Phys 321: Lecture 13 The Big Bang Theory
Prof. Bin Chen, Tiernan Hall 101, [email protected] The Big Bang Theory
• The prevailing cosmological model for the Universe • Main evidence • The Hubble’s Law • The cosmic microwave background radia on (CMB) • The abundance of light elements homogeneous Can be explained by Hubble’s Law and the Expansion ofSpace Radial Velocity and isotropic expansion of space on a large enough scale Distance + cosmological principle v = H 0 d : the Universe is Cosmological Redshi
• Cosmological Redshi results from the expansion of space itself
Let R be the scaling factor of the space when the light is emi ed, with R0 = 1 at present day t0 λ − λ R − R Z = 0 = 0 λ R E.g., Looking back at galaxies at z = 6, the space is 7 mes closer R = R0 / (1+ z) = 1/ (1+ z) The cosmic microwave background
• In 1948, Ralph Alpher and Robert Herman predicted a “le over heat” of the big bang has a blackbody temperature of ~5 K. • Due to the expansion of the space as well as redshi of the light • In 1964, Arno Penzias and Robert Wilson discovered a 3 K blackbody background in microwave wavelengths using the Holmdel Horn Antenna The cosmic microwave background
• About 377,000 years a er the big bang (redshi of z = 1100), the universe cooled enough for lots of protons and electrons combined to form neutral 2.725 K black body atoms (~3,000 K – recall the Saha Equa on) • At that moment the Universe becomes transparent (op cally thin) • Photons decouple from ma er and stream freely in space. They come off the surface of last sca ering • When we receive the photons today, CMB: The most-precisely measured black body they become highly redshi ed, spectrum in nature resul ng in the much cooler 2.725 K blackbody radia on—the CMB The CMB: A deriva on
Let R be the scaling factor of the (expanding) space, with R0 = 1 at present day
Recall energy density of radia on field is u = aT 4
Energy conserva on says uV = u0V0
Which gives 3 4 4 R aT = aT0 However, the energy of each photon we receive is redshi ed:
(λ − λ) / λ = (R − R) / R = z or R = R / (1+ z) = 1/ (1+ z) 0 0 0
A photon with λ0 at present me has a wavelength λ = Rλ0 at other mes. So we need another factor of R on the le
4 4 4 So R aT = aT0 T0 = RT = T / (1+ z) All-sky CME Observa ons
• CMB observa ons tell us the cosmological principle is correct: the Universe is highly isotropic. • The figure above shows anisotropies of the CMB at 1/100,000 level, possibly generated by ny quantum fluctua ons of ma er during the earlier expansion of the universe Big Bang Nucleosynthesis
• Between about 3-20 minutes a er the Big Bang, the temperature and pressure of the universe allow nuclear fusion to occur • Big Bang produces about 1 neutron for every 7 protons • Nucleosynthesis results in 75% hydrogen and 25% helium by mass, which is the amount we find today from old galaxies!