The Inflationary Universe

John Ellis, CERN, Geneva

Why is the Universe so large and old, while having a density today close to the critical density required to close it, and appearing homogeneous and isotropic on very large scales? These puzzles would be solved if the Universe had undergone an early period of exponential inflationary ex­ pansion, perhaps driven by an effective cosmological constant appear­ ing in a field theory of particles. The Universe we see around us today would have expected the Universe to Fig. 1 — Illustration of the expansion of is very large and very old, appears have been hotter when it was more com­ Universes with densities below, equal to and homogeneous and isotropic on large pressed during earlier stages of its ex­ above the critical closure density. It is sur­ scales, and is expanding perhaps eter­ pansion. On the basis of this simple re­ prising that our Universe is so close to the nally. These are the basic facts of cos­ mark, Gamow suggested that the Uni­ closure density, despite being much older mological life. Until recently one had to verse today should contain microwave than the Planck time. accept them as given, but in the past radiation left over from the time when The Planck mass is related by the un­ few years it has become possible to ex­ the size of the Universe was less than a certainty principle to a Compton wave­ plain them as consequences of a theory thousandth of its present value, and the length called the Planck length lp of the applying particle physics ideas to the ionized plasma condensed into neutral order of 10-33 cm, which would be tra­ evolution of the very early Universe. This atoms as it expanded and cooled. versed by light in the Planck time tp of new inflationary cosmology not only ex­ Just such a cosmic microwave back­ the order of 10-43 seconds. Since Ein­ plains the large-scale uniformity of the ground radiation was observed by stein's equations only contain Newton's Universe today, but also provides a pos­ Penzias and Wilson over 20 years ago 1 ) constant and hence these Planck scales, sible origin for the small perturbations in and is generally taken as confirmation how is it that the solution to those equa­ the early Universe which have subse­ that the Universe was once more than a tions which is our Universe today is so quently evolved into galaxies and galac­ thousand times smaller that it is today. much larger than the Planck length, and tic clusters. It also predicts that over Another astrophysical observation, na­ is about 1060 times older than the 90% of the matter in the Universe re­ mely that about a quarter of the observ­ Planck time? mains to be observed : this "dark mat­ ed matter in the Universe is helium-4 2) A related puzzle concerns the present ter" may play a key role in the formation suggests that it was once a million times density of the Universe which is within of galaxies and in their stability today. smaller still. It is difficult to explain this about an order of magnitude of the criti­ In this review I first formulate the and the abundances of other light ele­ cal density required to close it, despite puzzles which inflationary cosmology ments except as the result of nuclear fu­ its enormous expansion since the Big resolves, then outline the basic particle sion in the very early Universe when its Bang. For the density to be so close to physics mechanism for inflation and temperature was 109 to 1010 K — pri­ critical today it must have been fine- describe some of the observational con­ mordial nucleosynthesis. Thus it seems tuned to within about 10-60 of the criti­ sequences. Finally I mention some of the that the present expansion of the Uni­ cal density back when the Universe's unresolved problems in inflationary cos­ verse can be extrapolated backwards to age was of the order of the Planck time. mology. an epoch when the size of the Universe If not so finely tuned, the Universe The present day expansion of the Uni­ was less than 10-9 of its present value. If would either have been overdense, verse was discovered by Hubble in the one seeks to go further back, there are halted its expansion some time ago and 1920's when he observed the redshifts theorems based on General Relativity in­ started contracting under its own of distant galaxies. This observational dicating that in the past history of every weight, or it would be underdense and discovery meshed very well with Ein­ part of the Universe there must have be expanding much faster than it is to­ stein's realization a few years earlier that been a singular point at which the day, as seen in Fig. 1. Another puzzle is the equations of his General Theory of known laws of physics broke down — why has the Universe grown isotropical­ Relativity did not have a static solution the Big Bang. ly and homogeneously over distances which was stable. Einstein had tried to There are some baffling features of much larger than the particle horizon, evade this conclusion by introducing a this standard Big Bang theory of the the longest distance which a light wave new term into his equations called the Universe which we should like to under­ could have covered since the start of the cosmological constant — something he stand. The only fundamental parameter conventional Big Bang Universe? This subsequently regarded as his greatest appearing in Einstein's equations which dilemma is posed most acutely by the mistake. Hubble's redshift observations govern the expansion of the Universe is microwave background radiation, which suggested that one should instead focus Newton's constant GN, familiar from the is very isotropic today, implying that its on the expanding models of the Uni­ classical gravitational attraction bet­ intensity at the epoch of its production verse known to be solutions of Einstein's ween two massive objects : GN m1 m2 / must have varied by less than one part in equations without a cosmological cons­ r2. Newton's constant has the dimen­ 104 over distances a hundred times lon­ tant. Subsequently two other major sion of (mass)-2, and the mass value is ger than the horizon scale at that epoch. pieces of evidence have confirmed the often called the Planck mass Mp. It cor­ There are other cosmological puzzles, expanding Universe as the standard cos­ responds by special relativity to an ener­ such as the unexpectedly low density of mological model. Like any other gas, one gy of about 1.2 x 1019GeV. such unwanted elementary particles as 6 magnetic monopoles. I will not discuss ty. Thus not only are the great size and What might then have caused the ex­ them in detail here, since they are almost age of the Universe reasonable, but it is pansion of the Universe to be controlled exclusively a headache for particle phy­ also "natural" that the density of the for a while by a constant vacuum energy, sicists, but historically they are impor­ Universe should still be close to critical, analogous to the cosmological constant tant in that they motivated the particle as observed. We can also understand mentioned earlier? The most natural physicists' preoccupation with cosmo­ the great homogeneity of the Universe source to consider is a scalar field locked logical problems and this in turn led to on scales much larger than the apparent in a coherent configuration different the concept of the inflationary Universe. early particle horizon. Before the hypo­ from its minimum energy state. Scalar If we go back to the very early Uni­ thesized inflationary epoch, the entire fields are a general feature of modern verse before primordial nucleosynthesis, observable Universe would have been gauge theories of the fundamental in­ the temperature and typical kinetic ener­ infinitesimally smaller than in the naive teractions. They are used to provide the gies were so high that any description of Big Bang picture, as seen in Fig. 2, so spontaneous symmetry breaking need­ matter should be in terms of the elemen­ that a light wave could easily have cross­ ed to accommodate non-zero masses tary particles and their degrees of free­ ed it from one side to the other and for the W and Z° gauge bosons as well dom. Grand unified theories of elemen­ causality would permit coordination as for quarks and leptons. One expects tary particle interactions have already between opposite sides. The Universe to find associated with them physical demonstrated their relevance by provi­ would indeed be essentially homoge­ scalar particles called Higgs bosons, ding a qualitative mechanism for crea­ neous and isotropic during the exponen­ although none has yet been discovered. ting a small matter — antimatter asym­ tial inflation driven by a constant va­ Today when the Universe is cold, Higgs metry in the very early Universe, consis­ cuum energy, and it should be no sur­ fields sit in their lowest energy configu­ tent with the small fraction of baryons prise that it has remained so today. Final­ rations, breaking the symmetry of the relative to photons in the Universe today, ly, note that if there were any obnoxious original field equations as illustrated in and the absence of large amounts of elementary particles such as magnetic Fig. 3 where the lowest energy configu­ antimatter. monopoles present in the Universe be­ ration is away from the symmetric zero In Einstein's equations, the expansion fore inflation or during its early stages, point. Earlier in the history of the Uni­ of the Universe is driven by its energy the subsequent exponential expansion verse when it was hot, thermal fluctua­ density for which elementary particles would have made their separations grow tions would have pushed the Higgs Field offer three alternative dominant forms : so large that there would remain at most up, out of its lowest energy configura­ relativistic particles, non-relativistic par­ one in the entire observable Universe. tion to the symmetric zero point. This is ticles, or a constant vacuum energy ana­ logous to the cosmological constant in­ troduced by Einstein. Nowadays, matter in the Universe is predominantly non- The University of Tromsø invites applications relativistic although relativistic particles for a tenured faculty position in atmospheric are believed to have dominated back and space physics at the full professor level when it was an ionized plasma. In both The Professor will be appointed to teach physics at the undergra­ the relativistic and non-relativistic duate and graduate level and to conduct original research in solar- cases, the energy density falls as the terrestrial physics. Applications are particularly welcome from can­ temperature falls and the Universe ex­ didates with a strong interest in theoretical and/or experimental pands. This means that the rate of ex­ research connected with the European Incoherent Scatter Facility pansion steadily slows down, even (EISCAT), the Partial Reflection Experiment (PRE) and the Iono­ though it may still expand to an infinite spheric Modification Experiment (HEATING). extent if the energy density is less than Salary is NOK 2 3 3 .8 2 0 p.a. gross, of which NOK 4.010 is paid in or equal to the critical density required to pension contribution. The Professor is to accept without compen­ close the Universe. The situation would sation any changes in scientific duties, pension or retiring age made have been very different if at some early by law or by the King in agreement with Parliament. epoch the energy density was domina­ Applicants should submit 5 copies of their list of publications and ted by a constant vacuum energy. In this scientific works (published or unpublished), divided into five case the rate of expansion (1/R)(dR/dt) groups, each in numbered order, to the University of Tromsø no later than 3 months after the application deadline. If warning is would have been constant, and hence given no later than one month after the application deadline, the size R of the Universe would have ex­ manuscripts in preparation may also be submitted, but no later than panded exponentially. 3 months after the application deadline. Applicants are otherwise Such an exponential expansion is the referred to the current rules for the procedure to be followed in the core idea of inflationary cosmology. Pro­ appointment of full professors. vided the inflationary epoch lasted long Further information about the vacant position can be obtained from enough, the Universe would have ex­ Professors E. Leer and J. Trulsen, panded far beyond its "natural" Planck Department of Physics, University of Tromsø , size and even if the Universe is at some P. O. Box 953, N - 9001 Tromsø, Norway, Tel.: (83) 86 06. date to halt and reverse its post-inflatio­ In accordance with university policy, applications from women are nary expansion, only a slight excess in especially encouraged. the duration of the exponential expan­ Applications including a complete curriculum vitae, relevant tran­ sion would allow it to expand far beyond scripts, and a copy of the publication list, should be addressed to the size we see today. A Universe in this the King and submitted before 20 November 1985 to : state would be essentially indistinguish­ The University of Tromsø able from one with the critical energy P. O. Box 635, N - 9001 Tromsø, Norway. density required to expand out to infini- 7 holes in it! Early inflationary cosmolo- gists soon found that a first-order Higgs phase transition would never become complete, so a second order transition has since been favoured. In this case in­ flation takes place after the phase transi­ tion has already started, but while the Higgs field is still small and slowly growing. During this period the Higgs field can perhaps be viewed almost as a classical ball rolling down a hill, as seen in Fig. 3. To get a sufficiently long inflationary epoch the slope of the hill must be very small, while for matter creation to be Fig. 3 — Sketch of the Higgs field energy Fig. 2 — Different parts of the Universe can possible at the end of inflation, the hill be homogeneous if their distance of separa­ which may have driven inflation. The Higgs tion was once smaller than the particle hori­ must be quite high so that the Higgs field in our Universe may be regarded as a zon, shown by the full straight lines. In con­ "ball" reaches the bottom of the "hill" classical ''ball'' rolling down the "hill" from ventional cosmology a distant galaxy would with sufficient energy. To reconcile the symmetric ''liquid'' phase toward the have been outside the apparent particle hori­ these two requirements we need a hill asymmetric ''solid'' phase where matter zon during most of its history (dotted line). In with a very wide base — in other words would have been created. While the field inflationary cosmology the location of the the Higgs field order parameter must be energy is close to V0 the Universe expands galaxy would have been much closer at early as large as possible, say the Planck exponentially. times, well within the particle horizon. In scale. this case, causality enables us to under­ stand the large-scale homogeneity and iso­ A bonus feature of the inflationary tionally indistinguishable from the criti­ tropy of the Universe. concept is that for the first time one can cal density in Fig. 1. Since the "known" calculate large scale perturbations in the baryonic matter cannot have a density present-day Universe on the basis of of much more than a few percent of the analogous to the melting of an ordered microphysics. A thermal or quantum critical density, this means there must crystal to become a disordered liquid. fluctuation in the very early Universe will be a lot of non-baryonic dark matter in Under the right conditions, the Higgs have inflated to the scale of a galaxy or a the Universe. Supersymmetric theories "liquid" could have become supercool­ galactic cluster today. All inflationary contain several possible candidates, ed as the Universe expanded, remaining models give spectra of perturbations notably the photino, the neutral spin 1/2 in the disordered symmetric phase which are almost independent of the supersymmetric partner of the photon, although the ordered "solid" phase was present large astrophysical scale (as and the gravitino, the spin 3/2 super- energetically favoured. previously requested by cosmologists), symmetric partner of the graviton. If the Precisely because the Higgs field was although early inflationary models yield­ dark matter is made of photinos, it may stuck in an energetically disfavoured ed perturbations which were too large, a be possible to detect them directly as "liquid" phase, its configuration would defect traceable to the large slopes of they pass through sensitive terrestrial have had a positive vacuum energy (V0 their hills. Creating a sufficiently flat hill detectors, or indirectly as some of them in Fig. 3), and this positive vacuum requires a degree of fine-tuning of the collide and annihilate in the galactic halo. energy could have driven inflation. At parameters associated with the Higgs Supersymmetric inflationary cosmology some point, the Higgs "liquid" would field which seemed unnatural from the may prove an experimental and observa­ finally have completed its transition to point of view of conventional particle tional bonanza. the lower energy "solid" phase, and all physics. However, this fine-tuning could Problems remain in inflationary cos­ the latent vacuum energy would have be performed naturally in a supersym­ mology, however. We still cannot derive been released to create conventional metric particle theory, without fear of the required flatness of the hill from fun­ particles. In order to preserve the pre­ higher order (radiative) corrections stee­ damental principles; matter creation vious success of particle physics in ex­ pening up the shallow slope that is requi­ after inflation is not easy and one must plaining primordial matter creation, this red. be careful to keep the abundance of un­ should have taken place after the infla­ There are many "existence" proofs for stable supersymmetric particles below tionary epoch, so that the precious mat­ supersymmetric inflationary models. observational limits. Nor is it easy to ter was not subsequently diluted by en­ Most of them are based on supergravity, dispose of residual unwanted vacuum tropy created when the Higgs vacuum which is the appropriate framework for energy left over after inflation. Never­ energy converted into particles. incorporating supersymmetry into a theless, inflation is such an appealing This is the basic inflationary scenario theory containing the Planck scale asso­ and powerful link between particle phy­ but to make it work in practice is not ciated with gravity. These models are sics and cosmology that it is being in­ easy. One must keep the Higgs field not sufficiently constrained for the ma­ creasingly accepted by workers in the supercooled long enough for the Uni­ gnitude of the galactic perturbations to field. verse to expand to something like its pre­ be determined. However, models with sent size, and one must provide a sufficiently small perturbations inflate mechanism for the "liquid-to-solid" for much longer than the minimum time REFERENCES phase transition to take place eventually. needed to expand the Universe to its pre­ 1. Lequeux J., Europhysics News 10 (1979) Moreover, this transition must go to sent size. This means that the Universe 1/ 2. completion, since we do not live in a will expand much further in the future, 2. Andrillat H., Europhysics News 12 (1981) "Swiss Cheese" Universe with liquid and its present density must be observa- 8/9. 8