# A Level Physics day for teachers

Update on Cosmic Inflation and Dark Stuff

Malcolm Fairbairn, KCL Physics

malcolm.fairbairn@kcl.ac.uk

Research

Dr Fairbairn’s  research is concerned with the interaction between cosmology, particle physics and astrophysics. In particular he is interested in dark matter, dark energy, cosmological inflation and particle astrophysics.

Cosmic inflation, not to be confused with ……..

Historical note: The above right picture shows that money in 1920’s Germany was so worthless that it was used for fuel. This was a consequence of hyperinflation.

Or

Where has scientific thinking taken us?

What is the state of the art?

On a small scale: Chemistry leads to atomic physics which leads to nuclear physics which leads to particle physics

On a large scale: Newtonian Gravity leads to General Relativity

Particle Physics and Quantum field theory

We think particles are made out of oscillations of quantum fields. Below are some simple examples of oscillations, pendulum on the left and mass on a spring on the right.

In theoretical physics, quantum field theory (QFT) is a theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics, by treating a particle as an excited state of an underlying physical field. These excited states are called field quanta. For example, quantum electrodynamics (QED) has one electron field and one photon field, quantum chromodynamics (QCD) has one field for each type of quark, and in condensed matter there is an atomic displacement field that gives rise to phonon particles. Ed Witten describes QFT as “by far” the most difficult theory in modern physics.

https://en.wikipedia.org/wiki/Quantum_field_theory

Quantum fields can be thought of as oscillators spread out through space-time which are coupled to each other with springs so that any oscillation would move. This means that the room you are sitting in is full of fields and can be thought of as lots of tiny pendulums attached to each other and oscillating forming a chain reaction (an infinite group of simple harmonic oscillators), making each particle behave like a wiggle. A-level students learn that a simple harmonic oscillator’s acceleration is proportional to its displacement, but acts in the opposite direction.

http://www.s-cool.co.uk/a-level/physics/simple-harmonic-motion-and-damping/revise-it/simple-harmonic-motion

Note in the analogy, the position of the weight does not move in real space but in an internal quantum field space.

Force as a derivative of potential

On a map, contour lines are lines of constant height, which are also lines of constant gravitational potential energy.

You roll down the hill from high potential energy to low potential energy.

www.learner.org

The central vertical point of the graph above is the equilibrium point where the potential energy is zero. The left side shows force being used to compress the spring (the derivative is negative so the force is positive) and the right side shows the force to extend the spring (derivative is positive so the force is negative).

Quantum Field Theory

Minimum of potential that the field oscillates around can be at the origin of the internal field space i.e. f = 0. The field is normally zero (or minimum for the Higgs field).

www.gridpp.ac.uk

The left hand side of the above picture shows the fermions. In particle physics, a fermion (a name coined by Paul Dirac from the surname of Enrico Fermi) is any particle characterized by Fermi–Dirac statistics and following the Pauli Exclusion Principle; fermions include all quarks and leptons, as well as any composite particle made of an odd number of these, such as all baryons and many atoms and nuclei. We are all made of fermions.

http://en.wikipedia.org/wiki/Fermion

The right hand side of the picture shows the bosons. They are the force carriers and they have their own set of pendulums and they are connected to each other. The Higgs boson gives all fundamental particles (except the photon) mass.

https://en.wikipedia.org/wiki/Boson

https://en.wikipedia.org/wiki/Albert_Einstein

What is Einstein’s most famous equation?

E=mc^2 ————- NO!

Rμν is the curvature of space-time and Tμν is the momentum/energy. Therefore you can think of gravity as the curvature of space-time.

The Earth is warping space-time.

http://en.wikipedia.org/wiki/General_relativity

Newton and Einstein are in good agreement except when gravity is strong. This is when Einstein wins. General relativity is extremely successful.

It predicts bending of light round sun… and the orbit around Mercury                and the slowing down of gravitational waves.

https://en.wikipedia.org/wiki/Alexander_Friedmann

Alexander Alexandrovich Friedmann (also spelled Friedman or Fridman, Russian: Алекса́ндр Алекса́ндрович Фри́дман) (June 29 (17 old style) by himself, June 16 (4 old style) by J. O’Conor in 1888, Saint Petersburg, Russian Empire – September 16, 1925, Leningrad, USSR) was a Russian and Soviet physicist and mathematician. He is best known for his pioneering theory that the universe was expanding, governed by a set of equations he developed now known as the Friedmann equations.

https://en.wikipedia.org/wiki/Friedmann_equations

The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann in 1922 from Einstein’s field equations of gravitation for the Friedmann–Lemaître–Robertson–Walker metric and a perfect fluid with a given mass density ρ and pressure P. The equations for negative spatial curvature were given by Friedmann in 1924.

https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric

There are two independent Friedmann equations for modelling a homogeneous, isotropic universe and the equation below is a simplified version of the first

H is the Hubble parameter, G is the gravitational constant, a is a scale factor, ρ is potential and kinetic energy of the universe.

The expansion of the universe is often modelled using a balloon but raisin bread is better.

Imagine that the expanding Universe is a loaf of raisin. When baked in the oven, the bread expands, but the raisins do not. The bread represents the space in the Universe, and the raisins represent galaxies and other astronomical objects. While the bread itself undergoes a large change in structure, the raisins themselves stay the same.

Einstein modified his theory to stop the Universe from Expanding.

https://en.wikipedia.org/wiki/Cosmological_constant

In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) is equivalent to an energy density in otherwise empty space. It was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a static universe. Einstein abandoned the concept after the observation of the Hubble redshift indicated that the universe might not be stationary, as he had based his theory on the idea that the universe is unchanging. However, a number of observations including the discovery of cosmic acceleration in 1998 have revived the cosmological constant. The Lambda-CDM model of the Universe (the most accepted modern cosmological model) asserts that Λ is positive, although negligible even on the scale of the Milky Way.

http://en.wikipedia.org/wiki/Edwin_Hubble

Hubble is known for showing that the recessional velocity of a galaxy increases with its distance from the earth, implying the universe is expanding. This is known as “Hubble’s law”.

He therefore showed that galaxies are actually moving away from each other and us. The graph below shows that the recessional velocity is proportional to the distance the object is from us. The gradient is equal to the Hubble’s constant.

http://en.wikipedia.org/wiki/Hubble’s_law

During the 1960s/1970s expansion was finally accepted but one of the problems in Cosmology is that the Universe looks EXACTLY the same in all directions.

https://en.wikipedia.org/wiki/Chronology_of_the_universe

This chronology of the universe describes the history and future of the universe according to Big Bang cosmology, the prevailing scientific model of how the universe came into being and developed over time, using the cosmological time parameter of co-moving coordinates. The instant in which the universe is thought to have begun rapidly expanding from a singularity is known as the Big Bang. As of 2013, this expansion is estimated to have begun 13.798 ± 0.037 billion years ago. It is convenient to divide the evolution of the universe so far into three phases.

The very earliest universe was so hot, or energetic, that initially no particles existed or could exist (except perhaps in the most fleeting sense), and the forces we see around us today were believed to be merged into one unified force. Space itself expanded during an inflationary epoch due to the immensity of the energies involved. Gradually the immense energies cooled – still to a temperature inconceivably hot compared to any we see around us now, but sufficiently to allow forces to gradually undergo symmetry breaking, a kind of repeated condensation from one status quo to another, leading finally to the separation of the strong force from the electroweak force and the first particles. The universe consisted simply of a quark-gluon plasma. This phase lasted for about 400000 years. Photons moved in all directions.

In the second phase, this quark-gluon plasma universe then cooled further, the current fundamental forces we know take their present forms through further symmetry breaking – notably the breaking of electroweak symmetry – and the full range of complex and composite particles we see around us today became possible, leading to a matter dominated universe, the first neutral atoms (almost all of them hydrogen), and the cosmic microwave background radiation we can detect today. Modern high energy particle physics theories are satisfactory at these energy levels, and so physicists believe they have a good understanding of this and subsequent development of the fundamental universe around us. Because of these changes, space had also become largely transparent to light and other electromagnetic energy, rather than “foggy”, by the end of this phase.

Before and after recombination

In cosmology, recombination refers to the epoch at which charged electrons and protons first became bound to form electrically neutral hydrogen atoms.

Shortly after the first phase photons decoupled from matter in the universe, which leads to recombination sometimes being called photon decoupling, although recombination and photon decoupling are distinct events. Once photons decoupled from matter, they travelled freely through the universe without interacting with matter, and constitute what we observe today as cosmic microwave background radiation. The wavelength of the photons has increased from orange to the microwaves. Recombination occurred when the universe was roughly 378,000 years old, or at a redshift of z = 1,100.

https://en.wikipedia.org/wiki/Recombination_(cosmology)

http://en.wikipedia.org/wiki/Cosmic_Background_Explorer

The Cosmic Background Explorer (COBE), also referred to as Explorer 66, was a satellite dedicated to cosmology. Its goals were to investigate the cosmic microwave background radiation (CMB) of the universe and provide measurements that would help shape our understanding of the cosmos.

This work provided evidence that supported the Big Bang theory of the universe: that the CMB was a near-perfect black-body spectrum (in all directions) and that it had very faint anisotropies. Two of COBE’s principal investigators, George Smoot and John Mather, received the Nobel Prize in Physics in 2006 for their work on the project. According to the Nobel Prize committee, “the COBE-project can also be regarded as the starting point for cosmology as a precision science.

But why is the universe the same temperature in all directions?

Horizon Problem

http://en.wikipedia.org/wiki/Horizon_problem

The horizon problem is a problem with the standard cosmological model of the Big Bang which was identified in the late 1960s, primarily by Charles Misner. It points out that different regions of the universe have not “contacted” each other because of the great distances between them, but nevertheless they have the same temperature and other physical properties. This should not be possible, given that the transfer of information (or energy, heat, etc.) can occur, at most, at the speed of light. The horizon problem may have been answered by inflationary theory, and is one of the reasons for that theory’s formation.

Field theory affects expansion of Universe

Like springs and pendulums quantum fields have kinetic and potential energy

The x axis of the above right graph is field space and the y axis is potential energy. The field has mainly kinetic energy near the equilibrium point and mainly potential energy near the tops of the curves.

The kinetic energy stage robs the universe of energy.

Expansion of Universe affects Field Theory

ρ = Potential + Kinetic Energy, leads to expansion

Acts like friction on the oscillating pendulum, normally the energy is quickly lost…

Expansion causes a damped harmonic oscillator.

If the expansion is great enough, the oscillation is completely damped, field is trapped.

What happens?

Quantum field remains trapped close to the top of its potential. Large potential energy makes Universe expand rapidly. Universe trapped in rapid expansion…

THIS IS COSMIC INFLATION

Stuff/matter gets spread out. Cosmic inflation causes acceleration. Expansion makes it appear that photons are travelling faster than the speed of light.

End of Inflation – Reheating

Eventually, the field f slowly slides down the potential and as it does, the friction goes away. Eventually ends up oscillating around the bottom of the potential.

Coupling between inflation and other Standard model fields creates lots of random fluctuations in all the fields Corresponds to lots of high energy particles – Universe becomes HOT

https://en.wikipedia.org/wiki/Quark%E2%80%93gluon_plasma

A quark–gluon plasma (QGP) or quark soup is a (possible) phase of quantum chromodynamics (QCD) which exists at extremely high temperature and/or density. This phase consists of asymptotically free quarks and gluons, which are several of the basic building blocks of matter.

The study of the QGP is a testing ground for finite temperature field theory, a branch of theoretical physics which seeks to understand particle physics under conditions of high temperature. Such studies are important to understand the early evolution of our universe: the first hundred microseconds or so.

Primordial Nucleosynthesis

Around 1 second to 1 minute after the big bang

Here is the complete chain. EVERYTHING else is produced later in stars.

(See the section on recombination written earlier)

Then nothing for a while, not sure precisely how long. Maybe about 800 million years.

Inflation Solves the Horizon Problem

V(f) ~ constant during the period of inflation

Exponential expansion allows signals from a small region to be spread out all over the sky. This can explain why they have the same temperature. This also dilutes the density of monopoles and string exponentially from before inflation, and makes the vacuum the same everywhere after inflation. It explains why we don’t see them.

Inflation explains why the Universe is so flat

The exponential period of expansion flattens out any spatial curvature. This explains why the Universe is so flat.

Inflation and the Origin of Perturbations

The expansion leads to a cosmological horizon, which means that the size of the Universe is rather small during inflation. This leads to fluctuations in the value of the field  due to the Uncertainty principle. In one Hubble time Dt ~ 1/H the field f will fluctuate in a random direction an amount (on average) df ~ H.

Usually, the amount the field f moves due to these fluctuations is tiny compared to the classical slow roll of the field down the potential. However, because a change in the field leads to a change in the density, they represent density fluctuations.

After inflation, the field f will decay into other particles like photons and quarks, electrons etc. Where the density of V(f) was higher, the density of matter will be higher, hence the fluctuations.

http://en.wikipedia.org/wiki/Planck_(spacecraft)

Planck is a space observatory operated by the European Space Agency (ESA), and designed to observe anisotropies of the cosmic microwave background (CMB) at microwave and infra-red frequencies, with high sensitivity and small angular resolution. The project, initially called COBRAS/SAMBA, is named in honour of the German physicist Max Planck (1858–1947), who won the Nobel Prize in Physics in 1918.

On 21 March 2013, the European-led research team behind the Planck cosmology probe released the mission’s all-sky map of the cosmic microwave background. This map suggests the universe is slightly older than thought: according to the map, subtle fluctuations in temperature (tiny differences in energy density along with quantum fluctuations) were imprinted on the deep sky when the cosmos was about 370,000 years old. The imprint reflects ripples that arose as early, in the existence of the universe, as the first nonillionth (10-30) of a second. It is currently theorised that these ripples apparently gave rise to the present vast cosmic web of galactic clusters and dark matter. According to the team, the universe is 13.798 ±0.037 billion years old, and contains 4.9% ordinary matter, 26.8% dark matter and 68.3% dark energy. The Hubble constant was also measured to be 67.80 ±0.77 (km/s)/Mpc.

Dark Matter

http://en.wikipedia.org/wiki/Dark_matter

In astronomy and cosmology, dark matter is a type of matter hypothesized to account for a large part of the total mass in the universe. Dark matter cannot be seen directly with telescopes; evidently it neither emits nor absorbs light or other electromagnetic radiation at any significant level. Instead, its existence and properties are inferred from its gravitational effects on visible matter, radiation, and the large-scale structure of the universe. According to the Planck mission team, and based on the standard model of cosmology, the total mass–energy of the universe contains 4.9% ordinary matter, 26.8% dark matter and 68.3% dark energy. Thus, dark matter is estimated to constitute 84.5% of the total matter in the universe and 26.8% of the total content of the universe.

Calculating the mass of the baryons in the universe gives its density. A baryon is a composite subatomic particle made up of three quarks.

http://en.wikipedia.org/wiki/Baryon

http://en.wikipedia.org/wiki/Fritz_Zwicky

Fritz Zwicky (February 14, 1898 – February 8, 1974) was a Swiss astronomer. He worked most of his life at the California Institute of Technology in the United States of America, where he made many important contributions in theoretical and observational astronomy.

Velocity of galaxies in the cluster is too large for the visible mass of the cluster. There must be more mass than we can see.

http://en.wikipedia.org/wiki/Weakly_interacting_massive_particle

In astrophysics, weakly interacting massive particles or WIMPs, are hypothetical particles serving as one possible solution to the dark matter problem. These particles interact through the weak force and gravity, and possibly through other interactions no stronger than the weak force. Because they do not interact through electromagnetism they cannot be seen directly, and because they do not interact through the strong nuclear force they do not interact strongly with atomic nuclei. This combination of properties gives WIMPs many of the properties of neutrinos, except for being far more massive and therefore slower.

Much of the evidence for dark matter comes from the study of the motions of galaxies. Many of these appear to be fairly uniform, so by the virial theorem, the total kinetic energy should be half the total gravitational binding energy of the galaxies. Experimentally, however, the total kinetic energy is found to be much greater: in particular, assuming the gravitational mass is due to only the visible matter of the galaxy; stars far from the centre of galaxies have much higher velocities than predicted by the virial theorem. Galactic rotation curves, which illustrate the velocity of rotation versus the distance from the galactic centre, cannot be explained by only the visible matter. Assuming that the visible material makes up only a small part of the cluster is the most straightforward way of accounting for this. Galaxies show signs of being composed largely of a roughly spherically symmetric, centrally concentrated halo of dark matter with the visible matter concentrated in a disc at the centre. Low surface brightness dwarf galaxies are important sources of information for studying dark matter, as they have an uncommonly low ratio of visible matter to dark matter, and have few bright stars at the centre which would otherwise impair observations of the rotation curve of outlying stars.

HI velocity field of NGC 5055

This galaxy’s mass discrepancy emerges as a disagreement between light and mass distributions. This is evidence for dark matter.

http://en.wikipedia.org/wiki/Dark_matter

Unstable Dark Matter: Indirect Detection and Constraints

http://theory.fnal.gov/seminars/slides/2012/DTran.pdf

A determination of the particle identity of the dark matter is impossible using gravity alone. There are three methods for detection:

1) Collider searches: SM + SM → DM + photons + other particles

2) Direct detection: DM + nucleus → DM + nucleus

This is about Wimps, if dark matter is WIMPs then there are around 1000 WIMPs in a meter cubed and they are moving at around 200 km/s when they hit an object they leave around 1 X-ray worth of energy i.e. 1 keV then you can look for then using ionisation, scintillation or heating of a cryogenic system.

3) Indirect detection: DM + DM → SM + SM

DM or X = Dark matter particle, N = nucleus and SM = standard model particle

2) Direct detection of dark matter by looking for recoil of dark matter – nucleus scattering

X + N –> X +

http://cdms.berkeley.edu/

http://en.wikipedia.org/wiki/Cryogenic_Dark_Matter_Search

The Cryogenic Dark Matter Search (CDMS) is a series of experiments designed directly to detect particle dark matter in the form of WIMPs. Using an array of semiconductor detectors at mkelvin temperatures, CDMS has set the most sensitive limits to date on the interactions of WIMP dark matter with terrestrial materials. The first experiment, CDMSI, was run in a tunnel under the Stanford University campus. The current experiment, CDMSII, is located deep underground in the Soudan Mine in northern Minnesota.

The CDMS detectors measure the ionization and phonons produced by every particle interaction in their germanium and silicon crystal substrates. These two measurements determine the energy deposited in the crystal in each interaction, but also give information about what kind of particle caused the event. The ratio of ionization signal to phonon signal differs for particle interactions with atomic electrons (“electron recoils”) and atomic nuclei (“nuclear recoils”). The vast majority of background particle interactions are electron recoils, while WIMPs (and neutrons) are expected to produce nuclear recoils. This allows WIMP-scattering events to be identified even though they are rare compared to the vast majority of unwanted background interactions.

(A phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids.)

On Saturday April 13, Kevin McCarthy, from the MIT group on behalf of the SuperCDMS Collaboration, had presented the blind analysis results of the largest exposure with silicon detectors during CDMS-II operation. The collaboration had previously published the results of the entire germanium detector exposure [Science 327, 1619 (2010)] which resulted in 2 events in the signal region and an estimated background of 0.9 events. Afterward, the likelihood analysis concluded that these were more likely leakage surface electrons rather than nuclear recoils.

Increased interest in the low mass WIMP region motivated them to complete the analysis of the silicon detector exposure which is less sensitive than germanium for WIMP masses above 15 GeV/c², but more sensitive for lower masses. The analysis resulted in 3 events and the estimated background is 0.7 events.

Monte Carlo simulations have shown that the probability that a statistical fluctuation of the known backgrounds could produce three or more events anywhere in the signal region is 5.4%. However, they would rarely produce a similar energy distribution. A likelihood analysis that includes the measured recoil energies of the three events gives a 0.19% probability for a model including only known background when tested against a model that also includes a WIMP contribution. This ~3-sigma confidence level does not rise to the status of a discovery, but does call for further investigation.

If the result is interpreted as spin-independent scattering of WIMPs, a mass around 8.6 GeV/c² and a WIMP-nucleon cross section of 1.9E-41 cm² are favoured. For the simplest theories of WIMP interactions and using the standard dark matter halo model, the allowed region is in tension with exclusion limits from the XENON collaboration. A paper has been submitted to the arXiv and to PRL.

They will probe this WIMP sector with their operating germanium detectors in the SuperCDMS Soudan experiment, and they are considering using silicon detectors in future experiments.

CDMS-II was funded by DOE and NSF in the US and by NSERC in Canada.

http://cdms.berkeley.edu/press.html

3) WIMP indirect detection

WIMPS may be the major component of the haloes of galaxies. Their self-annihilations could produce an indirect signature of high energy cosmic rays including protons, quarks, bosons, muons, neutrinos, gamma photons, positrons and and anti-protons.

http://en.wikipedia.org/wiki/Cosmic_ray

The evidence could be the gamma radiation emerging from the galaxy

http://en.wikipedia.org/wiki/Weakly_interacting_massive_particles

In the above left picture the pink data points represent the gamma radiation. There is an excess of gamma rays from the centre of the galaxy, but is this evidence for dark matter?

Alternative explanation for spectrum

Boyarsky et al 1012.5839                                Chernyakova et al. 1009.2630

Positrons!

In the above graph the black points represent the flux of positrons, whose origin is cosmic ray. Red points are experimental data. Where do the positrons come from?

http://en.wikipedia.org/wiki/Alpha_Magnetic_Spectrometer

he Alpha Magnetic Spectrometer, also designated AMS-02, is a particle physics experiment module that is mounted on the International Space Station. It is designed to measure antimatter in cosmic rays and search for evidence of dark matter.

One of the leading candidates for dark matter is the neutralino. If neutralinos exist, they should be colliding with each other and giving off an excess of charged particles that can be detected by AMS-02. Any peaks in the background positron, antiproton, or gamma ray flux could signal the presence of neutralinos or other dark matter candidates, but would need to be distinguished from poorly known confounding astrophysical signals.

So Far AMS hasn’t changed the Situation

Where do the positrons come from? Are they really a product of the neutralino/dark matter?

Rate of annihilation should tell us how much dark energy there is. We have a pretty good idea how much dark matter there is local to us.

Where are we now?

Possible astrophysical origin of electrons/positrons 10 GeV – 10 TeV

SNR – Secondary                                            Pulsars – Primary

They could cause an excess of positrons.

Dark Energy

We have no idea about what dark energy is.

Time and the HR diagram

Age of the Universe from Globular Clusters

Gives us a figure of 12 billion years. Some stars are 12 billion years old. So how old is the Universe? (Hint:- It had better be older than 12 billion years.) To calculate age of the Universe we need to follow the expansion back to the beginning…

Universe used to expand faster than today…

If the Universe just contained matter, its age would be about 9.2 billion years!! i.e. Not old enough to contain the stars inside it! What is going on?

Type 1a supernovae as Standard Candles

https://en.wikipedia.org/wiki/Type_Ia_supernova

Type 1a supernovae occur in binary systems (two stars orbiting one another) in which one of the stars is a white dwarf while the other can vary from a giant star to even a smaller white dwarf.

Type 1a supernovae have a characteristic light curve, their graph of luminosity as a function of time after the explosion.

The similarity in the absolute luminosity profiles of nearly all known Type 1a supernovae has led to their use as a secondary standard candle in extragalactic astronomy. The cause of this uniformity in the luminosity curve is still an open question. In 1998, observations of distant Type 1a supernovae indicated the unexpected result that the Universe seems to undergo an accelerating expansion. (In astronomy, a standard candle is a source that has a known luminosity. luminosity = total power output, measured in watts or solar luminosities (L⊙).1 L⊙ = 3.84 x 1026 W)

The expansion of the universe is accelerating!

THE REAL STANDARD COSMOLOGICAL MODEL baryons = 100%

BUT THE UNIVERSE WE LIVE IN… baryons = 4%, dark matter = 24%, dark energy = 72%

NONE STANDARD ??

Epilogue

•We understand more and more about how the Universe evolved.

•We still don’t know how it started.

•Inflation solves some problems.

•We are trying to understand and detect dark matter

•We don’t know what Dark Energy is but we are working to find out

Does the Universe create itself? Chaotic Inflation

Very, very occasionally, a random fluctuation will put the field a bit further up the hill than normal. In that small region, expansion will increase, so it will become a bigger region, and because df ~ H  the fluctuations in that region will be bigger, so the field might go even higher up the hill, expansion would be even faster and fluctuations even bigger.

It is clear that the majority of the Universe will be inflating very rapidly with big quantum fluctuations and only occasionally will a part of the Universe drop out of this inflation due to a random fluctuation in the other direction so that classical slow roll will take over. This is chaotic inflation.

Chaotic Inflation

In each different pocket where the field drops out of inflation, there are many different ways that the Universe could cool, leading to many different kinds of symmetry breaking and many different kinds of Universe and even laws of physics.

We just happen to live in one Universe in the multiverse which is good for us. Alternatively, in order for us to exist as we do, we need to live in one very similar to the one we live in. Our little Universe is the way it is because if it were different we would not be here to observe it. This is called the WEAK ANTHROPIC PRINCIPLE.

http://en.wikipedia.org/wiki/Anthropic_principle

In astrophysics and cosmology, the anthropic principle (from the Greek, anthropos, human) is the philosophical consideration that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the anthropic principle reason that it explains why the Universe has the age and the fundamental physical constants necessary to accommodate conscious life. As a result, they believe it is unremarkable that the universe’s fundamental constants happen to fall within the narrow range thought to be compatible with life.