ASTR 340 Lecture Notes - Lecture 12: Cosmological Constant, Spherical Geometry, Cosmological Principle
Document Summary
Einstein ignored the details, imagined matter as smoothed out. Cosmological principle: the universe, on average, will look the same no matter where the observer is or where he looks. Two consequences: universe is homogeneous: every spot is like every other, universe is isotropic: there is no middle or preferred direction. If a system is isotropic, then it is homogeneous, however it is not commutative. Confirmed by distributions of galaxies and the cmb. Due to constraints of cosmo principles, there are only 3 possibilities: spherical geometry: 3d space is a surface of a 4d sphere. A starting point can lead back to itself: flat geometry: planes of 3d geometry. Space is infinite and volume is too: hyperbolic geometry: saddle theory. Right angles can be made in different ways. Contraction, expansion, etc essentially means changing of r (scale factor) Sphere: r= radius w/ pos curvature: can look flat on a local scale.
