Our Our Place Place in in the the Cosmos Cosmos the Universe - PDF document

The Big Bang • We saw in the last lecture that the Universe is expanding • Following that expansion backward in time, Our Our Place Place in in the the Cosmos Cosmos the Universe must have been much smaller in the past • We believe the Universe was created in an Lecture 18 event called the Big Bang about 13.6 billion The Big Bang years ago • This is an empirical model - does it make any testable predictions? Predictions of The Big Bang • When a gas is compressed it gets hotter • It thus seems reasonable to assume that the young Universe contained an extremely hot, dense gas, filled with high energy radiation with a Planck spectrum • In the 1940s, Ralph Alpher and Robert Herman reasoned that as the Universe expanded, this cosmic background radiation (CBR) would have have been redshifted to Planck radiation in the hot, dense, young Universe is longer and longer wavelengths, corresponding stretched by Hubble expansion to longer-wavelength to a much cooler blackbody [recall Wien’s law: radiation at a lower temperature T = (2,900 µ m)/ � peak ] Prediction of CBR Discovery of CBR • The first theoretical prediction of the residual • In the early 1960s Arno radiation from the Big Bang was published in Penzias and Robert Wilson 1948 by Alpher and Herman were puzzled by a faint microwave signal detected • They asserted that the radiation should be by the Bell Telephone Labs visible today with a temperature in the range radio telescope in Holmdel, 5-10 K, corresponding to radiation in the New Jersey microwave part of the spectrum • No matter where they • Telescope technology at the time was not far pointed the telescope, the enough advanced to detect this radiation and signal persisted their landmark paper languished largely unnoticed until the 1960s

Discovery of CBR Origin of the CBR • Meanwhile, Robert Dicke in nearby Princeton • The cosmic background radiation originates in the hot, young Universe when most hydrogen was ionized University independently arrived at Alpher and • Photons of radiation interact strongly with free Herman’s prediction of CMB radiation electrons and thus cannot travel far and acquire a • When Dicke heard of the signal that Penzias Planck spectrum and Wilson had found, it was realised that the • As the Universe expanded and cooled to a cosmic background radiation had been temperature of a few thousand degrees discovered [an achievement for which Penzias (corresponding to redshift z � 1100 around 10 5 years and Wilson shared the 1979 Nobel Prize] after the Big Bang) the protons and electrons of hydrogen were able to recombine, resulting in a • The temperature of their signal was around Universe transparent to radiation 3K, close to the predicted temperature and • The CBR photons were then able to stream freely, corresponding to radiation in the microwave being redshifted as the Universe expanded part of the spectrum COBE Satellite • Although Penizas and Wilson had detected the CBR at the predicted temperature, they were unable to confirm that it had a Planck spectrum as predicted • The COsmic Background Explorer (COBE) launched in 1989 made an accurate measurement of the spectrum of the CBR • The CBR spectrum corresponded perfectly to a Planck spectrum with corresponding temperature of 2.728 K • Very strong support for Big Bang model CBR Spectrum Earth’s Motion • The COBE satellite also discovered that the temperature of the CBR is not the same everywhere • The temperature differs by about 0.003 K in opposite directions on the sky • This is due to Earth’s motion with respect to the CBR - the CBR provides a frame of reference that is at rest with respect to the expansion of the Universe • The CBR is blueshifted (slightly hotter) in the direction of our motion and redshifted (slightly cooler) in the opposite direction • v � 368 km/s

CBR Temperature Anisotropy Nucleosynthesis • If we subtract from the COBE map the effects of our • Temperatures and densities when the Universe was motion and microwave emission from the Milky Way, less than a few minutes old were similar to those in very small fluctuations in temperature of about 1 the cores of stars today part in 10 5 remain • Nuclear fusion reactions could thus fuse hydrogen into • These temperature anisotropies result from equally heavier nuclei small density perturbations in the post-recombination • Only the lightest nuclei were synthesised during Big Universe Bang nucleosynthesis: deuterium (heavy hydrogen), • These density perturbations also give rise to the helium, lithium, beryllium and boron large-scale structures in the galaxy distribution that • The amounts of each isotope formed depend we see today sensitively on the temperature and density of matter • 2006 Nobel Prize in the early Universe, and hence on the present-day awarded to COBE density of baryonic (“normal”) matter team for this discovery Nucleosynthesis • About 24% of the mass of baryonic matter formed in the early Universe is in the form of 4 He regardless of the baryon density • The predicted abundances of other isotopes are sensitive to the baryon density • In order to agree with observed abundances, the present-day baryon density must be around 3 x 10 -28 kg/m 3 - again in good prediction with observations • Big Bang nucleosynthesis is inconsistent with dark matter being in the form of baryons such as protons and neutrons • Dark matter must thus be in non-baryonic form Agreement of predicted abundances with observations requires that the present-day baryon density lies within the vertical yellow band - the vertical black line shows the observed baryon density Successes of the Big Bang Fate of the Universe Model • We know the Universe is expanding today - will this The Big Bang model is supported by three • expansion continue forever? main pieces of observational evidence • This depends in part on the mass of the Universe 1. The observed expansion of the Universe • Recall our discussion of escape velocity - the fate of 2. The blackbody form and expected temperature of a projectile fired straight up from the surface of the the cosmic background radiation Moon depends upon its speed • If the speed is less than the escape velocity then gravity 3. The observed abundances of the light elements will eventually pull the projectile back to the Moon’s surface No other theory, such as the steady state • • If the speed is greater than the escape velocity the model, or plasma Universe, can explain these projectile can escape from the Moon • The gravity of the mass in the Universe acts in a observations so naturally similar way, slowing down the expansion

Fate of the Universe Critical Density • The faster the Universe is expanding, the more mass • If there is enough mass in the Universe then gravity is required to turn that expansion around will eventually stop the expansion • The critical density � c thus depends on the Hubble • The Universe will slow, stop and eventually collapse constant H 0 on itself in a Big Crunch • H 0 = 72 km/s/Mpc � � c = 8 x 10 -27 kg/m 3 • If there is not enough mass the expansion may slow, • We write the ratio of the actual density � 0 of the but will never stop Universe to the critical density as � m (omega-matter) • Escape velocity from a planet is determined by its • Recall that nucleosynthesis � � 0 � 3 x 10 -28 kg/m 3 mass and radius and so baryons alone fall far short of providing critical density • The escape velocity of the Universe is determined by its average density • The above argument supposes that gravity is the only important force in determining the fate of the • The critical density is the limiting density that Universe - an assumption which has recently been determines the future fate of the Universe overturned An Accelerating Universe! • Whatever the actual value of � m one would expect the expansion rate of the Universe to be slowing down • This can be checked by measuring the brightness of standard candles such as Type I supernovae at high redshift [brightness � distance � integrated expansion rate] • To astronomers’ great surprise, such observations carried out in the late 1990s showed that the expansion of the Universe is in fact speeding up ! Most supernovae Einstein’s “Greatest Blunder” at high redshift are fainter than • Einstein formulated his general theory of relativity in we would expect 1915, before Hubble had discovered the expansion of in the case of the Universe unaccelerated • In order to produce a static solution to his equations Hubble expansion describing the Universe, Einstein introduced a term he called the cosmological constant � , a repulsive term Those which balanced the attractive force of gravity observations • Once it was realised 14 years later that the Universe below the curve was expanding, the � term was no longer necessary suggest • Einstein apparently regarded his inclusion of the � expansion is term (and his failure to predict an expanding speeding up Universe) as “my greatest blunder”