Towards inflation and Towards inflation and dark energy cosmologies dark energy cosmologies

in string generated in string generated gravity modelsgravity modelsIshwaree NeupaneIshwaree NeupaneUniversity of CanterburyUniversity of Canterbury

March 1, 2006

40th Rencontres de Moriond, La Tuile 18-25 March 2006

OutlookOutlook The 20The 20thth Century Physics Century Physics

General Relativity vs Quantum MechanicsGeneral Relativity vs Quantum Mechanics The Physics of 80’s and 90’s The Physics of 80’s and 90’s

String Theory: A Theoretical Balancing ActString Theory: A Theoretical Balancing Act Ingredients: Extra Dimensions, Ingredients: Extra Dimensions,

SupersymmetrySupersymmetry String/M Theory: One Mo’ Time!String/M Theory: One Mo’ Time!

Beyond perturbative approach: Branes, Beyond perturbative approach: Branes, Fluxes, CyclesFluxes, Cycles

Inflation, Dark Energy and OpportunitiesInflation, Dark Energy and Opportunities

Big result in cosmology? still there in 2006?

High-z SNeIa are High-z SNeIa are fainterfainter

than expected in an than expected in an Einstein-deSitter Einstein-deSitter

modelmodel

The case for The case for 1)1)Hubble Hubble

diagramdiagram2)2)subtractionsubtraction

7.03.01

,3.0,1

Mtotal

Thanks to WMAP and Other Thanks to WMAP and Other Experiments for the Experiments for the coordinated support coordinated support

Already >50 dark energy Already >50 dark energy proposals in the market! proposals in the market!

Cosmological Concordance Cosmological Concordance ModelModel

Early InflationEarly Inflation de Sitter spacede Sitter space During 10^{-30} During 10^{-30}

secsec

Current AccelerationCurrent Acceleration Near de Sitter spaceNear de Sitter space During few billion During few billion

yearsyears

The ultimate laws of Nature might The ultimate laws of Nature might contain a fundamental and simple, contain a fundamental and simple, concise relation concise relation

between past and future between past and future

between close-by and far-awaybetween close-by and far-away

String Compactification?String Compactification?

How to get de Sitter or near de Sitter 4d space?How to get de Sitter or near de Sitter 4d space?

Duality WebDuality Web

gg /1 Cosmologically RichCosmologically Rich

Anti-de Sitter Holography, Brane WorldAnti-de Sitter Holography, Brane World

RR /1

A Remarkable Discovery in Physics (1995/1996)A Remarkable Discovery in Physics (1995/1996)

Cosmic Acceleration from Cosmic Acceleration from String Effective Action?String Effective Action?

Heterotic string theory, after its discovery back Heterotic string theory, after its discovery back in 1985/86, appeared to be the string theorist’s in 1985/86, appeared to be the string theorist’s dream as something like the real worddream as something like the real word

GVR

gxdS )()()(2

)(2

)(2

222

4

wherewhere abcd

abcdab

ab RRRRRG 42

is the Gauss-Bonnet integrandis the Gauss-Bonnet integrand

IPN (with Carter) IPN (with Carter) hep-th/0510109hep-th/0510109 (PRD/Rapid) , (PRD/Rapid) ,

hep-th/0512262 hep-th/0512262 (JCAP), (JCAP), hep-th/0602097hep-th/0602097

dilatondilaton

modulusmodulus

0)cosh(3

2)2ln()(

.....)( 0 e

In a known example of string In a known example of string compactificationcompactification

Unfortunately, we do not have a precise Unfortunately, we do not have a precise knowledge about the field knowledge about the field

potential . Any such potential might potential . Any such potential might take into account the non-perturbative take into account the non-perturbative

effects, as arising from the effects of effects, as arising from the effects of branes/fluxes present in the extra branes/fluxes present in the extra

dimensions.dimensions.

)(V

Frozen dilaton, no modulus Frozen dilaton, no modulus couplingcoupling

This simplifies the theory a lot This simplifies the theory a lot

2

24 )(

2)(

2

V

RgxdS

DefineDefine

22222 /),/(,)/(2

HHHVYHX

EOMsEOMs XY ,3

Different choice of implies different Different choice of implies different and hence different potentials! Is it and hence different potentials! Is it

then all worthy? then all worthy?

So Simple!So Simple!

Y

13

2

w

EOSEOS

Infinite number of Infinite number of possibilities?possibilities?

220 2

1)( mVV

n

V

04)(

0

4 cos)( cV

Quadratic/Quadratic/Chaotic Chaotic

Inverse power-Inverse power-law law

AxionAxion

eVV 0)(ExponetExponet

ialial

The issue is not merely to The issue is not merely to achieveachieve

1wFor the model to work a scalar For the model to work a scalar

field should field should relax its potential energy after relax its potential energy after

inflation down inflation down to a sufficiently low value, to a sufficiently low value,

presumably very close to the presumably very close to the observed value of the dark energyobserved value of the dark energy

Including stringy Including stringy correctioncorrection

eN

ttuHfU

22 )(8

GfVR

gxdS )()(2

)(2

22

4

)(24)(

24 223

2

HHHGaaa

AnsatzAnsatz

where ‘t’ can be where ‘t’ can be earlyearly or or latelate

))(ln( taN

Inflationary predictions with Inflationary predictions with can be significantly different from those can be significantly different from those

with with

constf )(constf )(

The solution isThe solution is

)(tanh 10 NN

2087294

1 ,

44 2

0

wherwhere e

)(cosh 10

0 NNHH eeNdN

ee

N

N

PHMV

X

1

10

t

220

20

uu

,

,)(2

ee

u

VV

)tanh(1(3)tanh(3

)cosh()(

00

22

00

Late-time Acceleration is Late-time Acceleration is possiblepossible

The solution is modelled such thatThe solution is modelled such that i

f

a

aNz ln)1ln(

Generation of Generation of PerturbationsPerturbations

51092.1~ HFixed value ofFixed value of e.g.e.g.

U=0U=0

01.0~ ,10~ 70 PMH

In a standard scenario In a standard scenario r <0.43r <0.43but with stringy correctionsbut with stringy corrections

0 ~ r < 0.40 ~ r < 0.4

Spectral IndexSpectral Index

1sn

89.0sn

95.0sn

Cmbgg OmOlCmbgg OmOlCMB

+

LSS

Nature of the dark energy

Tegmark et al 2004

Recent claim that w<-1

preferred with evolution from

w=0.

Alam et al.

?1w

pp

1w

Null dominant energy condition: Null dominant energy condition: energy doesn’t propagate outside the energy doesn’t propagate outside the

light conelight cone

A model withA model with

)(2

12

VL

negative kinetic energy fieldnegative kinetic energy field

Instabilities cured by higher Instabilities cured by higher derivative terms? string theory? …derivative terms? string theory? …

1w1w

Phantom Phantom Non-phantom Non-phantom Cosmology?Cosmology?

In the absence of (or trivial) scalar GB In the absence of (or trivial) scalar GB coupling, a transition between non-coupling, a transition between non-phantom and phantomphantom and phantom

cosmology is unlikely, but this cosmology is unlikely, but this is possible, e.g., with Gauss-Bonnet is possible, e.g., with Gauss-Bonnet

coupling coupling

)(

2.

0

eH

))(ln( ta

OutlookOutlook

Next 5-10 years dark sector of cosmology research will remain exciting to understand the theory of inflation and dark energy universe.

Thanks for your Thanks for your time….time….