Spring 2025 ASTR 3740 Homepage

Spring 2025 ASTR 3740 Final Review

This Final review sheet is posted at http://jila.colorado.edu/~ajsh/courses/astr3740_25/review_final.html

The final will be a take-home, 5-hour, open-book, open-internet exam. It will be published on canvas in the morning of Friday May 2. You can download the test from the link in canvas. You must upload your answers back to canvas no later than five hours after you downloaded the test. Canvas will record when you download the test, and when you upload your answer. The test is due by midnight Tuesday May 6. Do not collaborate.

The final will test all the material covered cumulatively during the semester, but with an emphasis on the material covered since Spring Break, that is, on Cosmology. Review the review sheets for the midterms to brush up on Special Relativity and General Relativity.

Please write your own answers, not something copied from elsewhere. If you do copy something, please quote it, and give the reference. Please write clear, grammatically correct sentences.

You agree to respect the CU Honor Code. If you use AI or other outside resources, you must credit the source. If you use language from AI, you must justify that use, using logic or other more credible resources.

Review Questions

1. Hubble expansion
   • Hubble law
   • Hubble parameter H, Hubble constant H₀
   • redshift
   • distances
     • Cepheid variables
     • Type Ia supernovae

2. Geometry
   • Cosmological Principle
   • Closed, flat, open
   • Omega: Ω ≡ ρ/ρ_crit
   • Horizon
   • Hubble distance c/H

3. FLRW (Friedmann-Lemaître-Robertson-Walter) metric
   • embedding diagram
   • comoving coordinates
   • cosmic scale factor a
   • curvature constant κ

4. Friedmann equations
   • = Einstein equations for FLRW metric
   • Newtonian derivation
   • relate curvature and energy density
   • determine evolution of cosmic scale factor

5. Matter, radiation, vacuum
   • mean, in a cosmological context?
   • equation of state p/ρ for each species of energy-momentum
   • deceleration, acceleration
   • evolution of the horizon
   • wavelength λ ∝ a ∝ 1/T
   • redshift z of an epoch: 1 + z ≡ λ_obs/λ_emit ∝ 1/a
   • which species dominated when?

6. Cosmic Microwave Background (CMB)
   • Observed:
     • blackbody spectrum with T = 2.725 K
     • dipole from our motion through it
     • after subtraction of constant and dipole, uniform to few × 10⁻⁵ on the sky
     • power spectrum of fluctuations
   • Theory:
     • comes from the epoch of Recombination
     • ⇒ Universe was simple! — uniform, and in thermodynamic equilibrium
     • before Recombination: ionized; opaque; baryons coupled to photons
     • sound waves in the photon-baryon fluid, generated during inflation ⇒ peaks in CMB power spectrum
     • after Recombination: neutral; transparent; baryons fall into CDM potential wells
   • Observed power spectrum fits inflationary model with just 6 parameters:
     • Hubble parameter today H₀ = 67 km/s/Mpc
     • Omega in Dark Energy (Λ), non-baryonic Cold Dark Matter, and baryons: Ω_Λ = 0.69, Ω_CDM = 0.26, Ω_b = 0.05
     • Amplitude A and spectral index n of the noise spectrum of vacuum fluctuations in the vacuum energy that drove inflation

7. Inflation
   • what is it?
   • Offers a solution to:
     • horizon problem
     • flatness problem
     • why the Universe is expanding
     • the origin of matter and radiation
     • the origin of flucutations in the Universe
   • Generically predicts:
     • almost flat Universe
     • scale-invariant initial fluctuation spectrum
     • causal acoustic peaks in CMB power

8. Dark Energy (Λ)
   • Observational evidence:
     • Hubble diagram of high redshift Type Ia supernovae
     • CMB
   • Ω_Λ = 0.7
   • What is it? No one really knows. Vacuum energy (of what)? Something else?

9. Dark Matter
   • Non-baryonic Cold Dark Matter (CDM):
     • solves the isotropy problem (how can the tiny fluctuations in the CMB grow into observed galaxies in “only” the age of the Universe)
     • required by CMB power spectrum
     • Ω_CDM = 0.26
   • Dark Matter, baryonic or non-baryonic
     • shows up in rotation curves of spiral galaxies
     • ubiquitous in galaxy clusters

10. Big Bang Nucleosynthesis
    • produces the light elements H, D, ³He, ⁴He, Li
    • reproduces the observed abundances provided that Ω_b ≈ 0.05

11. What happened in the beginning?
    • No one knows.

Updated 2025 Apr 23