Harrison B. Prosper Florida State University YSP Cosmology 1 Harrison B. Prosper Florida State University YSP

Topics Island Universes The Expanding Universe The Universal Scale Factor Models of the Universe Summary

Cepheid Variables She deserved, but did not get, a Nobel Prize Luminosity-Period Relation of Cepheid Variables Henrietta Leavitt 1912 She deserved, but did not get, a Nobel Prize Figure 18–11 The period-luminosity relation of Cepheid variable stars. Long-period Cepheids have higher average luminosities than short-period Cepheids.

Island Universes 1924 – Edwin Hubble Using the work of Henrietta Leavitt, Hubble measured the distances to several galaxies and found that they are immense star systems very far from Earth

The Expanding Universe 1929 – Red Shift Drawing on his own observations and those of others, Edwin Hubble discovered that the red shift, z = (o - e) / e of the light from distant galaxies increases with distance D. e = emitted wavelength o = observed wavelength

The Expanding Universe Hubble’s Law v = H0 D The Hubble Time D = v T D = (H0 d) T T = 1/H0 For H0 = 70 km/s / Mpc T ~ 14 billion years. 1 Mpc (Mega-parsec) = 3.26 x 106 light years (ly)

The Universal Scale Factor D(t1) t1 = past a(t) is the scale factor of the Universe D(t0) λo a = 1 t0 = today a > 1 D(t2) t2 = future λe = a(t) λo D(t) = a(t) D(t0) z = (λo - λe) / λe t is cosmic time

The Hubble Parameter t2 = future d(t2) a > 1 H(t) is called the Hubble parameter The Hubble constant H0 is simply the Hubble parameter H(t0) at the present epoch

Why Can We Assign a Cosmic Time? We have learned that your now and my now do not coincide as we move relative to each other. However, since our relative speeds are small relative to c, it is a very good approximation to take our nows to be the same. The same is true for galaxies. Their motions relative to space are << c. Consequently, we can assign each galaxy approximately the same cosmic time.

Models of the Universe General Relativity Einstein’s theory describes the evolution of spacetime. It can therefore be used to describe the evolution of the Universe The Cosmological Principle (Albert Einstein) The Universe is isotropic (looks the same in all directions) from every vantage point, at all times Such a Universe is necessarily homogeneous, that is, contains matter and energy uniformly distributed

Distribution of Galaxies APM Galaxy Survey, Steve Maddox, Will Sutherland, George Efstathiou & Jon Loveday

Models of the Universe – II The Friedmann-Lemâitre-Robertson-Walker Metric This describes a universe in which the proper distance, that is the distance between two events that are simultaneous (dt = 0), changes with cosmic time, t. The proper distance D(t) between simultaneous events in the Universe is given by where t0 is the lifetime of the Universe

How Far Is Far ? D0, t0 L = c (t0 – t1) D1, t1 t0 – t1 is the look-back time d0 = D(t0) proper distance between galaxies now d1 = D(t1) proper distance between galaxies then

Models of the Universe – III According to Newton’s laws, the total energy E of a galaxy of mass m at a distance D is given by v D where M is the total mass enclosed within the sphere of radius D writing gives

Models of the Universe – IV Alexander Friedmann 1888 - 1925 The Friedmann Equation We can write this differential equation as where

Models of the Universe – IV Problem 7: Using H0 = 70 km/s/Mpc, calculate the (critical) density ρ0 in kg/m3 as well as in the number of protons/m3. Calculate how much mass would be contained in a volume equal to that of the Earth. Give the answer in kg

Models of the Universe – V Since the Friedmann equation is a 1st order differential equation we can re-write it as follows where C is a constant determined by the initial conditions where

Models of the Universe – VI Georges Lemâitre 1927 Assume Ω0 = 1 a(0) = 0 Ω(a) = Ω0 / a3 and remember that a(t0) = 1 Problem 8: Using the above, and H0 = 70 km/s/Mpc, calculate the age of the Universe t0 in Gy according to the Lemâitre model

Summary Expansion of Space In 1929, Hubble discovered the expansion of the Universe. The Friedmann Equation This equation describes how the scale factor a(t) varies with cosmic time. Different cosmological models give different predictions for a(t)