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Cosmological Constant

Cosmological Constant. Quantum Field Theory – I Shahnoor Habib Fall 2005. Outline. Introduction History of Cosmological Constant  Role of  in the history of universe Estimate of  from QFT Estimate of  from Observations Critique of non-zero vacuum energy Conclusion. Introduction.

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Cosmological Constant

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  1. Cosmological Constant Quantum Field Theory – I Shahnoor Habib Fall 2005

  2. Outline • Introduction • History of Cosmological Constant  • Role of  in the history of universe • Estimate of  from QFT • Estimate of  from Observations • Critique of non-zero vacuum energy • Conclusion Cosmological Constant

  3. Introduction • A puzzle common between Einstein and Newton • Matter and energy gravitate • Counter the contraction • Repulsive gravity or • Negative pressure or • Dark energy Cosmological Constant

  4. General Relativity . R and R refer to the curvature of space-time, g is the metric, T the energy momentum tensor, G the gravitational constant, and c the speed of light. Cosmological Constant

  5. Vacuum Energy Density • Lowest energy state but not necessarily equal to zero • Two models for vacuum energy density are • Cosmological constant (w=-1) • Same every where in the universe • Constant with reference to space and time • Quintessence (w<-1/3) • Changes with reference to space and time Cosmological Constant

  6. Runaway Train & Dismissal of  • Runaway Train • Universe grew slightly by 1 part per million in size • matter density goes down by 3 parts but • Vacuum energy stays the same and the • g becomes negative causing expansion to increase • W. de Sitter formulated a cosmological model in which he made the following assumptions • Isotropic universe • Mean density and the curvature of space are constant • Added  to balance the attraction of matter • Conclusion: Even if the universe is devoid of matter, the  term will cause test particles to accelerate away from each other. • Friedman Model of expanding universe • Observations by Hubble (Red Shift of stars) Cosmological Constant

  7. Quantum History of  • Introduced in 1917 • Lamaitre introduced  in his non-static model in 1927 • Dismissed in 1931 • Models with  were developed to address “age of universe” problem • In the late 60s,  was re-introduced to explain peculiar observations of quasars data. More Data removed the motivation. • Observations of Supernova have indicated a non-zero cosmological  Cosmological Constant

  8. History of Non-Zero Vacuum Energy • Nernst in 1916 put forward the idea that vacuum is not empty but filled with radiation. • At absolute zero temperature the energy density at frequency  grows as 3, so the total energy density becomes infinite. Even at a cutoff of 0 of 1020 s-1, the total energy content ~ 1.521023 Erg. • In the 40s and 50s, QED quantized the electromagnetic field, thus introducing harmonic oscillators with non-vanishing zero point energy (ZPE). Cosmological Constant

  9. History of Non-Zero Vacuum Energy • In 1934, Lamaitre commented what  means. • Everything happens as though the energy in vacuum would be different from zero. In order that the absolute motion, that is, motion relative to vacuum, may not be detected, we must associate a pressure p=-c2 to the density of energy c2 of vacuum. This is the essentially the meaning of the cosmological constant  which corresponds to a negative density of vacuum 0 according to 0 =c2/(4G)~10-27 gm/cm3 Cosmological Constant

  10. Effects interpreted as ZPE consequences • Casimir effect • Lamb shift • Dirac and Schrödinger theory, states with the same n and j quantum numbers but different l ought to be degenerate but 2S(n=2,l=0,j=1/2) and 2P(n=2,l=1,j=1/2) states of Hydrogen are not degenerate. The s state has higher energy by E/h=1057.864 MHz. • One loop effect of QED and can be interpreted as virtual photons being emitted and absorbed by the atom. • Quantum Harmonic Oscillator with non-vanishing ZPE causes the electron to execute rapid oscillatory motions. • The Coulomb potential is therefore perturbed by a small amount and this removes the degeneracy. Cosmological Constant

  11. ZPE from QED Cosmological Constant

  12. Quantum Expectation • In 1968 Zel’dovich emphasizes that ZPE of particle physics theories cannot be ignored when gravitation is taken into account. • The vacuum state of the proton field contains virtual pairs of particles with an effective density n~1/3 where  is Compton wavelength of proton.The gravitational interaction is Gm2/ . • This gives us 0~1017 gm/cm3 which exceeds 46 orders of magnitude from observational bounds. • Taking the highest reasonable particle mass, the Planck mass of 20 micrograms, the density is ~1091 gm/cm3 which exceeds by 120 orders of magnitude. Cosmological Constant

  13. How does  affect the evolution of the Universe Cosmological Constant

  14. BEHAVIOR OF COSMOLOGICAL MODELS Cosmological Constant

  15. Observational Limits • Solar System • Third law of Kepler • Mercury’s perihelion shift • Supernova Data • Curvature of Hubble Diagram • Type Ia Supernova as standard candles • Cosmic Microwave Background radiation • Analysis of temperature anisotropies • Gravitational Lens • A positive • Limits on the frequency with which such lensing occurs can, therefore, put a limit on . Cosmological Constant

  16. Solar System • Test of Kepler’s Third Law • The Voyager spacecraft allowed precise distances to Uranus and Neptune to be determined. Anderson et al (1995, ApJ, 448, 885) found that dP/P=(1+/-1) parts per million at Neptune’s distance from the Sun. This gives us a Solar System limit of (vacuum) to be <2*10-17 gm/cc. • The  will cause a precession of the perihelion of a planet about 3(vacuum)/ (solar) cycles per orbit .Magnitude of  from mercury (43” per century) is ~10-45 km-2. • In 1974, a binary pulsar was discovered with periastron shift 4 per year. • The most likely bounds on  are -7</(3H*H)<2 • Kochanek found a formal limit of Cosmological Constant

  17. Curvature of Hubble Diagram Cosmological Constant

  18. The supernova data as of mid-2003 Cosmological Constant

  19. MICROWAVE BACKGROUND RADIATION – WILKINSON DATA Cosmological Constant

  20. Hubble Diagram Cosmological Constant

  21. Color Scheme Cosmological Constant

  22. SUPERNOVA – BEFORE AND AFTER THE EXPLOSION Cosmological Constant

  23. 19 NEW GRAVITATIONAL LENSES DISCOVERED !! Cosmological Constant

  24. MATTER/ENERGY DISTRIBUTION IN THE UNIVERSE Cosmological Constant

  25. Super Nova Data Cosmological Constant

  26. Critique of Non-zero Vacuum Energy • Schwinger’s source theory , not resting on vacuum energy • Vacuum effects result from the vacuum itself or are generated by the introduction of the measurement systems, for example, • Casimir effect can be derived by considering the fluctuations of the constituents of the two plates • Could the observation of non-zero  be the best probe of the vacuum energy? Cosmological Constant

  27. Conclusion Different cosmological models have been developed which incorporate not only the cosmological constant but also dark matter and dark energy and the role they played in the formation of large structure which we see today. One of the model is LCDM but that is for another talk. Cosmological Constant

  28. References • http://cmb.physics.wisc.edu/tutorial/cmb.html • http://www.lbl.gov/Science-Articles/Archive/Phys-HST-supernovae-sidebar1.html • http://en.wikipedia.org/wiki/Friedmann_equations • http://www.universetoday.com/am/uploads/hubble_ein_rings.jpg • http://www.universetoday.com/am/publish/quadruple_ptical_einstein_rings.html?18112005 • http://www.astro.ucla.edu/~wright/sne_cosmology.html • http://arxiv.org/abs/astro-ph/0305008 Cosmological Constant

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