1 / 16

Cosmology:  Mass and Energy I

Cosmology:  Mass and Energy I. by Robert Nemiroff Michigan Tech U. Physics X: About This Course. Officially "Extraordinary Concepts in Physics" Being taught for credit at Michigan Tech Light on math, heavy on concepts Anyone anywhere is welcome No textbook required

nixie
Download Presentation

Cosmology:  Mass and Energy I

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Cosmology: Mass and Energy I by Robert Nemiroff Michigan Tech U.

  2. Physics X: About This Course • Officially "Extraordinary Concepts in Physics" • Being taught for credit at Michigan Tech • Light on math, heavy on concepts • Anyone anywhere is welcome • No textbook required • Wikipedia, web links, and lectures only • Find all the lectures with Google at: • "Starship Asterisk" then "Physics X"  • http://bb.nightskylive.net/asterisk/viewforum.php?f=39

  3. Mass and Energy in the Universe: Overview • Standard GR cosmology only • Called Friedmann Robertson-Walker • It's the most standard GR set of cosmologies • This lecture is based (mostly) on my paper: •  "Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations" by Nemiroff & Patla • 2008AmJPh..76..265N

  4. Cosmology: Friedmann Equations • Two: Energy equation and Acceleration equation • Relates two variables: • "a": scale factor for the universe • "Omega": Ω: the energy density of the universe • Energy equation is the simplest  • Uses only the first derivative of "a" (and a) • Can be complicated if several types of energy involved

  5. Cosmology: Friedmann Equations • Acceleration equation is more complicated • Uses second derivative of "a" (and a) • time part of larger 4-vector • mathematically equivalent to Energy equation  • when spatially symmetric in all 3 spatial dimensions

  6. Cosmology: Cosmic Rest Frames • Every place in the universe has an intrinsic "rest frame" • This seems to violate Special Relativity • But Friedmann GR solutions establish it • Defined by rest frame of energy forms in the universe • Cosmic microwave background (main one) • Matter at rest "with respect to the universe"  • sees the microwave background the same in every direction

  7. Cosmology: Horizons • Event Horizon • Inside, events cannot effect outside • Particle Horizon • Also known as "Cosmological Horizon" • Furthest distance particles can reach you if they left at the Big Bang • Gravitational Horizon • Furthest distance gravity can reach you

  8. Cosmology: Scale Factor: "a" The scale length at any time in a Friedmann Robertson Walker (FRW) universe is given by the single parameter "a".   One way to visualize "a" is as the average distance between galaxies.   Even when there are no galaxies. In an expanding universe, "a" increases with time.

  9. Friedmann Equation of Energy: Generic Form Where: • H = (da/dt)/a = Hubble's parameter • G = gravitational constant • ρ = energy density • c = speed of light • R = un-normalized universe scale factor • k = dimensionless, related to curvature

  10. Friedmann Equation: different terminology Different energy types change differently as the universe expands: The total energy density of the universe includes all possible energy types:

  11. Friedmann Equation of Energy:General Form Where: Ho is H at the present time (z=0)

  12. Cosmology: Perfect Fluids A perfect fluid is defined by only two variables • density: ρ • pressure: P These are presumed defined everywhere in the universe to be the same at any given time.   This is also called the Cosmological Principle

  13. Cosmology: Perfect Fluids w = P/ (ρ c2) tells the type of perfect fluid. Each perfect fluid is a different type of energy. ρ ~ a-3(1+w) shows how density changes with w as the universe scale factor "a" changes.

  14. Cosmology: Perfect Fluids

  15. Friedmann Cosmology: Energy Conservation Energy is NOT conserved.  Matter dilutes EVERYWHERE in the universe.  So energy related to matter decreases.  There is no place for this energy to go.

  16. Cosmology: Gravity attraction or repulsion

More Related