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Particle Physics and Cosmology Particle Physics and Cosmology Edward W Kolb Fermi National Accelerator Lab oratory and The University of Chicago In these lectures on the early Universe I will discuss some recent developments in particle cosmology taking particular care to highlight the role of particle physics in our understanding of cosmology I will assume that the reader is familiar with basic particle physics but not necessarily basic astronomy Before starting I would like to discuss the motivation for particle physicists to b e interested in cosmology The aim of mo dern cosmology is to understand the origin and the largescale structure of the Universe on the basis of physical law The mo dern framework for this eort is the hot bigbang mo del With knowledge of the laws of physics the fundamental forces and the fundamental particles in principle the mo del should b e able to explain the gross features of our Universe It is also p ossible to reverse engineer this standard approach by observations of the outcome we might b e able to tell something ab out the fundamental ingredients that went in Therefore we might b e astro-ph/9403007 3 Mar 94 able to discover something ab out particle physics by studying cosmology Let me also describ e my own approach to cosmology How should one approach the study of the history of the ancient Universe There are two typ es of p eople who study old things antiquarians and historians An antiquarian is interested in things that are old simply b ecause they are old They do not attempt to dierentiate b etween the relative imp ortance of ob jects from antiquity In the extreme an antiquarian would see no dierence b etween a gro cery shopping list from and the Magna Carta A historian on the other hand is interested in events and ob jects from the past b ecause they have a b earing up on the present It is the job of the historian to sort through the past to nd the ob jects and events that had an impact up on the future development of history I consider it the job of the cosmologist to b e a historian of the Universe The cosmologist should not b e interested in the early Universe b ecause it was very old or very hot or very dense Rather a cosmologist studies the early Universe b ecause he or she has the faith that events in the early Universe are resp onsible for shaping the present Universe and that it is imp ossible to understand the Universe to day without an understanding of the early Universe Therefore in these lectures I will concentrate on events in the early Universe that Edward W Kolb have the p otential to explain the present state of the Universe In a very real sense the job of cosmology is to provide a canvas up on which other elds of science including particle physics can weave their individual threads into the tap estry of our understand ing of the Universe Nowhere is the inherent unity of science b etter illustrated than in the interplay b etween cosmology the study of the largest things in the Universe and particle physics the study of the smallest things A quick lo ok at the Universe Before concentrating on the particle physics asp ects of cosmology I will start with a lo ok at the most imp ortant observational features of the Universe I will then discuss the Rob ertsonWalker metric and discuss some particle kinematics in the expanding Universe Then I will develop the dynamics of the FriedmannRob ertsonWalker frw cosmology The nal part of the intro ductory section will b e a brief review of the radiationdominated era and primordial nucleosynthesis More details can b e found in Kolb and Turner Expansion of the Universe It was Hubble who discovered a linear relationship b etween the recessional velo cities of nebulae and their distances The recessional velo city is determined via the Doppler eect If the relative velo city b etween a source and observer is v then the measured R wavelength of the light will dier from the wavelength of the emitted light obs emitted This dierence is expressed in terms of a redshift z dened as obs emitted z emitted If one interprets the observation of a redshift of light from distant galaxies as a Doppler eect then z v c Of course this is a nonrelativistic expression The sp ecial R relativistic expression relating v and z is v c z z If the R R relative distance is increasing then z is p ositive The linear relationship b etween the distance and the redshift Hubbles law can b e written in several equivalent forms cz H d L v H d R L d h z Mp c h cz Mp c L where a megaparsec Mp c is cm As to the meaning of these symb ols c is the sp eed of light unless you are an astronomer the redshift z and recessional velo city v R have already b een dened d is the luminosity distance and H is Hubbles constant L Let us p ostp one for a moment questions ab out what exactly the luminosity distance is and just think of it as the distance to the ob ject without worrying whether it is the distance when the light was emitted the distance when the light was detected etc Particle Physics and Cosmology Sixtyfour years after the discovery of Hubbles law Hubbles constant H is still not well known It is traditional to express the uncertainty in Hubbles law in terms of a dimensionless parameter h km H h h s Mp c The Hubble constant is the fundamental parameter in cosmology and it is not known to b etter than a factor of two This uncertainty traces to the oldest and most fundamental problem of astronomythe distance scale for a review see RowanRobinson The uncertainty in H will result in a proliferation of factors of h in many of the equations in subsequent sections Figure Hubbles data The solid line is a guide to the eye It is somewhat amusing to lo ok at the original data up on which Hubble based his claim shown in Figure Clearly it to ok a leap of imagination intuition and genius to see a linear relationship in the data After all some of the nearby nebulae are approaching rather than receding With mo dern hop efully more reliable metho ds for determining distances astronomers are able to extend Hubbles program to much greater distances All agree on the linear nature of the relationship but do not agree on the value of H To orient the particle physicist I have included a small table of extragalactic dis tances The distance to nearby ob jects in our lo cal group of galaxies like Andromeda can b e determined by direct means Hence the distance is indep endent of h For more distant ob jects such as the Virgo cluster of galaxies we can accurately determine the red shift or equivalently v but not the distance Using the measured z Hubbles R Dep ending up on your law will give the distance in terms of the annoying factor of h favourite value of h the distance to Virgo is somewhere b etween and Mp c Edward W Kolb object z d v L R M Andromeda Mp c km s Virgo Cluster h Mp c km s Coma Cluster h Mp c km s Hydra h Mp c km s Clearly Hubbles law as given in Equation must break down for z Even if one adopts the sp ecial relativistic Doppler formula we will see in the section on kinematics that there are imp ortant corrections for z The expansion of the Universe and Hubbles law will b e discussed further but for our rst quick view of the Universe it will suce to note that the Universe is expanding and furthermore the expansion seems to b e isotropic ab out us The cosmic background radiation The cosmic background radiation cbr provides fundamental evidence that the Uni verse b egan from a hot big bang The surface of last scattering for the cbr was the Universe at an age of ab out years The rst thing to learn ab out the cbr is its sp ectrum It is a blackb o dy to a remarkable accuracy The b est measurement of the sp ectrum of the cbr was made with the Cosmic Background Explorer cobe satellite Mather et al The measurements are summarized in Figure Note that the true error bars for the measurements are a factor of times smaller than shown in the gure Clearly the cbr is a blackb o dy with the present temp erature of the Uni verse T K and deviations from a blackb o dy shap e over the wavelength interval cm to cm less than Once the temp erature of the cbr is known the numb er density and energy den sity of the background photons are also known For a temp erature of T K eV the numb er density and energy density of the cbr is given by n cm T T g cm After the sp ectrum the next most imp ortant feature of the cbr is its isotropy Anisotropy is exp ected due to several eects For instance a dip ole moment of the cbr is exp ected as a result of the motion of our lo cal reference frame with resp ect to the cbr rest frame Motion with velo city v c through an isotropic blackb o dy radiation eld of temp erature T results in a frequencyindep endent formula for the temp erature p j j cos distribution T T The most accurate measurement of the cbr dip ole anisotropy was by cobe an amplitude of mK corresp onding to a velo city of km s in the general direction of Hydra for our lo cal group of galaxies cobe has also determined that the dip ole anisotropy has a thermal sp ectrum Additional uctuations in the cbr temp erature are also exp ected due to the presence of density inhomogeneities presumed to have triggered structure formation The search Particle Physics and Cosmology Figure The spectrum of the cosmic background radiation for anisotropies in the cbr b eyond the dip ole anisotropy has o ccupied physicists since the discovery of the cbr itself in Finally in the long search was rewarded when
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