CASPER www.baylor.edu/~CASPER

String Cosmology of 11-Dimensional Spacetime

Dr. Gerald B. Cleaver EUCOS-CASPER Baylor University

Science Fiction has become ScienceScience Fiction has become Science Extra Dimensions (7 to be exact)Extra Dimensions (7 to be exact) Parallel Universes (at least 1 + maybe a few more) Parallel Universes (at least 1 + maybe a few more)

Multiple Universes (perhaps ~ 10Multiple Universes (perhaps ~ 1010^10010^100)) Warped SpacetimeWarped Spacetime Time before TimeTime before Time End of the Universe PredictedEnd of the Universe Predicted

Anti-Gravity is pulling apart our universe Anti-Gravity is pulling apart our universe

~ in Trillion yrs even atoms torn apart~ in Trillion yrs even atoms torn apart

5001010500101050010105001010500101050010105001010 .cbabcaa AgA 5001010

5001010500101050010105001010500101050010105001010 .cbabcaa AgA 5001010

Realized in String Theory (M-Theory)Realized in String Theory (M-Theory)

500 Physicists seeking Einstein’s final goal500 Physicists seeking Einstein’s final goal

the Theory of Everything (Physical)the Theory of Everything (Physical)

5001010500101050010105001010500101050010105001010 .cbabcaa AgA 5001010

String Theory impliesString Theory implies

nature of reality & existence isnature of reality & existence ismore complex …more complex …more beautiful …more beautiful …yet more simple …yet more simple …then ever imagined before!then ever imagined before!

5001010

Brief Intro to Strings/M-TheoryBrief Intro to Strings/M-Theory String CosmologyString Cosmology Destiny of the Stringy Universe &Destiny of the Stringy Universe &

Landscape of String TheoryLandscape of String Theory

OutlineOutline

Visible UniverseVisible Universe.cbabcaa AgA

trillion galaxies,trillion galaxies,

trillion stars per trillion stars per galaxygalaxy

13.7 billion13.7 billionlight yearslight yearsIn diameterIn diameter

= 8 x10= 8 x102222 mi mi

All Matter & Forces in the UniverseAll Matter & Forces in the UniverseUnified by String TheoryUnified by String Theory

Particles & ForcesParticles & ForcesLike Notes on a Violin StringLike Notes on a Violin String

B

♪♫

E

D

A

F

C

♪♫G

♪♫

♪♫ ♪♫

♪♫

Interactions of LinesInteractions of Lines(w/ infinites, (w/ infinites, anomalies, anomalies, nonsense probabilities)nonsense probabilities)

Interactions of SurfacesInteractions of Surfaces(w/ sensible probabilities)(w/ sensible probabilities)

String Interactions consistent w/ String Interactions consistent w/ Relativity Relativity

Quantum MechanicsQuantum MechanicsRequires String Theory w/Requires String Theory w/

9 + 1 Dimensional Spacetime9 + 1 Dimensional SpacetimeAstronomy, OFotU

Strings have two vibrations – CW & CCWStrings have two vibrations – CW & CCW

Spin = # of Vibrations in our 3+1 Dim. SpacetimeSpin = # of Vibrations in our 3+1 Dim. Spacetime

Gravitons = Spin 2 Particles Gravitons = Spin 2 Particles = Strings w/ both vibes in 3+1 Dim S-T= Strings w/ both vibes in 3+1 Dim S-T

Photons, Gluons, WPhotons, Gluons, W+,-+,-, Z (non-grav. force part.), Z (non-grav. force part.) = Spin 1 Particles= Spin 1 Particles = Strings w/ 1 vibe in 3+1 Dim S-T= Strings w/ 1 vibe in 3+1 Dim S-T & 1 vibe in 6 Dim Comp Space& 1 vibe in 6 Dim Comp SpaceSUSY-SUSY-Matter = Spin 0 ParticlesMatter = Spin 0 Particles = Strings w/ both vibes in 6 Dim Comp= Strings w/ both vibes in 6 Dim Comp SpaceSpace

Too SimpleToo Simple

SphericalSpherical

ToroidalToroidal

CircularCircular

too simple …too simple …

to generate exact “vibration” modes needed to generate exact “vibration” modes needed for strong & weak nuclear force particles for strong & weak nuclear force particles (Gluons & W(Gluons & W+,-+,-, Z),, Z),

to generate exact vibration modes needed forto generate exact vibration modes needed forall matter particles (three generations of all matter particles (three generations of quarks, electrons, neutrinos, along with quarks, electrons, neutrinos, along with Higgs)Higgs)

So more complex shapes investigated …So more complex shapes investigated …

2 Dim Surface C-Y Surface—Need to extend to 6 Dim2 Dim Surface C-Y Surface—Need to extend to 6 Dim

RequireRequireCalabi-Yau Compactification for all Calabi-Yau Compactification for all

6 Compactified Dimensions6 Compactified Dimensions

Energy ModesEnergy Modes

String DualityString Duality

Only 3 Directions Inflated-Why?Only 3 Directions Inflated-Why?

Finite Initial Size and Finite Initial Size and Temperature of UniverseTemperature of Universe

String Explanation for OnlyString Explanation for Only3 Large Dimensions!3 Large Dimensions!

P-dimensional Object P-dimensional Object InteractionsInteractions

Nagging Problem for 1Nagging Problem for 1stst Decade (1985-95): Decade (1985-95):Not Just 1 10-Dimensional String Theory Not Just 1 10-Dimensional String Theory

But 5!But 5!

Solution: Duality (Equality) of All 5 Solution: Duality (Equality) of All 5 String TheoriesString Theories

Each ‘Theory” is SAME THEORY Each ‘Theory” is SAME THEORY IN DIFFERENTIN DIFFERENT

MATHEMATICAL LANGUAGEMATHEMATICAL LANGUAGE

ΩOO Й אڜ

MembraneMembraneStringString

w/ 10 Dimw/ 10 Dim w/ 11 Dimw/ 11 Dim

Two 9-brane “Universes”= “Us & Them”Two 9-brane “Universes”= “Us & Them”and extra dimension betweenand extra dimension between

Compactify 6 of the 9 Spatial Compactify 6 of the 9 Spatial Directions of each Brane as BeforeDirections of each Brane as Before

Effective 5-Dimensional TheoryEffective 5-Dimensional Theory

10-33 cm < cm < y < 0.1 mmy < 0.1 mm

Size of 5th Dimension?Size of 5th Dimension?

Tests for sub-mm.directionsTests for sub-mm.directions

FFgrav grav = -Gm= -Gm11mm22/r/r22 -Gm -Gm11mm22/r/r

2+n 2+n

1/r1/r22 form of gravity being tested. form of gravity being tested.

Verified down to 0.15 mm at Univ. of Wash.Verified down to 0.15 mm at Univ. of Wash.

with 97% confidence levelwith 97% confidence level

Manufacturing of Manufacturing of Stringy Blackholes!Stringy Blackholes!

If sub-mm. dimension then it may be possible to If sub-mm. dimension then it may be possible to produce mini-black holes (with peco-second half-produce mini-black holes (with peco-second half-lives) at Fermilab & CERN this decade! lives) at Fermilab & CERN this decade!

NO THREAT TO THE EARTH (NOR EVEN NO THREAT TO THE EARTH (NOR EVEN CHICAGO OR GENEVA)!!!CHICAGO OR GENEVA)!!!

Mini-black holes have distinct decays—easily Mini-black holes have distinct decays—easily identifiable!identifiable!

Detectors for black holes under constructionDetectors for black holes under construction for Fermilab and CERNfor Fermilab and CERN

Proposed Explanation for Big BangProposed Explanation for Big BangImplying Time Before Time!Implying Time Before Time!

Astronomy, OFotU

The colliding Branes would not remain perfectly The colliding Branes would not remain perfectly flat as they approach each other due to quantum flat as they approach each other due to quantum effects. effects.

Big Bang Inflations occurs in bumps on Branes Big Bang Inflations occurs in bumps on Branes that collide first. that collide first.

Multiple, separated, Big Bang regions might have Multiple, separated, Big Bang regions might have been formed from distinct collision points of been formed from distinct collision points of Branes! Branes!

Multiple universes on our Brane besides 1+ Multiple universes on our Brane besides 1+ Parallel Branes along an extra spatial directionParallel Branes along an extra spatial direction

M-Theory & M-Theory & Our Standard 3 Large DimensionsOur Standard 3 Large Dimensions

Cosmic Microwave Background (CMB) Cosmic Microwave Background (CMB) historyhistory

CMBCMB

Temp variationsTemp variationsof 1 part in 100,000of 1 part in 100,000denoted by color denoted by color variationsvariations

Blue is hottest,Blue is hottest,Red is coldestRed is coldest

CMB Temp =CMB Temp = 2.73 Degrees2.73 Degrees above absolute above absolute ZeroZero

Recent Observation of Earliest Galaxies—Formed 1 billion years after Big BangRecent Observation of Earliest Galaxies—Formed 1 billion years after Big Bang

OBSERVATION: Eight distant infant galaxies -- essentially giant globs of hydrogen with a few hot young stars -- lie inside a thin filament, visualized with a computer overlay. The hot stars make the hydrogen glow. Other objects in the image are nearer galaxies or stars.

New Scientist, 5 Feb 2005

String LandscapeString Landscape

~ 10100 Models (with Fluxes) in M-Theory

String/M-Theory as presently understood has a large parameter space of String/M-Theory as presently understood has a large parameter space of variables (angles between each compactified direction, lengths of each, plus things variables (angles between each compactified direction, lengths of each, plus things called fluxes and torques) each leading to universes (observable, hidden, or both) called fluxes and torques) each leading to universes (observable, hidden, or both) with differing properties. On the order of > 10with differing properties. On the order of > 10100100 different universes all seem different universes all seem equally possible. Why our particular String/M-Theory universe?equally possible. Why our particular String/M-Theory universe?

Some scientists (e.g. Stephen Hawking) are suspicious that determination of a Some scientists (e.g. Stephen Hawking) are suspicious that determination of a particular choice of ALL of the M-Theory parameters might not be totally particular choice of ALL of the M-Theory parameters might not be totally determinable, based on Gödel’s Theorem, which says that one cannot formulate a determinable, based on Gödel’s Theorem, which says that one cannot formulate a finite system of axioms to prove every result in mathematics. This means that finite system of axioms to prove every result in mathematics. This means that inconsistencies or indeterminacies can arise if one tries to prove statements that inconsistencies or indeterminacies can arise if one tries to prove statements that refer to themselves.refer to themselves.

A physical theory is a mathematical model. So if there are mathematical results A physical theory is a mathematical model. So if there are mathematical results that cannot be proved, there are physical problems that cannot be solved. We do that cannot be proved, there are physical problems that cannot be solved. We do not live outside of the universe, but instead we and our theories are both part of not live outside of the universe, but instead we and our theories are both part of the universe we are describing. Hence our theories are also self-referring. And the universe we are describing. Hence our theories are also self-referring. And thus we might suspect that any Theory of Everything determined by a finite thus we might suspect that any Theory of Everything determined by a finite number of known parameters or variables might ultimately be incomplete or number of known parameters or variables might ultimately be incomplete or undetermined!undetermined!

String/M-TheoryString/M-Theory

Provides unified explanation of all 4 forces & Provides unified explanation of all 4 forces & matter particles.matter particles.

Develops deeper understanding of nature of Develops deeper understanding of nature of spacetime and gravity.spacetime and gravity.

Presents our universe with a simplicity, order and Presents our universe with a simplicity, order and beauty never before imagined. Simultaneously beauty never before imagined. Simultaneously provides for complexity of universe.provides for complexity of universe.

Suggests more to our universe than ever of Suggests more to our universe than ever of dreamed prior.dreamed prior.

String/M-Theory as likelyString/M-Theory as likely

GOD’S BLUEPRINT FOR THE UNIVERSE!GOD’S BLUEPRINT FOR THE UNIVERSE!

Astronomy, OFotU

Interesting String (Cosmology) Web Sites (also image sources):

Center for Astrophysics, Space Physics & Engineering ResearchCASPER

www.baylor.edu/~CASPER

http://www.superstringtheory.com/ John Schwarz’ "The Official String Theory Web Site"

http://www.sukidog.com/jpierre/strings/ String Tutorial with glossary, refs & links

http://www.superstring-theory.com/EnglishVersion.html another excellent intro

http://www.superstringtheory.com/cosmo/index.htmlhttp://www.ba.infn.it/~gasperin/http://feynman.princeton.edu/~steinh/ Great string cosmology sites

http://www.nuclecu.unam.mx/%7Ealberto/physics/string.html http://dmoz.org/Science/Physics/Quantum_Mechanics/ http://pages.wooster.edu/bboroson/clinks.html worthwhile collections of links to other major string sites