The Big Bang The Big Bang Key Concepts 1) The Hubble law (v = H0d) is expected in a uniformly expanding universe. 2) If the speed of galaxies has been constant, expansion began a Hubble time ago. 3) The Hubble law is consistent with the Big Bang theory (expansion from an initial dense state). There is nothing special about our galaxy. In a uniformly expanding universe, every galaxy moves away from every other galaxy. Hubble law: other galaxies are moving away from our own, with a velocity proportional to their distance. The universe considered as an expanding loaf of raisin bread: 1 Why it’s useful to know the Hubble constant, H0: With modern telescopes and spectrographs, astronomers have measured millions of spectra. Measure redshift of galaxy: z = (λ-λ0)/λ0 Compute radial velocity: v = c z Compute distance: d = v / H0 Cheap, fast way to find distance! A “redshift map” of a slice through the universe. Each tiny dot represents a galaxy. Why it’s intriguing to know H0: d Two galaxies are separated by a distance d. They are moving apart from each other with a speed v = H0 d. 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 dense initial state the • “Big Bang” 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. 2 Back to the Beginning How long has it been since the galaxies were touching? • The Universe is expanding now. • In the past: – Universe was smaller. – Galaxies were closer together in space. travel time • If we go back far enough in time: – All galaxies (matter) in one place. • How far back = “Age of the Universe” Kilometers per second per megaparsec?? What bizarre units! 1 megaparsec = 3.09 × 1019 kilometers H0 71 km/sec/Mpc 2.30 10 18 / sec 3.09 1019 km/Mpc H0 t distance speed d 1 4.35 1017 sec H 0d H 0 PLEASE NOTE: This length of time (t = 1/H0) is independent of the distance between galaxies!! If galaxies’ speed has been constant, then at a time 1/H0 in the past, they were all scrunched together. 1 4.35 1017 sec Heart of the “Big Bang” concept: At a finite time in the past (t ≈ 1/H0), the universe began in a very dense state. 1/H0, called the “Hubble time”, is the approximate age of the universe in the Big Bang Model. t 1 4.35 1017 sec H0 Since there are 3.16 × 107 seconds per year, the Hubble time is 1/H0 = 13.8 billion years 3 But… • Cosmic expansion is not expected to be constant over all times: • If faster in the past: – Expansion slowed by gravity of massive objects – T0 would overestimate the age of the Universe. • If slower in the past: The Big Bang model “de-paradoxes” Olbers’ paradox. If age of universe ≈ 1/H0, light from stars farther than a distance ≈ c/H0 has not had time to reach us. – accelerated by some “dark energy” – T0 would underestimate the age of the Universe. Hubble time: Is the universe infinitely old? 1/H0 = 13.8 billion years. Hubble distance: About 14 billion years have passed since the universe started expanding from its initial dense state. c/H0 = 13.8 billion light-years = 4200 megaparsecs. The Observable Universe has a finite age. Is the universe infinitely big? We don’t know: we can see only a region about 4200 megaparsecs in radius, with no boundary in sight. The Observable Universe is finite in size. 4

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