Dark Energy Cosmology

1. Dark Energy Cosmology Robert Caldwell Dartmouth College INPE Winter School September 12-16, 2005

3. Physics & Astronomy Dartmouth College Hanover, New Hampshire Dartmouth Cosmology, Gravitation, and Field Theory Group

4. Cosmology: the physics of the universe • goals • understand the origin, evolution, and future of the universe • determine the composition and distribution of matter and energy • test gravity on the largest scales • test the physics of the dark sector: dark matter and energy • introduce framework and tools of relativistic cosmology • introduce dark energy cosmology

5. Cosmology: current status Numerous observations and experiments support the hypothesis that our universe is filled by some sort of dark energy which is responsible for the cosmic acceleration. 2005: Low density Little curvature Accelerating simple explanation?

6. Cosmology: current status Freedman & Turner, Rev Mod Phys 75 (2003) 1433

7. Special Relativity Postulate 1 The laws of nature and the results of experiments in a given reference frame are independent of the translational motion of the system. Postulate 2 The speed of light is finite and independent of the motion of the source. SR spacetime Lorentz invariance t’ t x’ x

8. Relativistic Physics Action: free particle Geodesic equation Particle Kinematics

9. Special Relativity Experiment: search for preferred-frame effects eg CMB laboratory Mansouri & Sexl, 1977 SR:

10. Special Relativity Experiments: Michelson-Morley: orientation dependence Kennedy-Thorndike: velocity dependence Ives-Stillwell: contraction, dilation Stanwix et al, PRL 95 (2005) 040404 Wolf et al, PRL 90 (2003) 060402 Precision tests of Lorentz Invariance Saathoff et al, PRL 91 (2003) 190403

11. Special Relativity Experiments: isotropy of the speed of light Muller et al, PRL 91 (2003) 020401 Standard Model Extensions (SME) overview: Bluhm hep-ph/0506054 Muller et al, PRL 91 (2003) 020401 (astrophysical) Kostelecky et al, PRL 87 (2001) 251304 boost-invariance of neutron Cane et al, PRL 93 (2004) 230801

12. Special Relativity Theory: Lorentz Invariance violations The idea of a smooth, continuous spacetime breaks down near the Planck scale in many theories of quantum gravitational phenomena. As a practical consequence, such theories predict violations of Lorentz Invariance in the form of the dispersion relation Kip Thorne 1994 "Black holes and time machines: Einstein's outrageous legacy" overview: Mattingly gr-qc/0502097 • Forbidden decays now allowed • Relativistic -factor has different meaning • Possible CPT violation? numerous astrophysics, cosmology implications

13. Special Relativity Theory: Lorentz Invariance violations These effects may have greater implications within the full qft of the standard model p k due to LI violating terms Implies that different fields would have values of c that vary by as much as 10% Collins et al, PRL 93 (2004) 191301 minimal mixing with standard model? Myers & Pospelov, gr-qc/0402028

14. Curved-Spacetime Physics Spacetime, the set of all events, is a 4D manifold with a metric (M,g). The metric is measurable by rods and clocks. The metric of spacetime can be put in the Lorentz form momentarily at any particular event by an appropriate choice of coordinates. Freely-falling particles, unaffected by other forces, move on timelike geodesics of the spacetime. Any physical law that can be expressed in tensor notation in SR has exactly the same form in a locally-inertial frame of a curved spacetime.

15. Curved-Spacetime Physics Action: free particle Geodesic equation Gravitation & Inertia

16. Curved-Spacetime Physics Newtonian limit: a slowly-moving particle in a weak, stationary grav. field

17. Curved-Spacetime Physics Poisson equation Energy density belongs to the source stress-energy tensor Gravitational potential belongs to the spacetime metric Laws of fundamental physics as 2nd order differential equations

18. Curvature conventions Wald 1984 metric: -+++ examples

19. Weak Fields CODATA Rev Mod Phys 77 (2005) 1 gravitational potentials due to nearby sources Earth Sun Galactic Center

20. Weak Fields trace-reversed field select Lorentz gauge

21. Cosmology: Einstein “Cosmological Considerations on the General Theory of Relativity” Einstein (1917) [see Cosmological Constants, eds. Bernstein & Feinberg] Copernican Principle gives way to Cosmological Principle Model the universe as spatially homogeneous, isotropic Mach’s influence on relativity and inertia No inertia relative to spacetime, but inertia of masses relative to one another Observation and experiment Account for the small kinetic motions of stars and nebulae First mathematical model of the universe in general relativity.

22. Cosmology: Einstein This is a facsimile of Einstein’s lecture notes for a course he taught on general relativity in 1919. The final topic of the course was cosmology, which he had begun to investigate only two years earlier. On these pages he describes his methods in constructing the first mathematical model of cosmology in general relativity. This universe contains non-relativistic matter, stars and nebulae in agreement with the contemporary observations, but is spatially-finite following his failure to find boundary conditions satisfying Mach’s Principle. The current approach to theoretical cosmology is very similar, striking a balance between empirical and theoretical inputs. Einstein’s lecture notes: 1919

23. Cosmology: Einstein Homogeneous & Isotropic: and stationary: A, B depend on r only. Inertia and Gravitation gravitation inertia require: test particle momentum, from geodesic equation

24. Cosmology: Einstein No Boundary: spatial-surfaces are closed three-spheres Matter Content: t-t equation can balance, but not i-i Problem!

25. Cosmology: Einstein Imbalanced Gravitation: How to ensure that stars and nebulae reach equilibrium? ~ Newton’s objection to an infinite universe : a screening length . . . “…the newly introduced universal constant defines both the mean density of distribution  which can remain in equilibrium and also the radius … of the spherical space.”

26. Cosmology: Einstein “Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder of his life.” (George Gamow) The cosmic expansion of the universe had not been discovered at the time, so he proceeds to build a static universe by adding “” to the field equations, a cosmological constant. This seemed to solve a problem that troubled even Newton -- why did the entire universe not collapse under its own gravitational attraction. In his view, the  introduces a screening length which cuts off the influence of the gravitational potential beyond a certain radius, thereby allowing the motion of stars and nebulae to approach equilibrium. In fact, the compact geometry of this model sets a maximum distance for the reach of gravity, whereas the addition of  only increases large-scale kinetic motions. The gravitational field equations momentarily balance, like a tug-of-war, but this model universe is unstable to expansion or collapse. Willem de Sitter found inspiration in Einstein’s model, even though he wrote that the introduction of  “detracts from the symmetry and elegance of Einstein's original theory, one of whose chief attractions was that it explained so much without introducing any new hypothesis or empirical constant.” Shortly after the publication of Einstein’s results, he proposed a model universe containing only . This idealized solution features accelerated cosmic expansion, and closely resembles the origin of the Big Bang in the inflationary era, or our future in a Big Chill. Einstein’s lecture notes: 1919

27. Cosmology: deSitter “On Einstein’s Theory of Gravitation and Astronomical Consequences” deSitter (1917) [see Cosmological Constants, eds. Bernstein & Feinberg] Copernican Principle gives way to Cosmological Principle Mach’s influence on relativity and inertia Observation and experiment Universe contains no matter: stars and nebulae as test particles Confound Machians: relativity of inertia without “distant stars” meet Einstein’s requirements Idealized spacetime of the cosmological constant

28. Action Principle Einstein-Hilbert metric variation g,  variation Palatini identity

29. Action Principle Einstein’s cosmological term seems inevitable! “The genie () has been let out of the bottle”