(Non)-Euclidean Geometry - University of Arizonaeldora.as.arizona.edu/~yshirley/Arizona/AST250/Cosmology... · 2014. 10. 21. · (Non)-Euclidean Geometry . Differential Geometry Negative

Page 1 <img data-url='document/non-euclidean-geometry-university-of-yshirleyarizonaast250cosmology.html?page=1' data-page='1' class='cut-thumb lazyload' alt='Page 1: (Non)-Euclidean Geometry - University of Arizonaeldora.as.arizona.edu/~yshirley/Arizona/AST250/Cosmology... · 2014. 10. 21. · (Non)-Euclidean Geometry . Differential Geometry Negative' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader035.cupdf.com/reader035/viewer/2022071418/611690db40be8546d41ebe21/html5/thumbnails/1.jpg' width='140' height='200' /> (Non)-Euclidean Geometry

Page 2 <img data-url='document/non-euclidean-geometry-university-of-yshirleyarizonaast250cosmology.html?page=2' data-page='2' class='cut-thumb lazyload' alt='Page 2: (Non)-Euclidean Geometry - University of Arizonaeldora.as.arizona.edu/~yshirley/Arizona/AST250/Cosmology... · 2014. 10. 21. · (Non)-Euclidean Geometry . Differential Geometry Negative' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader035.cupdf.com/reader035/viewer/2022071418/611690db40be8546d41ebe21/html5/thumbnails/2.jpg' width='140' height='200' /> Differential Geometry

Negative curvature

Flat (Euclidean)

Positive curvature

Page 3 <img data-url='document/non-euclidean-geometry-university-of-yshirleyarizonaast250cosmology.html?page=3' data-page='3' class='cut-thumb lazyload' alt='Page 3: (Non)-Euclidean Geometry - University of Arizonaeldora.as.arizona.edu/~yshirley/Arizona/AST250/Cosmology... · 2014. 10. 21. · (Non)-Euclidean Geometry . Differential Geometry Negative' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader035.cupdf.com/reader035/viewer/2022071418/611690db40be8546d41ebe21/html5/thumbnails/3.jpg' width='140' height='200' /> Homogeneity & Isotropy

Page 4 <img data-url='document/non-euclidean-geometry-university-of-yshirleyarizonaast250cosmology.html?page=4' data-page='4' class='cut-thumb lazyload' alt='Page 4: (Non)-Euclidean Geometry - University of Arizonaeldora.as.arizona.edu/~yshirley/Arizona/AST250/Cosmology... · 2014. 10. 21. · (Non)-Euclidean Geometry . Differential Geometry Negative' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader035.cupdf.com/reader035/viewer/2022071418/611690db40be8546d41ebe21/html5/thumbnails/4.jpg' width='140' height='200' /> Large Scale Structure on the Sky

Page 5 <img data-url='document/non-euclidean-geometry-university-of-yshirleyarizonaast250cosmology.html?page=5' data-page='5' class='cut-thumb lazyload' alt='Page 5: (Non)-Euclidean Geometry - University of Arizonaeldora.as.arizona.edu/~yshirley/Arizona/AST250/Cosmology... · 2014. 10. 21. · (Non)-Euclidean Geometry . Differential Geometry Negative' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader035.cupdf.com/reader035/viewer/2022071418/611690db40be8546d41ebe21/html5/thumbnails/5.jpg' width='140' height='200' /> Isotropy and Homogeneity of CMB

ΔT/T < 10-5

Page 6 <img data-url='document/non-euclidean-geometry-university-of-yshirleyarizonaast250cosmology.html?page=6' data-page='6' class='cut-thumb lazyload' alt='Page 6: (Non)-Euclidean Geometry - University of Arizonaeldora.as.arizona.edu/~yshirley/Arizona/AST250/Cosmology... · 2014. 10. 21. · (Non)-Euclidean Geometry . Differential Geometry Negative' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader035.cupdf.com/reader035/viewer/2022071418/611690db40be8546d41ebe21/html5/thumbnails/6.jpg' width='140' height='200' /> Evolution of Scale Factor

Ω = 0 Ω = 1 Ω = 2

Ωm = 0.27 ΩΛ = 0.73 ΩΛ = 1 Steady State

Ned Wright

R(t)

Page 7 <img data-url='document/non-euclidean-geometry-university-of-yshirleyarizonaast250cosmology.html?page=7' data-page='7' class='cut-thumb lazyload' alt='Page 7: (Non)-Euclidean Geometry - University of Arizonaeldora.as.arizona.edu/~yshirley/Arizona/AST250/Cosmology... · 2014. 10. 21. · (Non)-Euclidean Geometry . Differential Geometry Negative' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader035.cupdf.com/reader035/viewer/2022071418/611690db40be8546d41ebe21/html5/thumbnails/7.jpg' width='140' height='200' /> Measuring Cosmological Distances