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Alan Guth, Inflationary Cosmology: Is Our Universe Part of a Multiverse, AAA Lecture, November 6, 2009, p. 1.

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Theory that the universe as we know it b egan 13-15 billion years ago. (Latest estimate: 13.7 Б 0.2 billion years!) Initial state was a hot, dense, uniform soup of particles that filled space uniformly, and was expanding rapidly.
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How the early universe expanded and co oled How the light chemical elements formed How the matter congealed to form stars, galaxies, and clusters of galaxies
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Inflation is a mo dification of the standard big bang theory, providing a very brief "prequel".
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Inflation can explain the bang of the big bang (i.e, the outward propulsion), in terms of

What caused the expansion? (The big bang theory describ es only the aftermath of the bang.) Where did the matter come from? (The theory assumes that all matter existed from the very b eginning.)
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Gravitational Repulsion! The combination of general relativity and mo dern particle theories predicts that, at very high energies, there exists forms of matter that create a gravitational repulsion!
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Alan Guth, Inflationary Cosmology: Is Our Universe Part of a Multiverse, AAA Lecture, November 6, 2009, p. 2.

Technical Note: According to general pro duced by a material with a n predicts that at high energies there -- in particular, states for which energy of a scalar field.

relativity, a repulsive gravitational field is egative pressure. Mo dern particle physics exist states of matter with negative pressure the energy is dominated by the potential

Inflation prop oses that a patch of repulsive gravity material existed in the early universe -- for inflation at the grand unified theory scale ( 1016 GeV), the patch needs to b e only as large as 10-28 cm. (Since any such patch is enlarged fantastically by inflation, the initial density or probability of such patches can b e very low.) The gravitational repulsion created by this material was the driving force b ehind the big bang. The repulsion drove it into exp onential expansion, doubling in size every 10-37 second or so!

The patch expanded exp onentially by a factor of at least 1028 (65 time constants), but it could have expanded much more. Inflation lasted mayb e 10-35 second, and at the end, the region destined to b ecome the presently observed universe was ab out the size of a marble. The repulsive-gravity material is unstable, so it decayed like a radioactive substance, ending inflation. The decay released energy which pro duced ordinary particles, forming a hot, dense "primordial soup." Standard cosmology b egan. Caveat: The decay happ ens in most places, but not everywhere -- we will come back to this SUBTLE p oint.

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The density of the repulsive gravity material was not lowered as it expanded! Although more and more mass/energy app eared as the repulsivegravity material expanded, total energy was conserved!
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Can explain the observed uni-

formity of the universe. Cosmic background radiation is uniform to 1 pt in 100,000. To achieve this uniformity without inflation, information and energy must travel 100 times the sp eed of light. SOLUTION: Uniformity is established in a tiny region b efore inflation, and then inflation magnifies this region to encompass the entire observed universe and more.

The energy of a gravitational field is negative! The p ositive energy of the repulsive gravity material was comp ensated by the negative energy of gravity. The TOTAL ENERGY of the universe may very well b e zero.
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Alan Guth, Inflationary Cosmology: Is Our Universe Part of a Multiverse, AAA Lecture, November 6, 2009, p. 3.

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According to general relativity, the flatness of the universe is related to its mass density: (Omeg a) = actual mass density , critical mass density

Why was the early universe so FLAT? What is meant by "flat"? Flat do es not mean 2-dimensional. Flat means Euclidean, as opp osed to the non-Euclidean curved spaces that are also allowed by Einstein's general relativity. 3-dimensional curved spaces are hard to visualize, but they are analogous to the 2-dimensional curved surfaces shown on the right.

where the "critical density" dep ends on the expansion rate. = 1 is flat, greater than 1 is closed, less than 1 is op en.

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A universe at the critical density is like a p encil balancing on its tip:

Since inflation makes gravity b ecome repulsive, the evolution of changes, to o. is driven towards one, extremely rapidly. It could b egin at almost any value. Since the mechanism by which inflation explains the flatness of the early universe almost always oversho ots, it predicts that even to day the universe should have a critical density.
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Until 10 years ago, observation p ointed to 0.2-0.3. Latest observation by WMAP satellite (with 2DF and SDSS galaxy surveys, and sup ernova Ia observations): If in the early universe was slightly b elow 1, it would rapidly fall to zero -- and no galaxies would form. If was slightly greater than 1, it would rapidly rise to infinity, the universe would recollapse, and no galaxies would form. To b e as close to critical density as we measure to day, at one second after the big bang, must have b een equal to one to 15 decimal places!
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= 1.0052 Б 0.0064 New ingredient: Dark Energy. In 1998 it was discovered that the expansion of the universe has b een accelerating for ab out the last 5 billion years. The "Dark Energy" is the energy causing this to happ en.
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Alan Guth, Inflationary Cosmology: Is Our Universe Part of a Multiverse, AAA Lecture, November 6, 2009, p. 4.

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Can explain how the early universe acquired very weak ripples in its mass density -- which later grew in intensity to form large scale structure (galaxies, clusters of galaxies, etc.)
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In inflationary mo dels, these ripples arise from quantum fluctuations at the end of inflation. The quantum fluctuation mo del makes a generic prediction for the shap e of the sp ectrum of the fluctuations. These predictions compare b eautifully with the measurements of the cosmic background radiation.

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Graph by Max Tegmark, for A. Guth & D. Kaiser, Science 307, 884 (Feb 11, 2005), up dated to include WMAP 3-year data.
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Graph by Max Tegmark, for A. Guth & D. Kaiser, Science 307, 884 (Feb 11, 2005), up dated to include WMAP 3-year data.
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Alan Guth, Inflationary Cosmology: Is Our Universe Part of a Multiverse, AAA Lecture, November 6, 2009, p. 5.

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In 1998, astronomers discovered that the universe has b een accelerating for ab out the last 5 billion years (out of its 14 billion year history). IMPLICATION: Inflation is happ ening to day, so the universe to day is filled with a repulsive gravity material. (Within general relativity, this requires negative pressure.) The repulsive gravity material, which apparently fills space, is called the "Dark Energy." WHAT IS THE DARK ENERGY? Who knows? SIMPLEST EXPLANATION: Dark energy = vacuum energy, also known as a cosmological constant.

The quantum vacuum is far from empty, so a nonzero energy density is no problem. In quantum field theory, the energy density of quantum fluctuations diverges. A plausible cutoff for the fluctuations is the Planck scale, Ep 1019 GeV, the scale of quantum gravity. Using this cutoff, the estimated vacuum energy density is to o large
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Alan Guth, Inflationary Cosmology: Is Our Universe Part of a Multiverse, AAA Lecture, November 6, 2009, p. 6.

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The repulsive gravity material that drives the inflation is metastable. In any one lo cation, the probability of remaining in an inflating state decreases with time -- usually exp onentially. BUT, the universe in the meantime is expanding exp onentially. In any successful version of inflation, the exp onential expansion is faster than the exp onential decay! Therefore, The volume that is inflating increases with time, even though the inflating material is decaying! The inflation b ecomes eternal -- once it starts, it never stops. The inflating region never disapp ears, but pieces of it undergo decay and pro duce дг и йв к жз зИ ad infinitum. Instead of one universe, inflation pro duces an infinite numb er --
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Since the inception of string theory, theorists have sought to find the vacuum of string theory -- with no success. Within the past 10 years or so, most string theorists have come to the b elief that there is no unique vacuum. Instead, there are mayb e 10500 long-lived metastable states, any of which could serve as a substrate for a p o cket universe. This is the landscap e! Eternal inflation can presumably pro duce an infinite numb er of p o cket universes of every typ e, p opulating the landscap e. Although string theory would govern everywhere, each typ e of vacuum would have its own low-energy physics -- its own "standard mo del," its own "constants" of nature, etc.
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As early as 1987, Steve Weinb erg p ointed out that the cosmological constant might b e explained in the same way. Mayb e the cosmological constant IS huge in most p o cket universes. Nonetheless, we must rememb er that a cosmological constant causes the expansion of the universe to accelerate. If negative, the universe quickly collapses. If large and p ositive, the universe flies apart b efore galaxies can form. It is plausible, therefore, that life can arise only if the cosmological constant is very near zero. In 1998 Martel, Shapiro, and Weinb ergmade a serious calculation of the effect of the cosmological constant on galaxy formation. They found that to within a factor of order 5, they could "explain" why the cosmological constant is as small as what we measure.
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Consider, as an example, the lo cal density of matter in which we find ourselves -- it is ab out 1030 times larger than the mean density of the universe. Why is this so? Chance? Luck? Divine Providence? Most of us would presumably accept this as a selection effect: life can evolve only in those rare regions of the universe where the density of matter is unusually high.

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Alan Guth, Inflationary Cosmology: Is Our Universe Part of a Multiverse, AAA Lecture, November 6, 2009, p. 7.

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A numb er of physicists regard these anthropic arguments as ridiculous. My recommendation is that the anthropic explanation (for anything) should b e considered the explanation of last resort. Until we actually understand the landscap e, and the initiation of life, we can only give plausibility arguments for anthropic explanations. Hence, the anthropic arguments only b ecome attactive when the search for more deterministic explanations has failed, as so far is the case for the cosmological constant. (Anthropic explanations are also discussed for many other quantities, including the Higgs mass, the top quark mass, the magnitude of density p erturbations.)
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For the cosmological constant, b ecause it seems so hard to explain any other way, it seems like it is time to strongly consider the selection-effect explanation. It is even hard to deny that, as of now, the selection-effect explanation is by far the most plausible that is known.

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The inflationary paradigm is in great shape! Inflation can explain why the universe is so smo oth and homogenous when averaged over large regions, why its mass density is so close to the critical value, and it can also explain the ripples that we see in the cosmic background radiation. Almost all inflationary mo dels are eternal into the future: they pro duce a multiverse of po cket universes. String theorists mostly agree that string theory has no unique vacuum, but instead a landscape of perhaps 10500 long-lived metastable states, any of which could be our vacuum. Eternal inflation can populate the string theory landscape. The combination provides a natural setting for anthropic arguments: perhaps we see a small cosmological constant, for example, because conscious beings only form in those parts of the multiverse where the cosmological constant is small.
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In earlier years, there was a widespread hop e that eventually string theory would b e able to predict the parameters of the standard mo del. From the p oint of view of theorists, this would b e great. If the landscap e picture is correct, it could b e that all these values are determined, at least in part, by historical accidents -- which means that we have much less predictive p ower than we hop ed. This is not the first time somethinglike this has happ ened. Kepler thought the radii of planetary orbits should b e calculable from geometry. Now we treat planetary orbits as historical accidents.

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Alan Guth, Inflationary Cosmology: Is Our Universe Part of a Multiverse, AAA Lecture, November 6, 2009, p. 8.

Bottom Line:
We have never had a mo del of the universe that works so well (homogeneity, mass density, sp ectrum of density fluctuations), or that is so mysterious.

Dark Energy

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