1Suppose the Universe were not expanding, but was insome kind of steady state. How should galaxy recessionvelocities correlate with distance? They should a) be directly proportional to distance. b) reverse the trend we see today and correlateinversely with distance. c) show a scatter plot with most recession velocitiespositive. d) show a scatter plot with equal numbers of positiveand negative recession velocities.Olber’s Paradox• Over very large distances, galaxiesin the universe are more or lessuniformly distributed(homogeneous)• If there are galaxies in everydirection, however, why do we nothave a fully-lit sky? We shouldsee a star in any direction we look!– This is called Olber’s Paradox• If there is an edge to the universe,we should be able to see our way“out of the woods”2Olber’s ParadoxA Solution?• In a sense, there is an edgeto the universe, an edge intime• Light travels at a finite(though fast) speed• The size of the visibleuniverse is defined as thedistance light can travel inthe age of the universe• Galaxies exist at greaterdistances, but light fromthem has not reached usyet.• The edge is called thecosmic horizon• If we wait long enough, thenight sky might becomebright!3The Meaning of Redshift• As light waves travel throughspace, they are stretched byexpansion• This increases the wave’swavelength, making it appearmore red!• An objects redshift, z, isHere, Δλ is the change inwavelength, and λ is the originalwavelength of the photon• This is equivalent to:!!"=zgalaxiesbetween distance Averagegalaxiesbetween distance averagein Change=zThe Age of the Universe• Thanks to the Hubble Law, we canestimate the age of the universe• At some point in the distant past,matter in the universe must havebeen densely packed.• From this point, the universewould have expanded at some highspeed to become today’s universe• Assuming a constant expansionover time, we find that the age ofthe universe is around 14 billionyears.4Suppose you've accepted that the universe is expanding, andwill always expand. You must then accept that a) there is no center to the universe b) the observable universe is infinite c) the distance between stars in the galaxies grows. d) either the density of the universe always decreases or newmatter must be continuously created.The Last Scattering Epoch• Minutes after the Big Bang,the Universe was opaque– High temperatures kept all matterionized– Photons could only travel a shortdistance before being absorbed• After 400,000 years, theUniverse cooled enough forelectrons and ions torecombine, allowing light topass• Now the Universe wastransparent!5Light from the Early Universe• So what should light from 400,000years after the Big Bang look like?– It should have a spectrum thatcorresponds to the temperature of theUniverse at that time, 3000 K.– Expansion of space will stretch thislight, however• The Universe has expanded by afactor of 1000 since this time, so thewavelength will have stretched by thesame amount– Spectrum will correspond to atemperature of 3K.• This light from the early Universehas been found, and is called theCosmic Microwave BackgroundClumpiness in the CMB6Clumpiness in the CMBClumpiness in the CMB7The Curvature of the Universe• Remember that mass andenergy can curve the spacearound it.• As the Universe expands,the distances between thegalaxies increases, likegalaxies painted on thesurface of an inflatingballoon• If the universe was like anexpanding balloon (butwith the galaxiesdistributed in threedimensions), travel in anydirection would eventuallybring you back to yourstarting place (a closeduniverse)• No Center, No Edge!Many galaxies have flat rotation curves!Dark matter is not unique to the Milky Way!8• 99 percent of the stars in a galaxy arewithin 20 kpc of the center• Gas extends far out into the disk, but isnot very massive!• Galaxies are now thought to beembedded in a dark matter halo thatsurrounds the entire galaxy• Unfortunately, dark matter cannot bedetected directly.Dark Matter in Clusters of Galaxies• Missing mass is also aproblem in clusters ofgalaxies!– Not enough visible mass tohold the clusters together bygravitation, and to keep hot gasin their vicinity– Cluster mass must be 100times greater than the visiblemass!– Once again, dark matter seemsto be the solution9Gravitational Lenses• Dark matter warps space just like ordinarymatter does• The path of light rays bends in the presenceof mass• A galaxy or other massive object can bendand distort the light from objects locatedbehind it, producing multiple images• This is called gravitational lensingFigure 78.0610Other Possible Curvatures of Space• In addition to a closed, or positive curvature ofspace, there are two other options– Space could be flat, or have zero curvature– Space could be curved away from itself, or havenegative curvature– Geometry behaves differently with each curvature!Expansion Forever? Or Collapse?• The fate of the universe isultimately controlled by itstotal amount of energy– Energy of expansion (positive)– Gravitational energy that canslow the expansion (negative)– Binding energy• If the total energy is positiveor zero, the expansioncontinues forever• If the total energy is negative,the expansion will halt, and theuniverse will contract andeventually collapse.11Density of the Universe• If we can measure thedensity of the universe,we can predict howmuch gravitationalenergy the universe has,and therefore whether itwill collapse or keepexpanding• The critical density ofthe universe, ρC, is thedensity at which thetotal energy of theuniverse is zero• ΩM = ρ/ρC, where ρ is the measured densityof the universe• If ΩM > 1, the universe will recollapse• If ΩM < 1, the universe will expand forever• If ΩM = 1, the universe is exactly at thecritical densityGHC!"832=If the Big Bang theory is correct, and there is not enough mass toclose the universe, then a) more Big Bangs will occur. b) there is no "dark matter". c) the universe will eventually be entirely cold. d) the expansion will slow to a halt.12Supernova Type Ia Findings• We also need to know how theuniverse is expanding – this can helpus determine the value of ΩM• We can measure the recessionvelocity of distant galaxies usingType Ia supernovae as standardcandles• It appears that the expansion rate at atime when the universe was half