Large Scale Isotropy and Homogeneity of theUniverse

Peter Balla

September 11, 2011

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

http://imgs.xkcd.com/comics/teaching-physics.png

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

Introduction

Intro, questions, references to future talks, few mathTheoretical expectations⇒ experimental validationHistorical order, not very scientific but verified in retrospectCosmology, Cosmogony (overview)Need for Symmetry (The Cosmological Principle)Isotropy and Homogeneity (notion)Empirical Evidence (Galaxy Distribution and CMBR)

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

Cosmology, Cosmogony (overview)

The ancient Greeks. . . (creation myths)Scientific Cosmology/-gony

Geometric cosmologyPhysical cosmology

General relativity theory: gravity is geometryObjective: gµνEinstein’s equations:

Rµν −12

gµνR + gµνΛ =8πGc4

Tµν (1)

Geometry ⇔ Matter (2)

10 coupled, nonlinear PDE’s

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

Need for Symmetry

Philosophy, AestheticsPhysics: simplify mathThe Cosmological Principle: for every typical observer, at a giveninstant, the universe looks the same in every directionQ: What do we mean about an instant? Problems in SpecRel,GenRel (e.g. Schwarzschild spacetime) *Corollary: homogenity and isotropy of instantaneous 3D-spaceSolution: FLRW spacetime (3 different geometries (assumingsimple global topology), time-dependent scale factor): next week

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

Friedmann-Lemaître-Robertson-Walker

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

Large Scale Structure

Is the distribution of matter and radiation homogeneous andisotropic?On a sufficiently large scale yes: average over large distances(galaxy-dust)ISO about every (a few) point(s)⇒ HOMOHOMO ; ISO (global-topological tricks, decorations)To get a grip on the notions of ISO and HOMO study 2D(Riemann-) surfaces

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

2D Riemann-surfaces, decoration

Isotropic and homogeneous 2D surfaces

Cylinder, torus, liquid crystal (not implying any cosmologicalrelevance, just illustrating a point)

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

Experimental: Homogeneity

Galaxy statistics: 3D spatial distribution of galaxies (cold matterwe can see)On a sufficiently large scale (a few hundred Mpc’s) ishomogeneous enoughGoogle "Galaxy Distribution"⇒ a bunch of really cool pictures(not very informative for the layman’s eye)Sky Surveys: galaxy distribution on the Celestial Globe(Planearium)Redshift surveys: galaxy distances (a formidable experimentaltask: Sloan Digital Sky Survey, Galaxy And Mass Assemblysurvey (GAMA))

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

Experimental: Isotropy

Cosmic microwave background radiation (CMBR): the universe isfilled with a faint glow of thermal (blackbody) radiation oftemperature ≈2,725KIt is really homogeneous and isotropicSmall anisotropy in a range of 0.0005 KExperiments: temperature, anisotropy, polarization. . .Experiments: COBE (’89–’93), WMAP (’01–), Planck(’09–). . . (for a comprehensive list cf. Wiki)More on the CMBR: next talk

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

COBE, WMAP

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

Questions, to be answered in the next talk

Q: Why is there any CMBR (what does it teach us about the earlyuniverse)?Q: Why is it so thermal (what was the physical body it was inequilibrium with)?Q: Why is its temperature precisely 2,725K (now)?Q: Why is it so highly homogeneous and isotropic?Q: OK, the CMBR is HOMO and ISO but what does it teach usabout the matter distribution of the universe (and about thegeometry of space itself)?Q: What are those small fluctuations and what are their statisticalproperties (angular power spectrum)?Q: What about the polarization?Q: Which of these questions are explained by std. cosmology?

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

Conclusion

Based on experimental evidence, the universe is highly HOMOand ISOSo it can be explained by the FLWR metricSmall deviations from the total symmetry contain usefulinformation for the refinement of the model parameters (age,history, dominating type of matter and interactions, size,curvature. . . )

Peter Balla Large Scale Isotropy and Homogeneity of the Universe

Resources

Bibliography and Further ReadingWikipedia (with care) and lecture notes from all over the WebKolb-Turner: The Early Universe (Addison Wesley, 1990)Weinberg: Cosmology (Oxford University Press, 2008)Hraskó: Relativitáselmélet (Typotex, 2002)Books with titles like "Differential Geometry for Physicists"Ned Wright’s Cosmology Tutorial, really good stuff (recommended)DGy talks

Funhttp://xkcd.com "A Webcomic of Romance, Sarcasm, Math andLanguage"Poul Anderson: Kyrie (Uram irgalmazz!, In: Analógia 1. - SF ésfantasy antológia, Valhalla Páholy 1992)

Peter Balla Large Scale Isotropy and Homogeneity of the Universe