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Extra spatial dimensions

Extra spatial dimensions. Claudia de Rham Black Hole Session. Perimeter Institute, 5 th May 2007. Main questions. How well does the Cosmological Paradigm work ? What are dimensions, and what are the different ways to think about extra dimensions ?

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Extra spatial dimensions

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  1. Extra spatial dimensions Claudia de Rham Black Hole Session Perimeter Institute, 5th May 2007

  2. Main questions • How well does the Cosmological Paradigm work? • What are dimensions, and what are the different ways to think about extra dimensions? • Why then do we live in three spatial dimensions?

  3. The Cosmology Paradigm The early Universe underwent exponential expansion in a tiny fraction of a second

  4. The Cosmology Paradigm Matter was created at the end of this accelerated expansion, as a transfer of energy, called “reheating”

  5. The Cosmology Paradigm The expansion of universe is currently accelerating Current Universe composition 4% Visible Matter 22% Dark Matter 74% Dark Energy

  6. The Cosmology Paradigm The expansion of universe is currently accelerating Current Universe composition 4% Visible Matter 22% Dark Matter 74% Dark Energy

  7. Other Cosmological puzzles

  8. Other Cosmological puzzles • What is the Big-Bang? • What created it? • Did time begin? • Was there anything before?

  9. Other Cosmological puzzles • What is the Big-Bang? • The Hierarchy Problem… • What created it? • Did time begin? • Was there anything before?

  10. What is the Hierarchy Problem? • A hierarchy problemarises when 2 fundamental quantities with same unit, don’t share the same order of magnitude. • Naïvely, oneexpects all numbers comingfrom a fundamental theory to share the same order of magnitude. • This is not the case for the scales at which quantum effects forgravity and for the other three forces of nature kick in. • We expect quantum gravity effect to kick in at ~ 1018 GeV (at the Planck mass), while quantum effects for the other forces kick in at ~ 250 GeV (at the Higgs mass) • The Planck mass is thus 1016 times heavier that the Higgs mass.

  11. What is the Hierarchy Problem? • A hierarchy problemarises when 2 fundamental quantities with same unit, don’t share the same order of magnitude. • Naïvely, oneexpects all numbers comingfrom a fundamental theory to share the same order of magnitude. • This is not the case for the scales at which quantum effects forgravity and for the other three forces of nature kick in. • We expect quantum gravity effect to kick in at ~ 1018 GeV (at the Planck mass), while quantum effects for the other forces kick in at ~ 250 GeV (at the Higgs mass) • The Planck mass is thus 1016 times heavier that the Higgs mass. ie. 10 000 000 000 000 000 times heavier

  12. How important is this Hierarchy? 1 New born baby 3 kgs Asian Elephant 5000 kgs 103 105 Boeing 747 400 tones 46 000 tones 107 The Titanic Egyptian Pyramid 1 million tone 109 200 thousand million tones Mount Everest 1014 Asteroid Gaspra 10 million million tones 1016

  13. Can extra dimensions have anything to say about these puzzles?

  14. Can extra-dimensions have anything to say about these puzzles? • what are dimensions? • how many dimensions do we live in / do we see?

  15. Can extra dimensions have anything to say about these puzzles? • what are dimensions? • how many dimensions do we live in / do we see? • Trains live in 1 dimension

  16. Can extra dimensions have anything to say about these puzzles? • what are dimensions? • how many dimensions do we live in / do we see? • Trains live in 1 dimension • Boats live in 2 dimensions

  17. Can extra dimensions have anything to say about these puzzles? • what are dimensions? • how many dimensions do we live in / do we see? • Trains live in 1 dimension • Boats live in 2 dimensions • Planes can travel in 3 dimensions

  18. “Our” dimensions • We live in a world with 3 spatial dimensions. • In addition to these spatial dim, there is time. • There is only one time-like dim, so we live in a (3+1)-dim world. • We will only consider extra spatial dimensions. • Extra dim of time are not compatible with quantum mechanics. • Extra dimensions will be represented by taking 1 or 2 dim out.

  19. Kaluza and Klein Idea • The notion of extra dimensions wasintroduced by Theodor Kaluza in 1919and Oscar Klein in 1926 • General Relativity was extended to (4+1)-dim • As an attempt to unify gravity and electromagnetism.

  20. Size of this extra dimension • If the extra dim was very large, we would see it. • The size of the extra dim should be so small, we wouldn’t be able to resolve it with our own eyes.

  21. Kaluza-Klein compactification • In KK compactification, our world is spread along a very small extra dimension. • At low-energy, gravity in (4+1)-dim compactified on a tiny circle would look like our gravity in (3+1)-dimplus electromagnetism (photons).

  22. Large extra dimensions • Alternative point of view:Extra dim could be “large”, but we would not be able to travel through them. • We could be confined to a surface which itself would live in higher dimensions. • All the particles we are made of could be forced to remain on that surface.

  23. Gravity Yet, some forces such as gravity would be free to spread along all the dimensions. • To fully understand the physics on the surface, we need to understand how gravity behaves along these extra dimensions. Hu DL, Chan B, Bush JWM.  Water-walkingPHYSICS OF FLUIDS 15 (9): S10 SEP 2003

  24. How would such a surface arise? • Naturally arise from string theory,they represent surfaces on which open strings end.

  25. How would such a surface arise? • Naturally arise from string theory. • But independently of string theory, they can spontaneously arise as topological defects. • What is a topological defect? Picture from National High Magnetic Field Laboratory Precholesteric to Cholesteric Phase transition

  26. What is a topological defect? • A topological defect arise when evolving from one configuration to another, there is a choice associated with the new configuration.

  27. What is a topological defect? • A topological defect arise when evolving from one configuration to another, there is a choice associated with the new configuration. • Example: Crystal structure and magnetic domains Picture from physics department, Brown University

  28. What is a topological defect? • In different regions of space, different choices can be made, (ex. magnet alignment). • The boundaries between these different regions are topological defects and carry energy. Movie from Oslo SuperConductor Lab • When the Universe cools down, the same kind of process happens, leading to some topological defects. • We could be “trapped” on one of these surfaces, “unaware” of other dimensions.

  29. Consequences for us • We could live on such a “membrane”. • This would modify the way we perceive gravity. • Gravity would be diluted, and would “leak” within the extra dimensions. • For a large volume of the extra dim, this could explain the Hierarchy problem.

  30. Newton’s law? • But if gravity is modified, what about Newton’s law? • Newton’s law (and general relativity) work remarkably well within the solar system. • But how well do they work at distances much smaller or much larger than the size of the solar system?

  31. Gravity at small distances • Newton’s law has only been tested at scales up to ~ 0.01 mm (in particular by the Eöt-Wash experiment in Seattle.) • At smaller distances, gravity could behave very differently. • This could be the signature of the presence of extra dimensions… Torsion pendulum, Eöt-Wash Group

  32. l Gravity at small distances • For instance when the size of the extra-dimension is finite (ex. bounded by two branes). • At large distances compared to l, the extra dim is not very much excited. • At small distances compared to l, the extra dim can be very much excited. l Gravity would behave very differently a small distances. Randall-Sundrum 1999 (RS model)

  33. Gravity at large distances • How well do we understand gravity at very large distances (cosmological scales)? • We think we understand it, but what we observe at these scales is also very surprising,

  34. Gravity at large distances • How well do we understand gravity at very large distances (cosmological scales)? • We think we understand it, but what we observe at these scales is also very surprising, • The expansion of the Universe seems to be accelerating. • To explain observations, the Universe should be composed of 70% of Dark Energy

  35. Gravity at large distances • How well do we understand gravity at very large distances (cosmological scales)? • We think we understand it, but what we observe at these scales is also very surprising, • The expansion of the Universe seems to be accelerating. • To explain observations, the Universe should be composed of 70% of Dark Energy • maybe gravity is actually not so well understood at these scale…

  36. Gravity at large distances • Extra dimensions can for instance provide a new way to think about the accelerated expansion of the Universe. • In a model where the size of the extra dim is not finite. • Gravity can be localized on the brane by another mechanism, • So at small distances, gravity will just behave as in four dimensions. • At large distances, gravity will feel the extra dimension, and would become higher-dimensional (ex. 5d gravity). • Gravity will then be weaker at large distances, • This could explain the accelerated expansion. Dvali, Gabadadze, Porrati 2000 (DGP model)

  37. Extra dim and the Big-Bang What is the Big-Bang ???

  38. Extra dim and the Big-Bang Our 4d big-bang may simply be a collision of two branes in some higher dimensions. Branes can have charges, like particles, and can attract or repulse each others. We could start with attracting branes initially parallel, the branes would then move towards each other and collide. Turok & Steinhardt 2001

  39. Extra dim for cosmology • Extra dimensions thus provide new potential ways to think about some of the key problems of particle physics and cosmology: • The cosmological evolution of the Universe can be described as the motion of a brane within an extra dimension. • Hierarchy problem, • Accelerated expansion and dark energy • Origin of the Big-Bang…

  40. Extra dim for cosmology • Extra dimensions thus provide new potential ways to think about some of the key problems of particle physics and cosmology: • The cosmological evolution of the Universe can be described as the motion of a brane within an extra dimension. • Hierarchy problem, • Accelerated expansion and dark energy • Origin of the Big-Bang… But if they existed, why would we live in (3+1)d ???

  41. Dimensionality puzzle Why do we live in (3+1)d? • In Kaluza-Klein compactifications, • In the brane setup, • Why only three dim are large, and all other dimensions are small? • Why is our surface 3-dimensional? Is there any selection mechanism?

  42. Collision of extended objects • Two point-like particles will • collide in 1 spatial dimension • but not in 2 • or any higher spatial dimensions

  43. Collision of extended objects • Strings will • Strings are “extended” objects with 1 intrinsic dimension. • occupy the entire world in 1 dim, • intersect in 2 spatial dim at all times, • find each other in 3 spatial dim • but not in higher dim.

  44. Collision of extended objects • Walls will • Walls are “extended” objects with 2 intrinsic dimensions. • occupy the entire world in 2 dim, • intersect in 3 spatial dim at all times, • find each other in 4 dim, etc…

  45. Collision of extended objects • The same will hold for any extended object. • By analogy, any two extended objects of intrinsic dimension p, living in a (d+1)-dimensional world,will collide and can annihilate each other if

  46. Collision of extended objects • The same will hold for any extended object. • By analogy, any two extended objects of intrinsic dimension p, living in a (d+1)-dimensional world,will collide and can annihilate each other if • p=0: points only collide in d=1 dim • p=1: strings only collide in d=3 dim or less • p=2: walls collide in d=5 dim or less • p=3: 3-d surfaces, collide in d=7 dim or less • etc…

  47. Annihilation of strings • Let’s consider a world with d dim, all of which are identical. • We consider them to be very small and wrapped with strings (p=1) (and other objects), • When some dim spontaneously grow large, strings compress them back. • But strings can annihilate in 3 dim (or less), • So the maximum number of dimensions that can grow large is 3 ! Brandenberger-Vafa 1989

  48. Annihilation of strings • Strings would naturally meet and annihilate each others only in 3 spatial dimensions or less, • So only 3 of these dimensions would be let free and allowed to grow while the other will remain naturally small. Extra dimensions à la Kaluza-Klein.

  49. Selection of 3d-branes • The same philosophy can be taken starting from a different scenario. • The Universe could be initially filled with branes of different dimensions. Majumbar-Davis 2003

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