Our Place in the Cosmos

1. Our Place in the Cosmos Lecture 18 The Big Bang

2. The Big Bang • We saw in the last lecture that the Universe is expanding • Following that expansion backward in time, the Universe must have been much smaller in the past • We believe the Universe was created in an event called the Big Bang about 13.6 billion years ago • This is an empirical model - does it make any testable predictions?

3. 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 longer and longer wavelengths, corresponding to a much cooler blackbody [recall Wien’s law: T = (2,900 m)/peak]

4. Planck radiation in the hot, dense, young Universe is stretched by Hubble expansion to longer-wavelength radiation at a lower temperature

5. Prediction of CBR • The first theoretical prediction of the residual radiation from the Big Bang was published in 1948 by Alpher and Herman • They asserted that the radiation should be visible today with a temperature in the range 5-10 K, corresponding to radiation in the microwave part of the spectrum • Telescope technology at the time was not far enough advanced to detect this radiation and their landmark paper languished largely unnoticed until the 1960s

6. Discovery of CBR • In the early 1960s Arno Penzias and Robert Wilson were puzzled by a faint microwave signal detected by the Bell Telephone Labs radio telescope in Holmdel, New Jersey • No matter where they pointed the telescope, the signal persisted

7. Discovery of CBR • Meanwhile, Robert Dicke in nearby Princeton University independently arrived at Alpher and Herman’s prediction of CMB radiation • When Dicke heard of the signal that Penzias and Wilson had found, it was realised that the cosmic background radiation had been discovered [an achievement for which Penzias and Wilson shared the 1979 Nobel Prize] • The temperature of their signal was around 3K, close to the predicted temperature and corresponding to radiation in the microwave part of the spectrum

8. Origin of the CBR • The cosmic background radiation originates in the hot, young Universe when most hydrogen was ionized • Photons of radiation interact strongly with free electrons and thus cannot travel far and acquire a Planck spectrum • As the Universe expanded and cooled to a temperature of a few thousand degrees (corresponding to redshift z 1100 around 105 years after the Big Bang) the protons and electrons of hydrogen were able to recombine, resulting in a Universe transparent to radiation • The CBR photons were then able to stream freely, being redshifted as the Universe expanded

10. 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

11. CBR Spectrum

12. 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

13. CBR Temperature Anisotropy • If we subtract from the COBE map the effects of our motion and microwave emission from the Milky Way, very small fluctuations in temperature of about 1 part in 105 remain • These temperature anisotropies result from equally small density perturbations in the post-recombination Universe • These density perturbations also give rise to the large-scale structures in the galaxy distribution that we see today • 2006 Nobel Prizeawarded to COBEteam for this discovery

14. Nucleosynthesis • Temperatures and densities when the Universe was less than a few minutes old were similar to those in the cores of stars today • Nuclear fusion reactions could thus fuse hydrogen into heavier nuclei • Only the lightest nuclei were synthesised during Big Bang nucleosynthesis: deuterium (heavy hydrogen), helium, lithium, beryllium and boron • The amounts of each isotope formed depend sensitively on the temperature and density of matter in the early Universe, and hence on the present-day density of baryonic (“normal”) matter

15. 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

16. Nucleosynthesis • About 24% of the mass of baryonic matter formed in the early Universe is in the form of 4He 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/m3 - 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

17. Successes of the Big Bang Model • The Big Bang model is supported by three main pieces of observational evidence • The observed expansion of the Universe • The blackbody form and expected temperature of the cosmic background radiation • The observed abundances of the light elements • No other theory, such as the steady state model, or plasma Universe, can explain these observations so naturally

18. Fate of the Universe • We know the Universe is expanding today - will this expansion continue forever? • This depends in part on the mass of the Universe • Recall our discussion of escape velocity - the fate of a projectile fired straight up from the surface of the Moon depends upon its speed • If the speed is less than the escape velocity then gravity will eventually pull the projectile back to the Moon’s surface • If the speed is greater than the escape velocity the projectile can escape from the Moon • The gravity of the mass in the Universe acts in a similar way, slowing down the expansion

19. Fate of the Universe • If there is enough mass in the Universe then gravity will eventually stop the expansion • The Universe will slow, stop and eventually collapse on itself in a Big Crunch • If there is not enough mass the expansion may slow, but will never stop • Escape velocity from a planet is determined by its mass and radius • The escape velocity of the Universe is determined by its average density • The critical density is the limiting density that determines the future fate of the Universe

20. Critical Density • The faster the Universe is expanding, the more mass is required to turn that expansion around • The critical densitycthus depends on the Hubble constant H0 • H0 = 72 km/s/Mpc  c = 8 x 10-27 kg/m3 • We write the ratio of the actual density 0of the Universe to the critical density as m (omega-matter) • Recall that nucleosynthesis  0  3 x 10-28 kg/m3 and so baryons alone fall far short of providing critical density • The above argument supposes that gravity is the only important force in determining the fate of the Universe - an assumption which has recently been overturned

22. 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!

23. Most supernovae at high redshift are fainter than we would expect in the case of unaccelerated Hubble expansion Those observations below the curve suggest expansion is speeding up

24. Einstein’s “Greatest Blunder” • Einstein formulated his general theory of relativity in 1915, before Hubble had discovered the expansion of the Universe • In order to produce a static solution to his equations describing the Universe, Einstein introduced a term he called the cosmological constant , a repulsive term which balanced the attractive force of gravity • Once it was realised 14 years later that the Universe was expanding, the  term was no longer necessary • Einstein apparently regarded his inclusion of the  term (and his failure to predict an expanding Universe) as “my greatest blunder”

25. The Cosmological Constant • With the recent discovery of an accelerating Universe, Einstein’s cosmological constant has made a comeback • The cosmological constant  opposes gravity and makes a contribution to the density of the Universe, written  • With a cosmological constant term the fate of the Universe is no longer controlled exclusively by gravity and hence m • The fate of the Universe depends on the values of both m and 

26. A cosmological constant  can cause the Universe to expand faster and faster It can even prevent the collapse of a m > 1 Universe

27. Supernova observations are compatible with a Universe that is 30% matter and 70% cosmological constant

28. Observational constraints from Type I supernovae and CBR anisotropies are consistent with our Universe having m 0.3, 0.7 m +   1  Universe has a “flat” geometry

29. Summary • Overwhelming observational evidence in favour of the Big Bang model: • The observed expansion of the Universe • The blackbody form and expected temperature of the cosmic background radiation • The observed abundances of the light elements • The Universe is currently undergoing accelerated expansion due to a cosmological constant or dark energy