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Research 1: I Neupane
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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
04/12/23 3Strings, Extra Dimensions and Cosmology
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
04/12/23 4Strings, Extra Dimensions and Cosmology
cm 10 17
cm 10 28
“Electro-weak length” size of universe
solar system
galaxy
universe
people
DNA
atom
quarks
LHC
?Two options
04/12/23 5Strings, Extra Dimensions and Cosmology
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?
04/12/23 6Strings, Extra Dimensions and Cosmology
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
04/12/23 7Strings, Extra Dimensions and Cosmology
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
04/12/23 8Strings, Extra Dimensions and Cosmology
Theoretical Physics
Thrives on
CRISES & PARADOXES
04/12/23 9Strings, Extra Dimensions and Cosmology
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
04/12/23 10Strings, Extra Dimensions and Cosmology
04/12/23 11Strings, Extra Dimensions and Cosmology
String Theory Pre `95
epoints
10 dimensions 6 “curled up” to yield 4
Our 4D
cm10 30
e
e
cm10 31
?
04/12/23 12Strings, Extra Dimensions and Cosmology
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
04/12/23 13Strings, Extra Dimensions and Cosmology
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 !
04/12/23 14Strings, Extra Dimensions and Cosmology
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.
04/12/23 15Strings, Extra Dimensions and Cosmology
Quantum gravity effect
cosmological perturbations
The power-law index of the primordial power spectrum ns = 0.968 ± 0.012 (68% CL)
04/12/23 16Strings, Extra Dimensions and Cosmology
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?
04/12/23 17Strings, Extra Dimensions and Cosmology
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
04/12/23 18Strings, Extra Dimensions and Cosmology
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?
04/12/23 19Strings, Extra Dimensions and Cosmology
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
04/12/23 20Strings, Extra Dimensions and Cosmology
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]
04/12/23 21Strings, Extra Dimensions and Cosmology
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.
04/12/23 23Strings, Extra Dimensions and Cosmology
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