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Astrophysics and Cosmology ASTROPHYSICS AND COSMOLOGY J. GarcÂõa-Bellido Theoretical Physics Group, Blackett Laboratory, Imperial College of Science, Technology and Medicine, Prince Consort Road, London SW7 2BZ, U.K. Abstract These notes are intended as an introductory course for experimental particle physicists interested in the recent developments in astrophysics and cosmology. I will describe the standard Big Bang theory of the evolution of the universe, with its successes and shortcomings, which will lead to inflationary cosmology as the paradigm for the origin of the global structure of the universe as well as the origin of the spectrum of density perturbations responsible for structure in our local patch. I will present a review of the very rich phenomenology that we have in cosmology today, as well as evidence for the observational revolution that this field is going through, which will provide us, in the next few years, with an accurate determination of the parameters of our standard cosmological model. 1. GENERAL INTRODUCTION Cosmology (from the Greek: kosmos, universe, world, order, and logos, word, theory) is probably the most ancient body of knowledge, dating from as far back as the predictions of seasons by early civiliza- tions. Yet, until recently, we could only answer to some of its more basic questions with an order of mag- nitude estimate. This poor state of affairs has dramatically changed in the last few years, thanks to (what else?) raw data, coming from precise measurements of a wide range of cosmological parameters. Further- more, we are entering a precision era in cosmology, and soon most of our observables will be measured with a few percent accuracy. We are truly living in the Golden Age of Cosmology. It is a very exciting time and I will try to communicate this enthusiasm to you. Important results are coming out almost every month from a large set of experiments, which pro- vide crucial information about the universe origin and evolution; so rapidly that these notes will proba- bly be outdated before they are in print as a CERN report. In fact, some of the results I mentioned dur- ing the Summer School have already been improved, specially in the area of the microwave background anisotropies. Nevertheless, most of the new data can be interpreted within a coherent framework known as the standard cosmological model, based on the Big Bang theory of the universe and the inflationary paradigm, which is with us for two decades. I will try to make such a theoretical model accesible to young experimental particle physicists with little or no previous knowledge about general relativity and curved space-time, but with some knowledge of quantum field theory and the standard model of particle physics. 2. INTRODUCTION TO BIG BANG COSMOLOGY Our present understanding of the universe is based upon the successful hot Big Bang theory, which ex- plains its evolution from the first fraction of a second to our present age, around 13 billion years later. This theory rests upon four strong pillars, a theoretical framework based on general relativity, as put for- ward by Albert Einstein [1] and Alexander A. Friedmann [2] in the 1920s, and three robust observational facts: First, the expansion of the universe, discovered by Edwin P. Hubble [3] in the 1930s, as a reces- sion of galaxies at a speed proportional to their distance from us. Second, the relative abundance of light elements, explained by George Gamow [4] in the 1940s, mainly that of helium, deuterium and lithium, which were cooked from the nuclear reactions that took place at around a second to a few minutes after the Big Bang, when the universe was a few times hotter than the core of the sun. Third, the cosmic mi- crowave background (CMB), the afterglow of the Big Bang, discovered in 1965 by Arno A. Penzias and 109 Robert W. Wilson [5] as a very isotropic blackbody radiation at a temperature of about 3 degrees Kelvin, emitted when the universe was cold enough to form neutral atoms, and photons decoupled from matter, approximately 500,000 years after the Big Bang. Today, these observations are confirmed to within a few percent accuracy, and have helped establish the hot Big Bang as the preferred model of the universe. 2.1 Friedmann±Robertson±Walker universes Where are we in the universe? During our lectures, of course, we were in Castaˇ Papiernicka,ˇ in ‘the heart of Europe’, on planet Earth, rotating (8 light-minutes away) around the Sun, an ordinary star 8.5 kpc1 from the center of our galaxy, the Milky Way, which is part of the local group, within the Virgo cluster of ¡£¢¤¢ galaxies (of size a few Mpc), itself part of a supercluster (of size Mpc), within the visible universe ¡£¢¤¢£¢ ( ¦¥¨§ © Mpc), most probably a tiny homogeneous patch of the infinite global structure of space- time, much beyond our observable universe. Cosmology studies the universe as we see it. Due to our inherent inability to experiment with it, its origin and evolution has always been prone to wild speculation. However, cosmology was born as a science with the advent of general relativity and the realization that the geometry of space-time, and thus the general attraction of matter, is determined by the energy content of the universe [6], ¡ "!# %$&')( +* (1) These non-linear equations are simply too difficult to solve without some insight coming from the sym- metries of the problem at hand: the universe itself. At the time (1917-1922) the known (observed) uni- verse extended a few hundreds of parsecs away, to the galaxies in the local group, Andromeda and the Large and Small Magellanic Clouds: The universe looked extremely anisotropic. Nevertheless, both Ein- stein and Friedmann speculated that the most ‘reasonable’ symmetry for the universe at large should be homogeneity at all points, and thus isotropy. It was not until the detection, a few decades later, of the microwave background by Penzias and Wilson that this important assumption was finally put onto firm experimental ground. So, what is the most general metric satisfying homogeneity and isotropy at large scales? The Friedmann-Robertson-W alker (FRW) metric, written here in terms of the invariant geodesic ¢£3 ¡£3 £314 2 ,-/. ,10 ,10 2 distance in four dimensions, , see Ref. [6], 87 ' ')?@ A . ,1< 3 . .¤9 .£9 . 8= ,5- ,16 6;: < ,> >B,5C : ¡ (2) < . 7 9 characterized by just two quantities, a scale factor 6;: , which determines the physical size of the universe, and a constant = , which characterizes the spatial curvature of the universe, =H ¡ IKJ#LNM = D¨EF * =H G ¢ OQPSRUT 7 (3) =H' ¡ VWPXIKYZL#[ 9 6;: . Spatially open, flat and closed universes have different geometries. Light geodesics on these universes behave differently, and thus could in principle be distinguished observationally, as we shall discuss later. Apart from the three-dimensional spatial curvature, we can also compute a four-dimensional space-time curvature, 7 7 = ^ _ D¨\]F ' * ' . G G G 7 7 7 (4) . Depending on the dynamics (and thus on the matter/energy content) of the universe, we will have different possible outcomes of its evolution. The universe may expand for ever, recollapse in the future or approach an asymptotic state in between. 1 One parallax second (1 pc), parsec for short, corresponds to a distance of about 3.26 light-years or `+acbedfhg cm. 2 I am using iBjkb everywhere, unless specified. 110 2.1.1 The expansion of the universe In 1929, Edwin P. Hubble observed a redshift in the spectra of distant galaxies, which indicated that they were receding from us at a velocity proportional to their distance to us [3]. This was correctly interpreted as mainly due to the expansion of the universe, that is, to the fact that the scale factor today is larger than when the photons were emitted by the observed galaxies. For simplicity, consider the metric of a 7 9 . , 6 6 :S,Ql0 spatially flat universe, ,- (the generalization of the following argument to curved 7 9 0 l space is straightforward). The scale factor 6 : gives physical size to the spatial coordinates , and the expansion is nothing but a change of scale (of spatial units) with time. Except for peculiar velocities, i.e. motion due to the local attraction of matter, galaxies do not move in coordinate space, it is the space-time fabric which is stretching between galaxies. Due to this continuous stretching, the observed wavelength of photons coming from distant objects is greater than when they were emitted by a factor precisely equal to the ratio of scale factors, mnpo;q 7t '8u ¡ 3 mres 7 (5) t where 7 is the present value of the scale factor. Since the universe today is larger than in the past, the observed wavelengths will be shifted towards the red, or redshifted, by an amount characterized by u , the redshift parameter. In the context of a FRW metric, the universe expansion is characterized by a quantity known as the t 7 7 _ 9 9 9 6 : 6;:xw 6 : v Hubble rate of expansion, v , whose value today is denoted by . As I shall deduce later, it is possible to compute the relation between the physical distance ,y and the present rate of expansion, in terms of the redshift parameter,3 ¡ E t t u' {z u '8| u * ¡ 9 9 . v ,y : : (6) u~} At small distances from us, i.e. at ¡ , we can safely keep only the linear term, and thus the recession u t v ,y velocity becomes proportional to the distance from us, , the proportionality constant t being the Hubble rate, v . This expression constitutes the so-called Hubble law, and is spectacularly confirmed by a huge range of data, up to distances of hundreds of megaparsecs.
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