Cosmology 3 1 Topics The Hot Big Bang The Flatness Problem The Horizon Problem Summary 2 The Hot Big Bang If the space between distant galaxies is growing, this suggests that galaxies were closer together in the past. t Indeed, assuming this continues into the distant past, all matter must have been squeezed together very tightly. le t0 = now d d0 d (t ) a(t )d0 lo 3 The Hot Big Bang Therefore, a basic assumption of the big bang theory of the universe is that the early universe was dense and hot. If so, it must have been filled with t le high energy t0 = now photons in d thermal equilibrium d0 with matter d (t ) a(t )d0 lo 4 The Hot Big Bang The integral over all photon energies of the number of photons per unit volume n(E)dE/V times the photon energy, E, gives the photon energy per unit volume (T) (T ) 0 En(E)dE V 3 8 ( E / kT ) 4 (kT ) E / kT dE / kT 3 0 e (hc) 1 4 8 4 4 4 3 (kT ) RadT 4732 T eV/m 3 (hc) 15 5 The Hot Big Bang The number density of photons scales like 1/a3. But the energy, E, of each photon scales like E = E0/a, where E0 is its energy today. Therefore, the photon energy density goes 4 like /a R But since (T ) 4732 T 4eV/m3 the photon temperature scales like T T0 / a where T0 is the current photon temperature 6 The Hot Big Bang The fact that T = T0 / a implies that the black body spectrum of photons from the early universe is preserved through time, but with t le the temperature t0 = now reduced by the d scale factor a to a predicted temperature of d (t ) a(t )d0 T0 ~ 3 K lo d0 7 The Hot Big Bang An important milestone came in 1965, with the (accidental) discovery of the predicted cosmic microwave background (CMB) radiation by Arno Penzias and Robert Wilson They were awarded the Nobel prize in 1978 8 The Hot Big Bang – The CMB The CMB is the most perfect black body spectrum known. No other convincing way has been found to explain the perfection of this spectrum 9 The Hot Big Bang Another important prediction is that when the universe was about a second old the number of protons increased relative to the number of neutrons t le to a ratio of t0 = now 7 to 1. d 3 minutes later, 1H and 4He nuclei formed in the ratio 3 to 1 d0 d (t ) a(t )d0 lo 10 The Hot Big Bang - Abundances 11 Burles, Nollett & Turner, 1999 The Hot Big Bang - Problems The Flatness Problem Why is the geometry of space so incredibly flat? The Horizon Problem Why is the temperature of the CMB so incredibly uniform across the entire sky? 12 The Flatness Problem The Friedman equation can be written as 8 Ga 2 a Kc 3 2 2 H 1(t ) Kc / a 2 where 2 2 H (t ) a(t ) / a(t ), (t ) (t ) / c (t ) 2 3H (t ) is the critical density at and c (t ) 8 G cosmic time t 13 The Flatness Problem H 1(t ) Kc / a 2 2 2 Since K is constant in time, we can find its value by evaluating this equation at our epoch: H 1 0 Kc 2 0 2 We can then re-write the Friedman equation as 2 0 2 H (t ) 1 10 H 14 The Flatness Problem We now consider the density parameter (t) in the very early universe. The energy density of photons exceeded that of matter when distance scales were about 13,000 times smaller t = now 0 At even smaller scales, radiation totally dominated the energy density of d (t ) a(t )d0 the universe d0 lo 15 The Hot Big Bang In this case, the energy density is given by = R / a4, where R is the photon energy density at the present epoch. The solution of the Friedman equation is then a(t ) bt 1/ 2 where b is a constant. Therefore, the Hubble parameter in the early universe goes like a 1 H a 2t 16 The Hot Big Bang When we put H(t) back into the equation for (t) we get 2 t (t ) 1 4 1 0 1/ H0 which is valid for very early times. Putting in the measured value of H0 we find (t ) 1 10 t 1 0 34 2 17 The Hot Big Bang (t ) 1 1034 t 2 1 0 This expression exhibits the flatness problem: In order to have an 0 ≈ 1, as observed, the density must have been equal to the critical value to better than 1 part in 1034 when the universe was about a second old. This fantastically fined-tuned adjustment of the density cannot be explained by the big bang 18 The Horizon Problem Portrait of the universe at t = 300,000 y CMB temperature fluctuations DT/T ~ 10-5 19 The Horizon Problem On the following slide, the spatial regions BC and DE are causally disconnected; that is, nothing in region BC can affect the region DE, and vice versa, because the regions do not overlap. Nonetheless, the temperature at G and H is measured to be the same to one part in 105 Before t ≈ 300,000 y, all matter was ionized. Consequently, photons could not travel far without scattering off charged particles. Thereafter, neutral atoms formed and 20 photons could then travel freely. The Horizon Problem t = 14 Gy time neutral atoms exist and universe is transparent to light G H ionized light cannot matter exists travel far A B C space D t = 300,000 y E F 21 Summary The big bang theory is successful in predicting the CMB and the abundances of the light elements. However, it cannot explain why space is flat Nor can it explain why the CMB is so isotropic 22

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