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Published on October 15, 2007

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Dark Energy Cosmology:  Dark Energy Cosmology INPE Winter School September 12-16, 2005 Robert Caldwell Dartmouth College Slide3:  Dartmouth Cosmology, Gravitation, and Field Theory Group Dartmouth College Hanover, New Hampshire Physics & Astronomy Slide4:  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 introduce framework and tools of relativistic cosmology introduce dark energy cosmology test gravity on the largest scales test the physics of the dark sector: dark matter and energy Slide5:  Cosmology: current status 2005: 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. Low density Little curvature Accelerating simple explanation? Slide6:  Cosmology: current status Freedman & Turner, Rev Mod Phys 75 (2003) 1433 Slide7:  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’ x’ t x Slide8:  Relativistic Physics Action: free particle Geodesic equation Particle Kinematics Slide9:  Special Relativity Experiment: search for preferred-frame effects eg CMB laboratory Mansouri & Sexl, 1977 SR: Slide10:  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 Saathoff et al, PRL 91 (2003) 190403 Precision tests of Lorentz Invariance Slide11:  Special Relativity Experiments: isotropy of the speed of light Muller et al, PRL 91 (2003) 020401 Standard Model Extensions (SME) Muller et al, PRL 91 (2003) 020401 Kostelecky et al, PRL 87 (2001) 251304 (astrophysical) boost-invariance of neutron Cane et al, PRL 93 (2004) 230801 overview: Bluhm hep-ph/0506054 Slide12:  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 overview: Mattingly gr-qc/0502097 Kip Thorne 1994 "Black holes and time machines: Einstein's outrageous legacy" Forbidden decays now allowed Relativistic -factor has different meaning Possible CPT violation? numerous astrophysics, cosmology implications Slide13:  Special Relativity Theory: Lorentz Invariance violations These effects may have greater implications within the full qft of the standard model Collins et al, PRL 93 (2004) 191301 p k Myers & Pospelov, gr-qc/0402028 minimal mixing with standard model? Implies that different fields would have values of c that vary by as much as 10% due to LI violating terms Slide14:  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. Slide15:  Curved-Spacetime Physics Action: free particle Geodesic equation Gravitation & Inertia Slide16:  Curved-Spacetime Physics Newtonian limit: a slowly-moving particle in a weak, stationary grav. field Slide17:  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 Slide18:  Curvature conventions Wald 1984 metric: -+++ examples Slide19:  Weak Fields CODATA Rev Mod Phys 77 (2005) 1 Earth Sun Galactic Center gravitational potentials due to nearby sources Slide20:  Weak Fields select Lorentz gauge trace-reversed field Slide21:  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. Slide22:  Cosmology: Einstein Einstein’s lecture notes: 1919 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. Slide23:  Cosmology: Einstein Homogeneous & Isotropic: and stationary: A, B depend on r only. Inertia and Gravitation inertia gravitation require: test particle momentum, from geodesic equation Slide24:  Cosmology: Einstein No Boundary: spatial-surfaces are closed three-spheres Matter Content: Problem! t-t equation can balance, but not i-i Slide25:  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.” Slide26:  Cosmology: Einstein Einstein’s lecture notes: 1919 “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. Slide27:  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 Idealized spacetime of the cosmological constant Universe contains no matter: stars and nebulae as test particles Confound Machians: relativity of inertia without “distant stars” meet Einstein’s requirements Slide28:  Action Principle metric variation Einstein-Hilbert g,  variation Palatini identity Slide29:  Action Principle Einstein’s cosmological term seems inevitable! “The genie () has been let out of the bottle”

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