ASTR 1040 Recitation: Cosmology Ryan Orvedahl Department of - PowerPoint PPT Presentation

ASTR 1040 Recitation: Cosmology Ryan Orvedahl Department of Astrophysical and Planetary Sciences April 21 & 23, 2014

This Week Last Night of Observing: Tuesday April 22 (8:30 pm) Heliostat Observing: Friday April 25 (2:30 - 4:30 pm) Review Session: Wednesday April 30 (5:00 pm G125) R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 2 / 17

Today’s Schedule Past/Current Homework or Lecture Questions? General Relativity (only a little bit) Cosmology Big Bang R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 3 / 17

FCQs: ASTR-1040-011/012/013 Email (Fri) from FCQ.Office@colorado.edu Check Spam folder, if you have not received it yet Can go to: http://fcq.colorado.edu/ucb fcq.htm Please complete FCQs by Mon April 28 11:59 pm R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 4 / 17

Comments on Exam # 3 R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 5 / 17

General Relativity – Yay!! Geometry you didn’t learn in High School Constant in any reference frame: Constant in any ds 2 = − c 2 dt 2 + dx 2 + dy 2 + dz 2 reference frame: ds 2 = dx 2 + dy 2 + dz 2 (FLAT Space ONLY) R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 6 / 17

What About Geometry of Expanding Universe? ds 2 = − c 2 dt 2 + a ( t ) ( dx 2 + dy 2 + dz 2 ) ds 2 = − c 2 dt 2 + a ( t ) � 1 − kr 2 + r 2 d θ 2 + r 2 sin 2 θ d φ 2 � dr 2 a ( t ) ≡ scale factor, relative expansion of the universe R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 7 / 17

More General Relativity – Yay!! Einstein tensor (Curvature): G µν ≡ R µν − 1 2 Rg µν Include cosmological constant (Dark Energy): Λ Include matter/energy: T µν Full Einstein Equations: G µν + Λ g µν = 8 π G c 4 T µν R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 8 / 17

What Is the Scale Factor? Solve the Einstein Field Equations Assume homogeneous & isotropic universe Only leaves 2 independent equations 2 + kc 2 ( da dt ) = 8 π G ρ +Λ c 2 a 2 3 d 2 a + Λ c 2 ρ + 3 p 1 dt 2 = − 4 π G � � c 2 a 3 3 R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 9 / 17

What Is the Hubble Constant? 1 da Simply defined to be H ( t ) ≡ a ( t ) dt R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 10 / 17

What Is the Hubble Constant? 1 da Simply defined to be H ( t ) ≡ a ( t ) dt Often see Ω parameters, what are those? R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 10 / 17

What Is the Hubble Constant? 1 da Simply defined to be H ( t ) ≡ a ( t ) dt Often see Ω parameters, what are those? Further assume that Λ = 0 and k = 0 Solve for critical density, ρ c , to get flat universe ρ c = 8 π G ρ Simply defined as: Ω ≡ ρ 3 H 2 R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 10 / 17

Density Parameters H 2 ( t ) = H 0 (Ω R a − 4 + Ω M a − 3 + Ω k a − 2 + Ω Λ ) H 0 is Hubble constant of today ( t = t 0 ) Ω j are density parameters of today ( t = t 0 ) R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 11 / 17

Density Parameters H 2 ( t ) = H 0 (Ω R a − 4 + Ω M a − 3 + Ω k a − 2 + Ω Λ ) H 0 is Hubble constant of today ( t = t 0 ) Ω j are density parameters of today ( t = t 0 ) Ω R = (2 . 47 ± 0 . 27) × 10 − 4 Ω M = 0 . 267 ± 0 . 0262 Ω k = − 0 . 020 ± 0 . 021 Ω Λ = 0 . 734 ± 0 . 029 R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 11 / 17

Mass-Energy Budget of the Universe R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 12 / 17

Different Epochs R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 13 / 17

Different Epochs R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 14 / 17

Inflation R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 15 / 17

Big Bang Nucleosynthesis Hot pre-CMB plasma Density of universe Nuclear Fusion ⇒ Primordial Composition R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 16 / 17

Big Bang Nucleosynthesis Hot pre-CMB plasma Primordial Composition Nuclear Fusion ⇒ Density R. Orvedahl (CU Boulder) Cosmology Apr 21 & 23 17 / 17