Slingshot Cosmology - Porto

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






4d metric

Einstein equationsHubble equation

Energy density

Curvature term

Equation of state


Energy Conditions

Equation of state






4d metric

Hubble equation

to

a

t

Plank

tPlank

Big

Bang

Solution







tot

tPlank


is constant in the observable region of 1028 cm

Causally disconnected regions are in equilibrium!







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)







It is a growing function

Since it is small today, it was even smaller at earlier time!

(10-8 at Nuc.)







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)



Plank

tPlank

Big

Bang

Solving to the problemsInflationPlank






tearlier < tNuc

to

a

t

It is nearly It is nearly homogeneous homogeneous


It is nearly It is nearly isotropicisotropic

Guth, PRD 23, 347 (1981)

Linde, PLB 108, 389 (1982)




Plank

Bounce


homogeneous homogeneous




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







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


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


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


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


to

a

ttearlier

What about isotropy?

Dominates at early time, avoiding chaotic behaviour

All the higher orders in r´

Isotropy problem is

solved


to

a

ttearlier

And about perturbations?

Induced scalar Bardeen potential


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


to

a

ttearlier

Power spectrum

= < >

Created by quantum perturbations

*

= lc Creation of the moder= kL/ lc Creation of the mode


to

a

ttearlier

Power spectrum *

> lc Classical mode< lc Quantum mode

Hollands, Waldgr-qc/0205058

= ka= kL / rWe get a flat

spectrum


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)


The perturbations around The perturbations around homogeneity have a flat homogeneity have a flat

spectrumspectrum


Slingshot cosmologySlingshot cosmologyIt is nearly It is nearly

homogeneous homogeneous



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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