Astro 101 Fall 2013 Lecture 12 Cosmology T. Howard
Cosmology = study of the Universe as a whole? What is it like overall?? What is its history? How old is it?? What is its future?? How do we find these things out from what we can observe?
In 1996, researchers at the Space Telescope Science Institute used the Hubble to make a very long exposure of a patch of seemingly empty sky. Q: What did they find? A: Galaxies as far as The eye can see (nearly everything in this photo is a galaxy!) 40 hour exposure
What do we know already (about the Universe)? Galaxies in groups; clusters; superclusters Nearby universe has filament and void type of structure More distant objects are receding from us (light is redshifted) Hubble s Law: V = H 0 x D (Hubble's Law)
Structure in the Universe
What is the largest kind of structure in the universe? The ~100-Mpc filaments, shells and voids? On larger scales, things look more uniform. 600 Mpc
Olbers Paradox Assume the universe is homogeneous, isotropic, infinte, and static Then: Why don t we see light everywhere? Why is the night sky (mostly) dark?
Olbers Paradox (cont d.) We believe the universe is homogeneous and isotropic So, either it isn t infinite OR it isn t static Big Bang theory universe started expanding a finite time ago Given what we know of structure in the universe, assume: The Cosmological Principle On the largest scales, the universe is roughly homogeneous (same at all places) and isotropic (same in all directions). Laws of physics are everywhere the same.
Hubble's Law might suggest that everything is expanding away from us, putting us at center of expansion. Is this necessarily true? If there is a center, there must be a boundary to define it => a finite universe. If we were at center, universe would be isotropic (but only from our location) but not homogeneous: Finite volume of galaxies expanding away from us into...what, empty space? Then part of universe has galaxies and part doesn t. Us
But if we were not at center, universe would be neither isotropic nor homogeneous: Us So if the CP is correct, there is no center, and no edge to the Universe! Best evidence for CP comes from Cosmic Microwave Background Radiation (later).
The Big Bang At time zero, all separations were infinitely small. Universe then expanded in all directions. Stars, galaxies formed as expansion continued. All galaxies now moving away from each other. A galaxy twice as far away from us, is moving twice as fast (Hubble's Law). So, how old is the Universe? Reversing the Hubble expansion, all separations go back to zero. How long ago?
H 0 gives rate of expansion. Assume H 0 = 75 km / sec / Mpc. So galaxy at 100 Mpc from us moves away at 7500 km/sec. How long did it take to move 100 Mpc from us? time = = distance velocity 100 Mpc 7500 km/sec We can do this same calculation for galaxies at other distances, getting a similar answer. = 13 billion years Age of universe is related to H 0. Note, H 0 may be in range 65 75 km/sec/mpc (Experts note that this time is just 1 ). The faster the expansion (the greater H 0 ), the shorter the time to get to the present separation. H 0
Redshift vs. Lookback Time Astronomers (and physicists) denote redshift by z = amount light has shifted relative to its (laboratory, at rest) wavelength = direct measure of speed of recession of distant galaxies z light travel time Age at redshift (Gyr) (Gyr) 0.037 0.5 13.360 0.075 1.0 12.860 0.254 3.0 10.860 0.488 5.0 8.860 1.04 8.0 5.860 1.74 10 3.860 6.54 13 0.860 10.13 13.38 0.480 1 Gyr = 1,000,000,000 years. Time (now) since Big Bang = 13.860 Gyr using H 0 = 70 km/sec/mpc Flat universe
But this is not galaxies expanding through a pre-existing, static space. That would be an explosion with a center and an expanding edge. If CP is correct, space itself is expanding, and galaxies are taken along for the ride. There is no center or edge, but the distance between any two points is increasing. A raisin bread analogy provides some insight:
But the bread has a center and edge. Easier to imagine having no center or edge by analogy of universe as a 2-d expanding balloon surface (this is only one possible analogy for our universe s geometry): Now take this analogy "up one dimension". The Big Bang occurred everywhere at once, but "everywhere" was a small place. (To understand what it would be like in a 2-d universe, read Flatland by Edwin Abbott: www.ofcn.org/cyber.serv/resource/bookshelf/flat10 )
The Cosmic Microwave Background Radiation (CMBR) A prediction of Big Bang theory in 1940's. "Leftover" radiation from early, hot universe, uniformly filling space (i.e. isotropic, homogeneous). Predicted to have perfect black-body spectrum. Photons stretched as they travel and universe expands, but spectrum always black-body. Wien's Law: temperature decreases as wavelength of brightest emission increases => was predicted to be ~ 3 K now.
Found in 1964 by Penzias and Wilson. Perfect black-body spectrum at T = 2.735 K. Uniform brightness (and thus temperature) in every direction. 1% of the snow on a blank TV channel is this radiation! Points are data on the spectrum of the CMBR from the COBE satellite (1989). Curve is a black-body spectrum at T=2.735 K.
All-sky map of the CMBR temperature, constant everywhere to one part in 10 5! For blackbody radiation, this means brightness is very constant too (Stefan s law). (WMAP satellite) Deviations are -0.25 millikelvin (blue) to +0.25 millikelvin (red) from the average of 2.735 Kelvin.
The Early Universe The First Matter At the earliest moments, the universe is thought to have been dominated by high-energy, high-temperature radiation. Photons had enough energy to form particle-antiparticle pairs. Why? E=mc 2. pair production annihilation
At time < 0.0001 sec, and T > 10 13 K, gamma rays could form protonantiproton pairs. At time < 15 sec, and T > 6 x 10 9 K, electron-positron pairs could form. Annihilation occurred at same rate as formation, so particles coming in and out of existence all the time. As T dropped, pair production ceased, only annihilation. A tiny imbalance (1 in 10 9 ) of matter over antimatter led to a matter universe (cause of imbalance not clear, but other such imbalances are known to occur).
Primordial Nucleosynthesis Hot and dense universe => fusion reactions. At time 100-1000 sec (T = 10 9-3 x 10 8 K), helium formed. Stopped when universe too cool. Predicted end result: 75% hydrogen, 25% helium. Oldest stars' atmospheres (unaffected by stellar nucleosynthesis) confirm Big Bang prediction of 25% helium.
We are now in a Matter-dominated epoch
Other Measurements Support the Big Bang Model of the Universe (Detailed Big Bang theory predicts some things we can measure)
We can t see all the way to the Big Bang [we see its echo ] (Now) < -- Time (Early Universe)
Radiation and Matter decoupled Nuclei and electrons combine to form atoms (H, He) More complex atoms form later from fusion This explains CMB Galaxies form around clumps of Dark Matter?
Opaque Transparent
Computer simulations of structure formation around clumps of Dark Matter predict a universe with shapes/sizes very similar to what we observe. Time since Big Bang.
Big Bang cosmology + Dark Energy, WMAP values Current mass density ratio 0.27 (incl. Dark Matter) Current value of Dark Energy equivalent density ratio, 0.73 H 0 ~ 71 km/s-mpc Era or Event Time Temp Planck Era < 5x10-44 > 10 19 GeV Planck transition 5 x 10-44 10 19 GeV ** Grand unification era ** Grand unification of forces ends 10-36 10 15 GeV Inflation 10-36 to 10-34 10 15 GeV ** Electro weak era ** Electroweak era ends 10-11 100 GeV ** Quark era ** Cosmic expansion timelines (1) Quark era ends 10-5 200 MeV
Cosmic expansion timelines (2) Era or Event Time Temp redshift Neutrino decoupling 0.1 s 3 MeV e - e + annihilation ends 1.3 s 1 MeV n-p ratio frozen 1.8 s 10 10 K Deuterium formation begins 176 s 10 9 K Matter-dominated era begins 55000 year 8920 K z = 3233 ** Matter era ** CMB visible ~300,000 yr 3000 K 1 st stars form 200Myr 1 Gyr 1 st galaxies form 1 Gyr 5 Gyr universal expansion accelerates ~ 7.1 Gyr z= 0.76, R =0.57 Dark Energy dominates ~ 9.5 Gyr z = 0.39, R = 0.72 ** Dark Energy era** Today ~ 13.7 Gyr z = 0, R = 1
The Early Universe Inflation A problem with microwave background: Microwave background reaches us from all directions. Temperature of background in opposite directions nearly identical. Yet even light hasn't had time to travel from A to B (only A to Earth), so A can know nothing about conditions at B, and vice versa. So why are A and B almost identical? This is horizon problem.
Solution: Inflation. Theories of the early universe predict that it went through a phase of rapid expansion. Separation between two points (m) If true, would imply that points that are too far apart now were once much closer, and had time to communicate with each other and equalize their temperatures.
More on Dark Matter Dark matter thought to be necessary in cosmology theory to explain clumpy distributions of matter massive enough for galaxies to form Could have been either CDM or HDM CDM = non-relativistic (speed << c) HDM = relativistic (speed ~ c) Usual predictions of CDM candidates require modifications or extensions to Standard Model of particles Non-baryonic candidates Neutrinos (neutrino oscillation implies neutrino mass) WIMPs hypothetical Possibly heavy neutrinos or something equally exotic Axions
Dan Hooper - Closing In On Dark Matter Current Status
Evidence For Dark Matter!Galactic rotation curves!gravitational lensing!light element abundances!cosmic microwave background anisotropies!large scale structure Dan Hooper - Closing In On Dark Matter
Evidence For Dark Matter!There is a wide variety of independent evidence that dark matter exists!each of these observations infer dark matter s presence through its gravitational influence!still no observations of dark matter s electroweak interactions (or other non-gravitational interactions) Dan Hooper - Closing In On Dark Matter
What Happens to the Universe? The Geometry of Curved Space Net density of matter and Fate of the Universe are related
The universe as a curved space Analogy using the Earth s surface
What Happens to the Universe? The Geometry of Curved Space (cont d.) Possibilities: 1) Space curves back on itself (like a sphere). "Positive" curvature.
2) Saddle-like, with curvature in the opposite sense in different dimensions: "negative" curvature. 3) A more familiar flat geometry. In general relativity, the geometry of the universe depends on the total mass and energy of the universe (including dark energy). Latest CMBR measurements are consistent with flat, infinite universe (curved, finite universe still possible, with enormous radius of curvature).
All-sky map of the CMBR temperature, constant everywhere to one part in 10 5! For blackbody radiation, this means brightness is very constant too (Stefan s law). (WMAP satellite) Deviations are -0.25 millikelvin (blue) to +0.25 millikelvin (red) from the average of 2.735 Kelvin.
Sizes of patches in CMBR constrain geometry of universe. Curvature of universe makes it act like lens or pair of glasses some known size measure this angle ( 1 ) we know this distance Size of patches simply related to speed of light and age of universe when CMBR photons started streaming freely. This we know quite well. Also know how far away we are looking. Then angular size of patches tells us how light has traveled to us => curvature of space.
Supernovae extremely violent stellar explosions Several types & subtypes (called type I, Ia, II, etc.) Different types arise from pre-explosion stellar conditions Type Ia has been shown to have a change in brightness over time that has a shape related to its total luminosity Implies that SNe Ia can be used as standard candles Example supernova remnant Crab nebula in Taurus
Supernovae Ia Standard Candles for Cosmology Brightness Time
The Cosmological Distance Ladder Standard candles: Type Ia Supernovae [SNe Ia]
Recent Discovery: The Expansion of the Universe Seems to be Accelerating The gravity of matter should retard the expansion. But a new distance indicator shows that the expansion rate was slower in the past! Type I supernovae: from ones in nearby galaxies, know luminosity. In distant galaxies, determine apparent brightness. Thus determine distance. Works for more than 3000 Mpc. From redshifts, they are not expanding as quickly from each other as galaxies are now. Taking this into account, best age estimate of Universe is 13.8 Gyrs. Redshift (fractional shift in wavelength of spectral lines) H 0 was smaller in past (i.e. for distant galaxies) Note, 2011 Nobel Prize in Physics was awarded for this discovery
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What can explain the acceleration? Current theory: Dark Energy Einstein in 1917 introduced a special mathematical term, Lambda ( Λ ) as part of General Relativity. He thought it was needed to balance gravitational attraction and create a static Universe (turned out to be wrong!). But, we can think of Λ as repulsive force that exists even in a vacuum. The accelerating universe indicates there is (something akin to) a Λ. More generally called "dark energy". We have little idea of its physical nature. The measured amount of acceleration implies that there is actually more dark energy than the energy contained in matter!
Current Theories : Universe is 70% + Dark Energy!! Supported by CMBR measurements Statistical studies of Supernovae Ia measurements Galaxy Clusters
Will this change? Stay tuned! Astronomers and physicists are seeking advanced methods to study the early universe to try and understand Dark Energy One leading candidate a new space telescope, WFIRST
Successes of the Big Bang Theory 1) It explains the expansion of the universe. 2) It predicted the cosmic microwave background radiation, its uniformity, its current temperature, and its black-body spectrum. 3) It predicted the correct helium abundance (and lack of other primordial elements).
Misconceptions about the Big Bang 1. The universe was once small. The observable universe, which is finite, was once small. The nature of the entire universe at early times is not yet understood. It is consistent with being infinite now (or has enormous radius of curvature). 2. The Big Bang happened at some point in space. The CMBR showed that it happened everywhere in the universe. 3. The universe must be expanding into something. It is not expanding into empty space. That would imply the Big Bang happened at some location in space. It is a stretching of space itself.
4. There must have been something before the Big Bang. The Big Bang was a singularity in space and time (like the center of a black hole). Our laws of physics say the observable universe had infinitesimally small size, and infinite temperature and density. Such infinities indicate a breakdown of our theories. In these conditions, we don t have a physics theory to describe the nature of space and time. At the Big Bang, time took on the meaning that we know it to have. "Before" is only a relevant concept given our everyday understanding of time. We must await a better understanding of the nature of space and time. Such theories are in their infancy. Why did Big Bang occur? We don t know. Shouldn t be surprising that these concepts are hard to grasp. So was the heliocentric Solar System 400 years ago.