Chapter 17 Cosmology
Over one thousand galaxies visible
The Universe on the Largest Scales No evidence of structure on a scale larger than 200 Mpc On very large scales, the universe appears to be: Homogenous - the same everywhere Isotropic - the same in all directions
Figure 17.1 Galaxy Survey
Cosmology The study of the structure and evolution of the universe Cosmological principle - twin assumptions of homogeneity and isotropy Generally accepted by astronomers No edge (violates homogeneity) No center (violates isotropy)
Olbers s Paradox Assume that universe is infinite and unchanging in time When you look at sky at night, your line of sight will eventually encounter the bright surface of a star Entire sky should be as bright as the sun But sky is dark at night - Olbers s Paradox From nineteenth century Heinrich Olbers
Figure 17.2 Olbers s Paradox
Analogy 17-1 Every sight line intersects a tree
Olbers s Paradox Since sky is dark at night, either universe is not infinite and/or universe evolves in time
Hubble s Law Recession velocity = H 0 X distance How long did it take a galaxy to reach its current distance from us? Distance = velocity X time time = Distance/velocity = Distance/(H 0 X distance) = 1/H 0 = 14 billion years (for H 0 = 70 km/s/mpc)
Birth of the Universe Hubble s law implies that 14 billion years ago, all galaxies were at the same location Everything in the universe was confined to a single point then The point exploded - this is the Big Bang This was the beginning of the universe and the beginning of time
Big Bang Big Bang explains Olbers s paradox - even if universe is infinite, we only see a finite part within 14 billion light-years Light from beyond has not yet reached us
Where was Big Bang? Big Bang was not an explosion of matter into space Big Bang was an explosion of the universe itself, or of space itself Galaxies don t rush into empty space - instead space itself expands Entire universe was a point - the Big Bang happened everywhere at once
Receding galaxies Think of galaxies as coins taped to an expanding balloon Surface of balloon represents universe Every coin sees every other coin recede No coin is at center
Figure 17.3 Receding Galaxies
Cosmological Redshift For expanding universe, Doppler interpretation not technically correct Galaxies are not moving apart through space Instead, space itself is expanding Redshift represents expansion of wavelength as universe expands
Figure 17.4 Cosmological Redshift
Fate of the Universe Will universe expand forever? Similar to escape velocity from a planet Will object tossed upward rise forever or fall back? Depends on launch speed and mass of planet
Figure 17.5 Escape Speed
Critical Density Low density universe expands forever High density universe collapses in a Big Crunch Critical Density is the dividing line For H 0 = 70 km/s/mpc, critical density is 9 X 10-27 kg/m 3 0.1 Milky Way galaxies per cubic Mpc
Figure 17.6 Model Universes
Geometry of space Mass/energy warps space The greater the total density, the greater the curvature Density includes mass (visible and dark matter) Also includes all energy
Cosmic density parameter 0 is ratio of actual to critical density 0 > 1.0 is a closed universe 0 < 1.0 is an open universe 0 = 1.0 is a critical universe
Flat space Euclidean geometry Parallel lines never meet Angles in triangle add to 180 Circumference of circle is 0 = 1, critical universe Infinite in extent X diameter
Positively curved space Studied by Georg Riemann Like surface of sphere Parallel lines intersect twice Angles in triangle add to more than 180 Circumference of circle is < 0 > 1, closed universe Finite in extent X diameter
Figure 17.7 Einstein s Curve Ball - Closed Universe
Negatively curved space Studied by Nikolai Lobachevsky Imagine a saddle shape Infinite number of lines through a point parallel to another line Angles in triangle add to less than 180 Circumference of circle is > 0 < 1, open universe Infinite in extent X diameter
More Precisely 17.1 Curved Space
Cosmic density parameter Counting all luminous matter gives several percent Adding in estimated dark matter in galaxies and clusters gives 0 0.25 On a larger scale distribution of dark matter not well known 0 of Overall cosmic density less than critical
Cosmic acceleration Use Type I supernovae to measure distances (independent of Hubble s law) If gravity slowing expansion - universe is decelerating - objects at great distances - (long ago) - should be receding faster than Hubble s law predicts Data seems to show expansion is accelerating
Figure 17.8 Accelerating Universe
Cosmic acceleration What causes this acceleration? Dark energy - exerts repulsive force Dark energy may greatly exceed total mass (luminous and dark) of universe
Cosmological Constant Vacuum pressure force associated with empty space First suggested by Einstein in 1917 - his equations showed universe evolved in time Expansion of universe not known then When discovered, he discarded Cosmologial Constant as the biggest mistake of his scientific career May be making a comeback as a dark energy explanation
Discovery 17-1 Einstein and the Cosmological Constant
Cosmic Composition Theoretical studies suggest universe is flat A variety of measurements lead to 0 = 1.0 Density is made of both matter (27%) and dark energy (73%) Gravity tends to slow expansion Dark energy tends to increase expansion Universe will expand forever
Figure 17.9 Geometry of the Universe
Age of universe For H 0 = 70 km/s/mpc, Age of critical density universe with no cosmological constant is 9 billion years Age of low density universe > 9 billion y Age of high density universe < 9 billion y Age of accelerating universe is about 14 billion y
Figure 17.10 Cosmic Age
Age of universe Globular clusters formed 10-12 billion years ago Consistent with 14 billion years age for universe with 2 billion years for galaxies to evolve Inconsistent with critical density with no dark energy
Cosmic Microwave Background Penzias and Wilson in 1964 discovered a hiss in all directions of space Microwave wavelengths - blackbody curve at 2.7 K Gamma ray wavelengths in early universe cosmologically redshifted to microwave wavelengths Radiation is isotropic (same in all directions) Contains far more energy than all of energy emitted by all stars and galaxies
Figure 17.11 Microwave Background Discoverers
Figure 17.12 Cosmic Blackbody Curves
Figure 17.13 Microwave Background Spectrum
Matter and Radiation Currently density of matter much greater than density of radiation Matter-dominated universe In past, both radiation and matter more dense But radiation cosmologically redshifted Early universe radiation-dominated
Figure 17.14 Radiation-Matter Dominance
Formation of nuclei and atoms Early universe almost entirely radiation In first minute photons had sufficient energy to transform into electrons, protons, neutrons and exotic particles Primordial nucleosynthesis - formation of elements heavier than hydrogen shortly after Big Bang
Deuterium and helium Below 900 million K, about two minutes after Big Bang, protons and neutrons fused into deuterium After short while, deuterium fused into heavier elements, mostly He-4 Almost all neutrons consumed By 15 minutes, elemental abundance set
Figure 17.15 Helium Formation
Deuterium abundance Not all primordial deuterium converted to He Present day density of universe indicated by deuterium remaining Gives density of normal matter of 3 to 4 percent of critical Total matter density is about 1/3 of critical Most of matter is dark and not composed of protons and neutrons
Formation of Atoms At age of tens of thousands of years, matter began to dominate over radiation Cooled enough for nuclei and electrons to form atoms - known as de-coupling Before then, free electrons scattered radiation Universe went from opaque to transparent After about 400,000 years, temperature fell to 3000 K, and microwave background we see now released when universe was 1100X smaller than today
Figure 17.16 Radiation-Matter Decoupling
Horizon Problem Observe two regions at opposite directions in sky Microwave background same at both Density and temperature same at both But not enough time, even at speed of light, to connect them
Figure 17.17 Horizon Problem
Flatness Problem Universe is very close to being flat today Universe must have been extremely close to critical in the past Why is universe s density nearly critical, out of all possibilities?
Figure 17.18 Flatness Problem
Horizon and Flatness problems explained Grand Unified Theory (GUT) describes superforce made up of electromagnetism and strong and weak nuclear forces 3 forces unified at very high temperatures Predicts that at 10-34 s after Big Bang, at 10 28 K, universe greatly expanded by factor of 10 50 until 10-32 s Epoch of inflation
Figure 17.19 Cosmic Inflation
Cosmic inflation Explains horizon problem Inflation took parts of universe that had communicated, then dragged them far apart Explains flatness problem Curved space, greatly expanded, appears flat
Figure 17.20 Inflation and the Flatness Problem
Formation of large-scale structure Small inhomogeneities in early universe grew into large scale structures Dark matter, unaffected by radiation, clumped and gravitationally affected normal matter
Figure 17.21 Structure Formation
Figure 17.22 Structure Simulated
COBE map Dark matter doesn t emit or absorb radiation Its gravity affects redshift of cosmic microwave background radiation Measured by COBE satellite Map shows universe is of critical density
Figure 17.23 Cosmic Microwave Background Map
Figure 17.24 Early Structure - WMAP spacecraft