14.40 o1 i neupane

Strings, Extra Dimensions and Cosmology

Ishwaree NeupaneDept of Physics & Astronomy

University of Canterbury

Quantum Mechanics is the framework for studying the physics of very short distances.

Special Relativity: A novel framework for describing the physics of objects moving at speeds close to the speed of light.

Theory of General Relativity is the extension of this theory to include gravity.

Synthesis of Special Relativity + Quantum Mechanics = Quantum Field Theory

Amazing Unification of Space-time & QM doubled the world :

;, ;, ppee

04/12/23 2Strings, Extra Dimensions and Cosmology

72.6±1.5%

22.8±1.3%13.73 ± 0.1 Gyr

A preposterous universe!

Our present understanding of cosmology is grounded in General Relativity and Quantum Field Theory, which have individually passed a remarkable panoply of experimental tests; we are still not able to account for what seems to be 73% of the energy budget of the universe and hence its mystic name

Dark Energy

%6.4

%,8.22

%,6.72

SM

DM

DE

Accelerating Universe! 2011 Nobel prize in physics


Tc

GgRgR N

4

8

2

1

Einstein (1917)

Dark Energy is explained by Einstein’s theory with a Cosmological Constant

256-22810 cm10~r~R cm,10~H~ r

This is consistent with the present size and age of the Universe

-100 H~Gyr 73.13~t

2562120-235 cm10~M10~sec10~ Po


cm 10 17

cm 10 28

“Electro-weak length” size of universe

solar system

galaxy

universe

people

DNA

atom

quarks

LHC

?Two options


Today theoretical physics deals basically with two options:• (1) Grand desert stretching from 250 GeV (10∼ -18 cm) 10∼ 19

GeV (10-33cm) with no new physics inside (highly unlikely);

• (2) Theory of Extra Dimensions – a paradigm in which one expects a new physics at a much lower energy scale

The aim is to bring the scale of new fundamental physics from inaccessible 1019 GeV down to 1-100 TeV or so

What are those two options?


cm 10 17 cm 10 28

“weak length” size of universe

cm 10 33

“Planck length”

Quantum-Gravity

Emergent SpaceTime

String Theory + Beyond

Hierarchy Problem

Taming the vacuum (cosmological constant) dark energy problem

The hope is that the ultimate theory of Nature contains a fundamental and simple, concise relation between close-by and far-away, and past and future


Taming the Vacuum

Even vacuum (empty space) has energy!

bigger fluctuationat smaller distances

Estimate:

Vol.Planck

EnergyPlanck ~

Volume

Energy~

But energy curves spacetime! curvature

The universe would double in size every

cm10~ 33

sec10~ 43

An interesting experimental discovery of last 20 years -- the Universe is accelerating, but doubles in size every yrs10~ 10

estimate120

obs 10~ paradox


Theoretical Physics

Thrives on

CRISES & PARADOXES


In string theory Inflation is likely to be linked to moduli fields, e.g., size and shape of extra (hidden) dimensions

Λ – could depend on fundamental (UV) structure of theory: internal space geometry, branes, fluxes, etc

Λ>0

Λ<0Λ=0

Prospects of describing the observed universe in string theory


String Theory Pre `95

epoints

10 dimensions 6 “curled up” to yield 4

Our 4D

cm10 30

e

e

cm10 31

?


String Theory Post `95

Not a theory of strings!

•Strings + extra dimensions can have any size •Particle string unification

HOLOGRAPHY

Apparently, the best understanding of string theory is in terms of a particle theory via the incredible idea of

pointsstrings

photon

photino

Ordinary dimension

Quantumdimensions

Gravity lives everywhere

3-d Membrane floating in extra dimensions


Holographic Universe

4D particle theory(no gravity)

static, highly curved space

10D theory of strings, gravity + everything

Presumably, most important theoretical discovery of last 20 years !


AdS/CFT (Maldacena, 1997)

Boundary

R4

AdS5

z = 0

z

22132

225 dzds

z

Rds

N = 4 SU(N) Yang-Mills theory AdS5 x S5

String theory on

sYMAdSSlNgRR 4/12

55

String theory has led to an impressive and growing array of insights on diverse problems in theoretical physics but there has been comparatively little progress in understanding whether string theory actually describes our universe.


Quantum gravity effect

cosmological perturbations

The power-law index of the primordial power spectrum ns = 0.968 ± 0.012 (68% CL)


Observations give us important new windows into the Properties of the very early universe

Extra dimensions: motivation

very early universe – general relativity breaks down

key idea: precision cosmology = test of Quantum Gravity superstring theories M theory

1 time +10 space dimensions new view of dimensional reduction

1+4 1+3+1 1+3+(1) 5D Brane-world gravity (Randall-Sundrum’99) matter on brane / gravity in bulk

matter

gravity

An important features of our late-time low-energy world: Why it appears to be four-dimensional?


Can an embedding of a four-dimensional spacetime in dS5 explain the observed cosmic acceleration?

dS 4

dS 5

2224

)(225 dzLdseds zA

Effective Planck mass:

3)5(2

3

3A(z)35

2

2

e

ML

dzMLM

dS

Pl

This is different from the result obtainable in a static AdS5 background

AdSPl MM 35

2

IPN, PRD83, 2011 (arXiv:1011.6357)IJMP D19, 2010 (arXiv:1004.0254)

55

35 2

2 Rgxd

MSg

2/30)cosh(

1)(

Hzz

zero-mode solution

is normalizable


Compactification of D=10 string theory

The Klebanov-Strassler geometry in D=10

has some common features with warped

Randall-Sundrum 5D braneworld model

12211,116 )( SSSSTSY

Does it work in higher dimensions?


2

1

22

1

)(222)(22)(22/1

23

226)(22/1210

cos)()sin()( )(

)()()(

i iiiii dfdymedykedyeyh

dxadaeyhds

IPN: Phys. Rev. Lett: 98 (2007) [hep-th/0609086]

The first explicit realisation of a cosmological compactification of 10D Einstein theory for which all extra dimensions except one can be stabilised by introducing time-dependent metric moduli or Weyl scalars leading to a “4+1+compact space”

Essentially, all of our knowledge of string theory in the cosmological setting is founded on approximations


22

2

22

24

2

2210

5

0

tanh1

tanh2

3

4

sinhcosh

X

p

A

dsdyyc

ycp

Lds

ycy

eds

Freezing the time-dependent metric moduli

27

216

)2(

6

868)10(2

0

A

Pl

eLMM

10 c

IPN: CQG,28 (2011) 1006.4495 [hep-th]

The discovery of a new class of simple warped vacuum solutions with a 4D de sitter part and non-compact internal space with still a finite 4D Planck mass and normalizable zero-mode graviton wave-function

IPN:Nucl. Phys. B847 (2011)1011.5007 [hep-th]


A disturbing realisation (?)

String theory is “unique” – no adjustable parameters. But it has zillions of (possible) solutions!

Pre ‘95 : zillions ~ millions

Post `95 : zillions ~ 10500 !All part of same theory, but different looking at long distances (in Infrared limit) “Multiverse” or “String Landscape” – A Controversial Subject!

There are hints that inflationary cosmological model can be naturally obtained from string theory other than that string theory is a mathematically consistent quantum gravity theory

Testing string theory itself by any means is extremely difficult. 04/12/23 22Strings, Extra Dimensions and Cosmology

Summary:

Inflation and Dark Energy both require new microphysics, solutions must rely on the intimate connection between GR and QFT.

Most examples worked out as string cosmology invoke string theory, branes, or extra dimensions, and may be identified as quantitative approximations to solutions in string theory. A reliably anchoring cosmology in string theory is hard, and success is rare.

A successful grounding of cosmology in string theory remains a worthy and realistic goal.

If Dark Energy is vacuum energy, cosmological observations won't tell us anything; we'll have to understand fundamental physics, probably through experiments – LHC is a great hope.


Signatures for New Physics, Signatures for New Physics, Extra dimensions, SupersymmetryExtra dimensions, SupersymmetryHiggs scalar, String Theory, …Higgs scalar, String Theory, …

Large Hadron Collider

04/12/23 24Strings, Extra Dimensions and

Cosmology

14.40 o1 i neupane

Technology

theory of extra dimensions

einsteins theory

new physics

curvaturethe universe

preposterous universe

physics of objects

string theory inflation

theory of general relativityis