ttearlier

Power spectrum h*

l > lc Classical mode

l < lc Quantum

mode

Hollands, Waldgr-qc/0205058

l = k /a = kL / rWe get a flat

spectrum

Slingshot cosmologyPlank

to

a

ttearlier

Gravity is ten dimensional

Late time cosmology

Formation of structure

Kepler 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 Points

The price we paid is an unknown transition region between local and mirage

gravity (reheating)

It is nearly isotropic

The perturbations around homogeneity have a flat

spectrum

The space is almost flat

Slingshot cosmologyIt is nearly

homogeneous

The vacuum energy density is very small

It is expanding It is accelerating

Nice Results

Klevanov-Strassler geometry gives a slightly red spectral index, in agreement with

WMAPProblems with Hollands and Wald proposal are avoided in

the Slingshot scenario

An effective 4D action can be found

There is no effective 4D theory

Back-reaction effects should be studied

Thanks!