Cosmology

1. Cosmology Part 2

2. Olber’s Paradox • Assume that the universe is infinite in spatial extent and unchanging in time. Then, every line of sight must eventually lead to a star (assuming universe is uniformly populated with galaxies). • Stars further away are dimmer but greater in number (the number of stars we see increases as the square of the distance). The brightness of stars decreases as the square of the distance. These two effects should balance, so stars at all distances contribute equally to the total amount of light received on Earth. • Implication - no matter where you look in the sky, it should be bright! This idea, combined with fact that the night sky isn’t bright, is known as Olber’s paradox. • So why is the sky dark at night? Either the universe is finite in extent, or it evolves in time, or both.

3. The Birth of the Universe • Hubble’s law describes the expansion of the universe - all galaxies are rushing away from us according to: • Recession velocity = H0 x distance • H0 = 70 km/s/Mpc • We can determine how long it has taken a galaxy to move away from us using Hubble’s law: • Time = distance / velocity = distance / (H0 x distance) = 1 / H0. • This comes out to an age of 14 billion years. • Hubble’s law implies that 14 billion years ago, all galaxies lay on top of each other.

4. The Birth of the Universe • Almost unanimous view among astronomers: everything in the universe - matter and radiation alike - was confined to a single point at 14 billion years ago. The point exploded, flying apart at high speeds (the Big Bang) marking the beginning of the universe. • The present locations and velocities of the galaxies are a direct consequence of that primordial blast. • The solution to Olber’s paradox - we can only see a finite extent of the universe (even if it’s infinite) - that which lies within 14 billion light-years. Anything further would not have had time to reach us.

5. Where did the Big Bang occur? • At a single point in the center of the universe. • Everywhere in the universe all at once. • At a point outside of our universe.

6. We see galaxies moving away from us in all directions. Are we at the center of the universe? • Yes, that’s the only way most everything else can move away from you. • No, we are not at the center of the universe, but the universe does have a center somewhere. • No, no matter where you are located at, you would see most other galaxies moving away from you. It’s a trick question - the universe has no center.

7. The Universe on the Largest Scales Distribution of galaxies from the Sloan Digital Sky Survey. • No evidence for structures larger than about 200 Mpc (1 pc is 3 ly, so 200 Mpc is 6,000,000 ly). • Universe appears to be homogenous on large scales (the same everywhere) and isotropic (the same in all directions). • Cosmological principle - assumptions that the universe is both homogenous and isotropic on large scales. • Implications - the universe has no edge (would break homogeneity) and no center (would break isotropy).

8. The Cosmological Redshift • The cosmological redshift is a consequence of the changing size of the universe (not related to velocity at all, unlike the Doppler shift). • A photon is attached to the expanding fabric of space, so the photon is lengthened (redshifted). • Often think of this as Doppler shift, even though it’s not completely correct. • The redshift of a photon measures the amount by which the universe has expanded since that photon was emitted. Therefore, redshift can be used to express time.

9. Two Futures • The universe can either expand forever, or it can start to contract in the future back into a singularity (the big crunch). • The present time is the point at which the two curves above intersect. • What determines which future the universe will have? Density! A high density universe contains enough mass to stop the expansion and reverse it. • In reality, there may be other factors involved other than just gravity alone.

10. The Shape of the Universe • Space is curved (not flat!). The degree of curvature depends on the total density of the universe. This density includes everything (visible matter, dark matter, energy, etc.). • The ratio of the universe’s actual density to the critical density (the distinction between future expansion or contraction) is called the cosmic density parameter 0. • High-density universe (0>1) - universe is closed (space curves so much it bends back in on itself) - think of the surface of a sphere (although this is not quite correct - we need another dimension added to the sphere to be a more accurate picture). A sphere is said to have positive curvature. • A low-density universe (0<1) would look akin to a saddle (again, need an extra dimension to make this correct). This is called an open universe. • A critical universe (0=1) has no curvature, it is flat. This is the only universe in which Euclidean geometry works on large-scales.

11. The Density of the Universe • Most of the matter in the universe is dark (we can only detect it through its gravitational effects on matter we can see). • Most believe the amount of dark matter will not raise the density above about 30% the critical value (in other words, most likely, the universe will expand forever).

12. Cosmic Acceleration • Using type 1 supernovae, we can measure the expansion. • If the universe were decelerating, objects further away should be receding faster than predicted by Hubble’s law. In a denser universe, gravity is more effective at slowing the expansion, so the effect would be greater. • Supernovae measurements actually indicate that the expansion is accelerating - something other than gravity is acting on the universe. • Known as dark energy, this other (yet unknown) force carries energy but has a repulsive effect on the universe, causing empty space to expand. • Leading candidate - the cosmological constant. This is an additional vacuum pressure force associated with empty space and effective only on very large scales. This is neither required nor explained by any known laws of physics. It was first introduced by Einstein (who later called it his biggest blunder). Its influence increases as the universe expands.

13. Cosmic Composition • Consensus (as of early 2006) is that we are at the critical density. • Density is made up of matter (mostly dark) and dark energy. • Best estimate - matter accounts for 27% of the total, with dark energy accounting for the remaining 73%. • Such a universe will expand forever, and is perfectly flat.

14. The Age of the Universe • Globular star clusters - oldest objects in existence, roughly 10 to 12 billion years old. • Their ages are not consistent with a critical-density universe without dark energy. • This gives an independent verification of currently held cosmology beliefs.

15. Matter and Radiation • At the present moment, the density of matter in the universe greatly exceeds the density of radiation. • We live in a matter-dominated universe. • Early on, the universe was radiation-dominated. • According to current theory, the density associated with dark energy remains constant as the universe expands - even though it is important now, it was unimportant in the early universe.

16. The Formation of Nuclei and Atoms • According to Big Bang theory, at the very earliest times the cosmos consisted entirely of radiation. During the first minute or so, temperatures were high enough that individual photons of radiation had sufficient energy to transform themselves into matter in the form of elementary particles. • This period saw the creation of all the basic building blocks of matter we know today. • Everything we see around us formed out of radiation as the early universe expanded and cooled.

17. Helium Formation • No matter where you look, stars all have at least around 25% helium by mass. • This base level of helium is primordial - created during the early, hot epochs of the universe. • The production of elements heavier than hydrogen by nuclear fusion shortly after the Big Bang is called primordial nucleosynthesis. • The cosmic elemental abundance was set within 15 minutes after the Big Bang (once the universe cooled and thinned too much, fusion reactions ceased).

18. Nucleosynthesis and the Composition of the Universe • Heavy hydrogen, known as deuterium (nucleus contains one proton and one neutron) was produced on the way to making the primordial helium. • The left-over amount of deuterium is another indication of the density of the universe. But it only tells us the density of normal matter. • Most matter is made up of dark matter, exotic particles whose existence we have yet to conclusively demonstrate in the lab.

19. The Formation of Atoms • Period during which nuclei and electrons combined to form atoms is called the epoch of decoupling. • Early on, electrons interacted with the radiation. A photon could not travel far without being scattered off by an electron, so the universe was opaque to radiation. • During decoupling, the universe became transparent. • Decoupling happened when the universe was 400,000 years old.

20. The Horizon and Flatness Problems • Horizon problem - Some regions of the universe that have very similar properties are too far apart to have exchanged information within the age of the universe. • Flatness problem - There is no natural way to explain why the density of the universe is so close to the critical density.

21. The Epoch of Inflation • Grand unified theories - electromagnetism, and the strong and weak forces were all joined into one “superforce.” • The universe remained in “unified” formation a little too long, and this resulted in the epoch of inflation during which an enormous pressure overcame gravitation. • During inflation, the universe doubled in size every 10-34 s or so. • The entire episode lasted only 10-32 s, but during this time the universe grew in size by a factor of about 1050.

22. Implications for the Universe • Inflation solves the horizon problem - it took places that had already had time to communicate and moved them far apart. • Inflation also solves the flatness problem - any curvature that existed before inflation has been spread out so much that the universe now appears effectively flat.

23. The Formation of Large-Scale Structure in the Universe • All present large-scale structure in the universe grew from small inhomogeneities (slight deviations from perfectly uniform density). • Dark matter clumped first as it interacts least with everything else. Normal matter was drawn to the regions of highest density. Thus, normal matter clumped where dark matter already had. • COBE detected slight variations in the background radiation, consistent with the clumping of matter.