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Overview of Astronomy 201 Cosmology: Midterm Grading, Upcoming Project, and Lecture Insights

Midterm II has been graded and grades are now available online. Please check your performance. Additionally, a reminder that the 1st draft of your project is due on Friday, April 6. In Lecture 29, we explored the Big Bang model and the role of the cosmological constant. Key topics included the Friedmann equation, different geometrical models of the universe, and how the density of the universe influences its fate. We examined the deceleration parameter and the implications of an accelerating universe. Don't miss the chance to delve deeper into these cosmic concepts.

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Overview of Astronomy 201 Cosmology: Midterm Grading, Upcoming Project, and Lecture Insights

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  1. Announcements • Midterm II has been graded • grades are online • Friday, April 6: Project, 1st draft due Astronomy 201 Cosmology - Lecture 29

  2. Final grade boundaries • >90% : A • 75%-90% : B • 60%-75% : C • 45%-60% : D • <45% : E Astronomy 201 Cosmology - Lecture 29

  3. Lecture 29The big-bang model II: The cosmological constant: Einstein's greatest blunder or tomorrow's Nobel prize ? Astronomy 201 Cosmology - Lecture 29

  4. Let’s switch to general relativity • Friedmann equation • k is the curvature constant Astronomy 201 Cosmology - Lecture 29

  5. Let’s switch to general relativity • Friedmann equation • k is the curvature constant • k=0: flat space, forever expanding • k>0: spherical geometry, eventually recollapsing • k<0: hyperbolic geometry, forever expanding Astronomy 201 Cosmology - Lecture 29

  6. k>0 k=0 k<0 Astronomy 201 Cosmology - Lecture 29

  7. Can we predict the fate of the Universe ? • Friedmann equation: • k=0: Astronomy 201 Cosmology - Lecture 29

  8. Can we predict the fate of the Universe ? • If the density  of the Universe •  =crit:flat space, forever expanding •  >crit:spherical geometry, recollapsing •  < crit:hyperbolic geometry, forever expanding • so what is the density of the universe? • We don’t know precisely •  >critvery unlikely • currently favored model: 0.3crit Astronomy 201 Cosmology - Lecture 29

  9. How big is crit ? • crit=810-30g/cm3 1 atom per 200 liter • density parameter0 • 0 =1:flat space, forever expanding (open) • 0>1:spherical geometry, recollapsing (closed) • 0<1:hyperbolic geometry, forever expanding • currently favored model:0= 0.3 Astronomy 201 Cosmology - Lecture 29

  10. How can we measure 0 ? • Count all the mass we can “see” • tricky, some of the mass may be hidden … • Measure the rate at which the expansion of the universe is slowing down • a more massive universe will slow down faster • Measure the geometry of the universe • is it spherical, hyperbolic or flat ? Astronomy 201 Cosmology - Lecture 29

  11. Let’s try to measure the deceleration • Acceleration according to Newton: • deceleration parameter Astronomy 201 Cosmology - Lecture 29

  12. So what’s the meaning of q0 ? • deceleration parameter q0 • q0>0.5: deceleration is so strong that eventually the universe stops expanding and starts collapsing • 0<q0<0.5: deceleration is too weak to stop expansion • What’s the difference between q0, 0and k? • k: curvature of the universe • 0: mass content of the universe • q0: kinematics of the universe Astronomy 201 Cosmology - Lecture 29

  13. So let’s measure q0 ! • How do we do that? • Measure the rate of expansion at different times, i.e. measure and compare the expansion based on nearby galaxies and based on high redshift galaxies • Gravity is slowing down expansion  expansion rate should be higher at high redshift. Astronomy 201 Cosmology - Lecture 29

  14. So let’s measure q0 ! q0 = 0 q0 = 0.5 Data indicates: q0 < 0  Expansion is accelerating fainter more distant Astronomy 201 Cosmology - Lecture 29

  15. Science discovery of the year 1998 • The expansion of the universe is accelerating !!! • But gravity is always attractive, so it only can decelerate • Revival of the cosmological constant  Astronomy 201 Cosmology - Lecture 29

  16. Friedmann’s equation for >0 • k is the curvature constant • k=0: flat space, flat universe • k>0: spherical geometry, closed universe • k<0: hyperbolic geometry, open universe • k is the curvature constant • k=0: flat space • k>0: spherical geometry • k<0: hyperbolic geometry • but for sufficiently large  a spherically curved universe may expand forever Astronomy 201 Cosmology - Lecture 29

  17. Acceleration according to Newton: • deceleration parameterwith Deceleration parameter q for >0 • Acceleration according to Newton: • deceleration parameter Astronomy 201 Cosmology - Lecture 29

  18. The fate of the Universe for >0 k=+1 >0 =0 Astronomy 201 Cosmology - Lecture 29

  19. Is the fate of the Universe well determined ? • deceleration: • ½0 – > 0: decelerating • ½0 – < 0: accelerating • curvature • 0 + = 1: flat • 0 + < 1: hyperbolic • 0 + > 1: spherical • two equations for two variables  well posed problem Astronomy 201 Cosmology - Lecture 29

  20. Cosmology: the quest for three numbers • The Hubble constant H0 • how fast is the universe expanding • The density parameter 0 • how much mass is in the universe • The cosmological constant  • the vacuum energy of the universe • current observational situation: • H0= 65 km/s/Mpc • 0 = 0.3; = 0.7  flat space Astronomy 201 Cosmology - Lecture 29

  21. Announcements • Midterm II has been graded • grades are online • Friday, April 6: Project, 1st draft due Astronomy 201 Cosmology - Lecture 29

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