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Extra Dimensions and the Cosmological Constant Problem

Extra Dimensions and the Cosmological Constant Problem. Cliff Burgess. Partners in Crime. CC Problem: Y. Aghababaie, J. Cline, C. de Rham, H. Firouzjahi, D. Hoover, S. Parameswaran, F. Quevedo, G. Tasinato, A. Tolley, I. Zavala Phenomenology:

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Extra Dimensions and the Cosmological Constant Problem

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  1. Extra Dimensions and the Cosmological Constant Problem Cliff Burgess Dark Energy 2007

  2. Partners in Crime • CC Problem: • Y. Aghababaie, J. Cline, C. de Rham, H. Firouzjahi, D. Hoover, S. Parameswaran, F. Quevedo, G. Tasinato, A. Tolley, I. Zavala • Phenomenology: • G. Azuelos, P.-H. Beauchemin, J. Matias, F. Quevedo • Cosmology: • Albrecht, F. Ravndal, C. Skordis Dark Energy 2007

  3. The Plan • The Cosmological Constant problem • Why is it so hard? • How extra dimensions might help • Changing how the vacuum energy gravitates • Making things concrete • 6 dimensions and supersymmetry • Prognosis • Technical worries • Observational tests Dark Energy 2007

  4. ‘Naturalness’ as an Opportunity • Cosmology alone cannot distinguish amongst the various models of Dark Energy. • The features required by cosmology are difficult to sensibly embed into a fundamental microscopic theory. • Progress will come by combining both Dark Energy 2007

  5. The Cosmological Constant Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? Dark Energy 2007

  6. The Cosmological Constant Problem Concordance cosmology points to several types of cosmic ‘matter’: • Dark energy vs vacuum energy • Why must the vacuum energy be large? Dark Energy 2007

  7. The Cosmological Constant Problem N. Wright, astro-ph/0701584 • Dark energy vs vacuum energy • Why must the vacuum energy be large? w = pDE/rDE = -1 for a cosmological constant Dark Energy 2007

  8. The Cosmological Constant Problem • Hierarchy Problems • Why Extra Dimensions? A cosmological constant is not distinguishable from a Lorentz invariant vacuum energy vs Dark Energy 2007

  9. The Cosmological Constant Problem • Hierarchy Problems • Why Extra Dimensions? A cosmological constant is not distinguishable* from a Lorentz invariant vacuum energy vs * in 4 dimensions… Dark Energy 2007

  10. The Cosmological Constant Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? Dark Energy 2007

  11. The Cosmological Constant Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? The observed dark energy density corresponds to a very small vacuum energy: implies Dark Energy 2007

  12. The Cosmological Constant Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? BUT: particles of mass m contribute m» m: Dark Energy 2007

  13. The Cosmological Constant Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? BUT: particles of mass m contribute m» m: Dark Energy 2007

  14. The Cosmological Constant Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? BUT: particles of mass m contribute m» m: Dark Energy 2007

  15. The Cosmological Constant Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? BUT: particles of mass m contribute m» m: Must cancel to 32 decimal places!! Dark Energy 2007

  16. The Cosmological Constant Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? BUT: particles of mass m contribute m» m: Dark Energy 2007

  17. The Cosmological Constant Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? BUT: particles of mass m contribute m» m: Must cancel to 40 decimal places!! Dark Energy 2007

  18. The Cosmological Constant Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? Seek to change properties of low-energy particles (like the electron) so that their zero-point energy does not gravitate, even though quantum effects do gravitate in atoms! Why this? But not this? Dark Energy 2007

  19. Another Naturalness Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? r is a constant if it is vacuum energy Dark Energy 2007

  20. Another Naturalness Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? More complicated time-dependence is possible Dark Energy 2007

  21. Another Naturalness Problem • Dark energy vs vacuum energy • Why must the vacuum energy be large? When time dependence is due to scalar field motion, the scalar field mass must be very small: BUT: contributions to mf are of order so are too large if M > 10-2 eV Dark Energy 2007

  22. The Plan • The Cosmological Constant problem • Why is it so hard? • How extra dimensions might help • Changing how the vacuum energy gravitates • Making things concrete • 6 dimensions and supersymmetry • Prognosis • Technical worries • Observational tests Dark Energy 2007

  23. How Extra Dimensions Help • 4D CC vs 4D vacuum energy • Branes and scales Dark Energy 2007

  24. How Extra Dimensions Help New Tools motivated by string theory (or condensed matter): Particles can be localized on surfaces (branes, or defects) within the extra dimensions Gravity is not similarly localized • 4D CC vs 4D vacuum energy • Branes and scales Dark Energy 2007

  25. How Extra Dimensions Help In higher dimensions a 4D vacuum energy, if localized in the extra dimensions, can curve the extra dimensions instead of the observed four. • 4D CC vs 4D vacuum energy • Branes and scales Arkani-Hamad et al Kachru et al, Carroll & Guica Aghababaie, et al Dark Energy 2007

  26. How Extra Dimensions Help Gibbons, Guven & Pope • 4D CC vs 4D vacuum energy • Branes and scales • Most general 4D flat solutions to chiral 6D supergravity, without matter fields. • l3 nonzero gives curvature singularities at branes Dark Energy 2007

  27. How Extra Dimensions Help To be useful it must be that extra dimensions can be as large as the observed Dark Energy density: ~ c/r » 10-2 eV or r » 1 m-metre This is possible! provided all known particles except gravity are trapped on a brane, since tests of Newton’s law allow r < 50 m-metre • 4D CC vs 4D vacuum energy • Branes and scales Arkani Hamed, Dvali, Dimopoulos Adelberger et al Dark Energy 2007

  28. How Extra Dimensions Help Arkani Hamed, Dvali, Dimopoulos If there are extra dimensions as large as r » 1 m-metre then there can only be two of them (although others could exist if they are much smaller), or else the observed strength of gravity would require the scale of extra-dimensional physics to be smaller than mw with n extra dimensions • 4D CC vs 4D vacuum energy • Branes and scales Dark Energy 2007

  29. How Extra Dimensions Help • 4D CC vs 4D vacuum energy • Branes and scales These scales are natural using standard 4D arguments. Dark Energy 2007

  30. How Extra Dimensions Help Must rethink how the vacuum gravitates in 6D for these scales. SM interactions do not change at all! • 4D CC vs 4D vacuum energy • Branes and scales Only gravity gets modified over the most dangerous distance scales! Dark Energy 2007

  31. The Plan • The Cosmological Constant problem • Why is it so hard? • How extra dimensions might help • Changing how the vacuum energy gravitates • Making things concrete • 6 dimensions and supersymmetry • Prognosis • Technical worries • Observational tests Dark Energy 2007

  32. The SLED Proposal Suppose physics is extra-dimensional above the 10-2 eV scale. Suppose the physics of the bulk is supersymmetric. Aghababaie, CB, Parameswaran & Quevedo Dark Energy 2007

  33. The SLED Proposal Suppose physics is extra-dimensional above the 10-2 eV scale. Suppose the physics of the bulk is supersymmetric. Bulk supersymmetry SUSY breaks at scale Mg on the branes; Trickle-down of SUSY breaking to the bulk is: Dark Energy 2007

  34. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Dark Energy 2007

  35. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Several 6D SUGRAs are known, including chiral and non-chiral variants. None have a 6D CC. Dark Energy 2007

  36. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Several 6D SUGRAs are known, including chiral and non-chiral variants. None have a 6D CC. Nishino & Sezgin Dark Energy 2007

  37. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Generates large 4D vacuum energy This energy is localized in the extra dimensions (plus higher-derivatives) Dark Energy 2007

  38. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Solve classical equations in presence of branes Plug back into action Dark Energy 2007

  39. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Solve classical equations in presence of branes Plug back into action Dark Energy 2007

  40. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Solve classical equations in presence of branes Plug back into action Chen, Luty & Ponton Tensions cancel between brane and bulk!! Dark Energy 2007

  41. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Solve classical equations in presence of branes Plug back into action Aghababaie et al. Smooth parts also cancel for supersymmetric theories!! Dark Energy 2007

  42. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Bulk is a supersymmetric theory with msb ~ 10-2 eV Quantum corrections can be right size in absence of msb2 Mg2 terms! Lifts flat direction. Dark Energy 2007

  43. The Plan • The Cosmological Constant problem • Why is it so hard? • How extra dimensions might help • Changing how the vacuum energy gravitates • Making things concrete • 6 dimensions and supersymmetry • Prognosis • Technical worries • Observational tests Dark Energy 2007

  44. Prognosis • Theoretical worries • Observational tests Dark Energy 2007

  45. The Worries • ‘Technical Naturalness’ • Runaway Behaviour • Stabilizing the Extra Dimensions • Famous No-Go Arguments • Problems with Cosmology • Constraints on Light Scalars Dark Energy 2007

  46. The Worries • ‘Technical Naturalness’ • Runaway Behaviour • Stabilizing the Extra Dimensions • Famous No-Go Arguments • Problems with Cosmology • Constraints on Light Scalars Dark Energy 2007

  47. The Worries • ‘Technical Naturalness’ • Runaway Behaviour • Stabilizing the Extra Dimensions • Famous No-Go Arguments • Problems with Cosmology • Constraints on Light Scalars • Classical part of the argument: • What choices must be made to ensure 4D flatness? • Quantum part of the argument: • Are these choices stable against renormalization? Dark Energy 2007

  48. The Worries Tolley, CB, Hoover & Aghababaie Tolley, CB, de Rham & Hoover CB, Hoover & Tasinato • ‘Technical Naturalness’ • Runaway Behaviour • Stabilizing the Extra Dimensions • Famous No-Go Arguments • Problems with Cosmology • Constraints on Light Scalars • Classical part of the argument: • What choices must be made to ensure 4D flatness? • Now understand how 2 extra dimensions respond to presence of 2 branes having arbitrary couplings. • Not all are flat in 4D, but all of those having only conical singularities are flat. • (Conical singularities correspond to absence of dilaton couplings to branes) Dark Energy 2007

  49. The Worries • ‘Technical Naturalness’ • Runaway Behaviour • Stabilizing the Extra Dimensions • Famous No-Go Arguments • Problems with Cosmology • Constraints on Light Scalars • Quantum part of the argument: • Are these choices stable against renormalization? • So far so good, but not yet complete • Brane loops cannot generate dilaton couplings if these are not initially present • Bulk loops can generate such couplings, but are suppressed by 6D supersymmetry Dark Energy 2007

  50. The Worries • ‘Technical Naturalness’ • Runaway Behaviour • Stabilizing the Extra Dimensions • Famous No-Go Arguments • Problems with Cosmology • Constraints on Light Scalars Dark Energy 2007

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