The Big Bang Olber s Paradox Why is the night sky dark? The Universe is expanding and We cannot see an infinite Universe Hubble s Law v = H0 d v = recession velocity in km/sec d = distance in Mpc H 0 = present-day expansion rate or Hubble Parameter In words: The more distant a galaxy, the faster its recession velocity.
Interpretation Hubble s Law demonstrates that the Universe is expanding in a systematic way: Hubble Parameter: Rate of expansion today. Nature of the Expansion General Expansion of Spacetime: All observers in different galaxies see the same expansion around them. No center - all observers appear to be at the center. What is the recession velocity? NOT motions through space... Expansion of spacetime: galaxies carried along. The Big Bang If we run the clock back far enough, eventually the Universe would be: Zero size and therefore infinite density Infinitely hot This initial state must have existed at some finite time in the past. We call this hot, dense initial state the Big Bang Recession Velocity Light Wave As Universe Expands: Recession velocities gets larger Light waves get stretched & redder Cosmological Redshift of light Cosmological Redshifts All galaxies (with very few exceptions) are receding from us. Recession is quantified in terms of the cosmological redshift of the galaxy, z Not a Doppler shift: measures expansion of spacetime, not motions through space. Cosmological Redshift Expansion of space also stretches light: Wavelengths get stretched = longer = redder Bigger distances = bigger stretching Result: The redshift of an object gets larger with increasing distance. Big Bang naturally explains the observed Cosmological redshifts.
The Hot Big Bang What we see Now: the Universe is cold & low density. as it expands, it cools matter (galaxies) gets further apart. In the past: Universe was smaller, hotter, & denser Is there any evidence of this early hot, dense phase in the past? Cosmic Background Radiation The Universe is filled with diffuse, relic blackbody radiation. As the Universe expands further: Blackbody photons redshift. Spectrum peak shifts to redder wavelengths, and hence cooler temperatures. By today, the spectrum is redshifted down to T 3K Discovery 1965: Penzias & Wilson (Bell Labs) Mapping sky at microwave wavelengths. Found a faint microwave background noise. First thought it was equipment problems (noisy amplifiers, pigeons in the antenna). Finally determined it was cosmic in origin. Won the Nobel Prize in 1978 for discovering the Cosmic Background Radiation. But, is it Blackbody Radiation? The Big Bang model makes very specific predictions: the spectrum is a perfect blackbody characterized by a single temperature. 1965-1990: Experiments with balloons, rockets, & radio antennas show a rough blackbody spectrum Temperature ~2.7 K COBE: Cosmic Background Explorer Satellite Launched in Nov 1989: Mapped the entire sky at Near-IR to Microwave wavelengths. Searched for fluctuations in the background as evidence of early large-scale structure. Far-IR spectrometer mapped the spectrum in detail from 0.1 to 10 mm. Spectacular Blackbody with T=2.726 K
Spectacular Confirmation The COBE results confirm and greatly strengthen the Big Bang Model: The cosmic background radiation has Perfect blackbody spectrum - as predicted Has a single temperature - as predicted Uniformly fills the Universe - as predicted Details: Fine structure at 1 part in 10 5 level is related to the large-scale structure we see in the galaxies. The Big Bang is a Testable Model These basic assumptions are plausible: Empirical support for the most part. Reasonably sound physical basis. But, they are not required to be true. Real Test: Does the Big Bang Model explain the properties of the observed Universe? Predictions of Big Bang Theory Cosmic Microwave background - found with exact black body spectrum as expected Primordial Helium - There is one He atom per 10 H atoms in the Universe - Cannot be explained by H-burning in stars - Natural consequence of nucleosynthesis in the early Universe - Another confirmation of the big bang theory
Lookback Time Light moves at a finite speed: Takes time for light to reach you from a distant source. Example, we see the Sun as it was ~8.5 minutes ago due to the light-travel time. At cosmic distances: The deeper we look into the Universe, the further we look-back in time to when the Universe was younger & smaller. Back to the Beginning The Universe is expanding now. In the past: Universe was smaller. Galaxies were closer together in space. If we go back far enough in time: All galaxies (matter) in one place. How far back = Age of the Universe Road Trip Analogy You leave Columbus by car for Florida, but leave your watch behind. How long have you been on the road? Your average speed = 100 km/h Your odometer reads: distance = 230 km Time since you left: T = distance speed T = 230 km 100 km/h = 2.30 hours The Hubble Time: T 0 Hubble s Law says a galaxy a distance d away has a recession speed, v = H d If locally, v is its average speed, then: T = d / v but since, v = H 0 d, T = d / H 0 d = 1 / H 0 Hubble Time: T 0 = 1 / H 0 Estimate of the Age of the Universe But Cosmic expansion is not expected to be constant over all times: If faster in the past: Expansion slowed by gravity of massive objects T 0 would overestimate the age of the Universe. If slower in the past: accelerated by some dark energy T 0 would underestimate the age of the Universe. Best Estimate of the Age: 13.1 1.4 Gyr This age is consistent with the ages of the oldest stars seen in globular clusters.