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Chapter 6 Big Bang Cosmology a;ç"'1fi}t-ís{:\{ f:¡¡j if.ifli*åJi.i {:lt{}t'¿'it-} t''t"t"l"7l{:'i ¡"¡'¿yj CHAPTER 6 4,ZzE*9ï.a{:c?,89 BIG BANG COSMOLOGY - QUESTIoN s.11 THE EVOTVING UNIVERSE Anumberofimportanteventsinthehistoryofcosmologyhavebeenmentionedin starling with the irri, compile a chronological listing of these events, puUfi"*ion"r.,upt"r. of Einìtein's theory of general relativity in 1916' #""8 ãsæäræs#acsäåæäE In Chapter 5 we saw how general relativity can be used to construct models of the QUESTION s.12 Universe. These models describe how the scale factor varies in a Universe that is models and List the assumptions that underpin the Friedmann-Robertson-walker filled with a smooth distribution of matter and radiation, but say very little about the the Friedmann equation. properties and behaviour ofthese components. So, for instance, they do not account for the consequences of microscopic processes such as the interactions QUESTION 5.13 between the parlicles that make up the matter within the Universe. Describesomeofthepossibleconsequencesofpositivecurvatureinathree- However, such interactions play an impofiant role in cosmology. One example dimensional space' in the context of the FRW models' that we shall see later in this chapter is that cosmological theories can offer an explanation for the observation that most of the stars in the Universe have a QUESTIoN 5.14 composition that is approximately 75o/ohyûogen and 25Yohelium (by mass). A that the behaviour described fundamental aspect of the process that forms helium is that it involves reactions The detailed argument given in Section 5.4.1 showed in a FRW model' between nuclei and parlicles at an early stage in the history of the Universe. Thus by Hubble's law is an e-xpected consequence of expansion was only approximately physical processes on small scales must be taken into consideration in order to However, in Section s.+.i itwas stated that this argument ofthe expansion' Carefully develop an understanding of the evolution of the Universe. This chapter starts by true because it ignored the acceleration or deceleration the key step at which acceleration examining the conditions under which parlicles interacted in the early Universe reread the argument in section 5.4.1 and identify (Section 6.2).The main focus, however, is to follow a chronological sequence is ignored. from very early times in the history of the Universe (Section 6.3) through the formation of the first nuclei (Section 6.4) and the first neutral atoms (Section 6.5) QUËSTION s.1s to the stage at which gravitational clustering gives rise to the large-scale structure parameters mentioned List the values that have been assigned to all the observational that we observe in the present-day Universe (Section 6.6). inSection5.4.Whereaquantityisexpressedinmorethanoneunitsystem,confirm At first sight, it might seem impossible to use the models in Chapter 5 to make any the equivalence of all the given values' predictions about the small-scale behaviour of matter. Cosmological models describe how the scale factor varies with time, but at the present time any change in the scale factor ceftainly does not have any effect on, for instance, the atoms that make up your body. However one of the major assumptions made in Chapter 5 was that the matter in the Universe is smoothly distributed. This assumption of a uniform distribution of matter is a key to linking the large-scale dynamical behaviour of the Universe to small-scale effects. To see why this is so, consider a volume of the Universe that, at some particular time, is bounded by an imaginary cube, as shown in Figure 6.1. Let us further suppose that we want to follow the evolution of the matter within this cube at all times using some particular Friedmann-Robertson-Walker model with scale factor R(r). To do this, the edges of the cube must follow the expansion (or contraction) of the model universe. I Each edge of the cube has an associated length /. How must the length of each edge change with time if the cube is to follow the expansion or contraction of the model universe? I The length of each edge of the cube must be proportional to the scale factor, i.e.l æ R(t). 6 BIC BANE COSMOLOCY * THE EVOLVING UNIVËRsE ,AN INTRÕDUETION TO 6ALAXIES AND EOSMOLOGY is proportional n(t) x R(l) x R(r) volume /:) of the cube at any time ¡ 1o 6.2 The thermal history at the Universe Thus the 1: Although by the changó in volumé shown in Figure 6'l' time ll : (Ã(l))3.This is iffustíaie¿ A key physical parameter in particle interactions is temperature. It may seem to a volume of any shape that we have chosen to discuss a cubic volume here' a volume make no sense to talk of the 'temperature' of the Universe. The temperature of qái contraction) of such a model universe will have follows the expansion matter seems to range from a few degrees above absolute zero within giant volume is called a co-moving volume' i æ (R(t))3. Such a molecular clouds, up to temperatures of over 107 K that are found in extreme l*-/(rr)-l BecausethevolumeZofaco-movingregion,suchasthecube,changesasthe astrophysical environments. However, we will see shorlly that there is a cosmic is constant, the density of matter the malter within the Universe, but scale factor changes, but the mass ø within it temperature; it does not refer to temperature of p^, also varies with scale within the co-movirrgìotu*., which we denote by to the radiation that pervades the Universe. This radiation, which is observable time tz (CMB), plays impofiant factor. In fact, today as the cosmic microwave background an extremely role in modern cosmology. V/e shall discuss several aspects of the CMB in this, and M1* (6.1) in the following chapter, but in this section we shall consider how the existence of P^=T t*1ry this background radiation in an expanding Universe allows us to determine how j temperature has changed over cosmic history. The starting point for this discussion l physical parameter in determining how Now, the density of matter is an imporlant is to consider the cosmic microwave background in a liule more detail. scale' For example' the interactions between particles progress on a microscopic with one another increases as utwhich molecules in u ,ample of gas collide 6.2"1 The tennp€rature of the background radÊatÊor¡ ,it" is related to gas is increaseà. Thui, the large-scale behaviour Q)-1 the density ofthe In Section 5.2.2 you saw that the most significant contribution to the radiation small-scale effects. content of the Universe is the cosmic microwave background radiation. The 6.1 An imaginarY cubic Figure spectral flux density of the CMB peaks at a wavelength of about I mm - this is (with sides of length I that ThisstillmaynotappeartobeagleathelpinunderstandingtherealUniverseas at uolu-. since we know that the matter in the universe illustrated in the spectrum of the background radiation that is shown in Figure 6.2. of a to u modJ, evolves with the exPansion we saw in Chapter 4 "pp"r"¿ "o.mól,ogicaldoes ãot have a uniform density. Specifically, The form of this spectrum is highly significant: it is, to a very good approximation, model universe such that the mass the present time of matter is homogeneous only when we c_onsider scales a black-body spectrum implying it can be associated with a particular temperature. within the volume is constant' AnY that the distribution - Mpc: if we look at the Universe on smaller scales' we see volume that behaves in this waY, Ërrut",. than about 200 the average density of the matter in the universe whatever its shaPe, is called a íarge density variations. ihus 7 lri co-moving volume. wouldseemtobeaquantityoflimitedpracticaluse.However,weshallseelater past the matter in the that there is good evidence'that at timei in the distant it is at present even on universe wai much more smoothly distributed than - does telate to the small- x Ir small scales. At such times, the average density 6 I relatively ! 5.0 Irl scale behaviour of matter. p rl d I that is described by Equation 6'1 The relationship between density and scale factor s 4.0 in Chapter 5' The majority b ,il holds true for any of the cosmoiogical models described gtú ofthesemodelsarecharacterizedbyascalefactorR:0attime/:0'Aswas * notedinSection5.3'5theearlyexpansionphaseofanysuchmodelisreferredto strongly favours a model of the Ë as the big bang. cwreÀt"orfnologi"ul evidence Universethatwentthroughabig-bangphase-andfortheremainderofthis consequence that .fruf,., we shall only coÃider b1g bang models. An immediate bang model, early stages in the can be noted from Equation 6.1, i-s thaiin a big historyoftheuniverse(when,R(l)wasverysmall)arecharacterizedbyhigh speaking, the_mathematical densities. you may also irave noticed that, sìrictly relationshipp^æ' 'lR3impliesaninfinitedensitywhenR:0.Weshallreturnto Figure 6.2 The spectrum of the cosmic microwave background. (Note that this spectrum later' consider the'signifrcance of such infinite quantities shows the spectral flux density F¿.) I Finally,weshouldmakeabriefnoteaboutterminology:muchofthediscussionof i the Universe' A convention that this chapter 1".r.r, to ti*e, in the history of Ç."ific by I (so' The characteristic temperature T indicated by any given black-body spectrum is iÄe chapter is that ,h: ug" tf th. Uniu.rse is àenoted we adopt throughout (tr'¡) is a Universe was 1 second old)' The related to the wavelength Âp,ut at which the spectral flux density for instance, / : I s denotes ihe time at whicñ the to as 16' So, /0 represents maximum. According to Wien's displacement law, time now, at which we observe the Universe, is referred the current value of the age of the Universe' 2.90 x l0-3 (ip.*/m) = glK) (6.2) 257 256 EIC AN ¡N]"RODUCTION TO CALAXILS AND COSMÕLÕCY 6 BANú CÛsMOLûçY - THE F,VÕLVINC UNIV¡:¡i5E Calculate the characteristic temperature of the cosmic microwave background r If a microwave background photon currently has L : I mm, what wavelength radiation.
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