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**Announcements**• Midterm II has been graded • grades are online • Friday, April 6: Project, 1st draft due Astronomy 201 Cosmology - Lecture 29**Final grade boundaries**• >90% : A • 75%-90% : B • 60%-75% : C • 45%-60% : D • <45% : E Astronomy 201 Cosmology - Lecture 29**Lecture 29The big-bang model II: The cosmological constant:**Einstein's greatest blunder or tomorrow's Nobel prize ? Astronomy 201 Cosmology - Lecture 29**Let’s switch to general relativity**• Friedmann equation • k is the curvature constant Astronomy 201 Cosmology - Lecture 29**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**k>0**k=0 k<0 Astronomy 201 Cosmology - Lecture 29**Can we predict the fate of the Universe ?**• Friedmann equation: • k=0: Astronomy 201 Cosmology - Lecture 29**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: 0.3crit Astronomy 201 Cosmology - Lecture 29**How big is crit ?**• crit=810-30g/cm3 1 atom per 200 liter • density parameter0 • 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**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**Let’s try to measure the deceleration**• Acceleration according to Newton: • deceleration parameter Astronomy 201 Cosmology - Lecture 29**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**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**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**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**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**Acceleration according to Newton:**• deceleration parameterwith Deceleration parameter q for >0 • Acceleration according to Newton: • deceleration parameter Astronomy 201 Cosmology - Lecture 29**The fate of the Universe for >0**k=+1 >0 =0 Astronomy 201 Cosmology - Lecture 29**Is the fate of the Universe well determined ?**• deceleration: • ½0 – > 0: decelerating • ½0 – < 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**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**Announcements**• Midterm II has been graded • grades are online • Friday, April 6: Project, 1st draft due Astronomy 201 Cosmology - Lecture 29