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A Big Bang with Inflation

The last and final embellishment of the Big Bang theory is the concept of “inflation.” As developed by Alan Guth, Andrei Linde, and others,For a highly readable account of inflation, see Alan H. Guth's The Inflationary Universe, Addison Wesley: Reading, Massachusetts, 1997.inflation should be regarded as an enhancement of the Big Bang, not a replacement of it, as some popular accounts have implied. To understand inflation, we need to start first with a “normally” expanding universe whose gravity is generated purely by matter. In such a universe, matter becomes more dilute with the expansion, and gravity weakens. The expansion is thus a measured, stately affair, and one can show that the size of the universe (i.e., the distance between any two freely expanding particles) varies only as some power of the time (tn).

Inflation is produced when gravity is produced not by ordinary matter but by a repulsive Λ. This is equivalent to putting a negative pressure into the GR equations, and one that remains constant despite the expansion. Einstein's Λ was a mysterious term that arose, literally, out of nothing, i.e., the vacuum. Modern particle physics is teaching us, however, that a vacuum, despite being empty of matter, is far from inert. A revolutionary new concept is the idea that, under certain conditions such as those reached in the early Universe, the vacuum can possess a finite energy density even when empty of matter. Being disjoint from ordinary matter, this energy density does not become more dilute as the Universe expands, yet, being energy, it does generate a gravitational field. Voila, modern physics has produced a physical raison d’être for a constant Λ! The resultant gravity turns out to be repulsive and propels the Universe in an eyeblink into uncontrolled, stupendous expansion - hence the term “inflation.” The expansion rate is exponential, i.e., the size of the Universe varies as 10Kt, where K in proportion to the energy density of the vacuum. The presence of t in the exponent produces an expansion that is far more powerful that the measured power-law expansion of a normal matter-dominated universe.

This early epoch of inflation was very brief. The early vacuum of high-energy particle physics proves to be unstable, and the inflation phase lasted from only 10-35 seconds to 10-32 seconds (in the classic picture). Nevertheless, in this briefest of instants our entire visible Universe (now 30 billion light years across) inflated by a factor of 1060 or so, from an indescribably small speck to about the size of a grapefruit. Thereafter it expanded “normally”. All of the space we see today was created out of virtually nothing during inflation.

Though totally at odds with common sense, the inflationary theory is taken seriously because it solves, in one fell swoop, several conceptually difficult puzzles that had been dogging the standard hot Big Bang model. I will mention just three of these:

1) Why do all parts of the visible Universe look the same and obey the same laws of physics? Though clumpy on small scales, the Universe on large scales looks statistically the same everywhere. The ultimate test of this is the cosmic microwave background radiation, whose temperature of 2.7 degrees is the same wherever we look. A classic question in cosmology is how the temperature of the CMB got to be so uniform over the whole sky. CMB photons coming to us today from opposite sides of the sky were emitted long ago by patches of matter that, in the classic Big Bang picture, were so far apart that they never could have exchanged energy with one another. How then could they have reached a common temperature? Historically this equality of temperature everywhere had to be built in by ad hoc assumption, a “deus ex machina.” Inflation solves this problem by creating the entire visible universe (and much more) out of a tiny speck that was so small that there was ample time before inflation for temperature fluctuations to even out. Born entirely within this uniform speck, the Universe we see today naturally looks uniform.

This explanation for the CMB can be expanded to answer the deeper question of why the properties of matter and values of the physical constants are also the same in all parts of the visible Universe. This is a question that has plagued natural philosophers for centuries. A plausible answer is that the same equilibrating processes acting to smooth out temperature irregularities before inflation could have ironed out any irregularities in basic physics, too. Einstein's famous quote says “the most incomprehensible thing about the Universe is that it is comprehensible.” Inflation goes a long way toward answering the implied question by providing a means whereby the Universe manages to present a consistent face at all times and locations - in short, why physics works.

2) Where did the matter and energy in the Universe come from? The vacuum of the early Universe that gave rise to inflation had the property that it was unstable and decayed, hence its brief lifetime from 10-35 seconds to 10-32 seconds. The decay of the vacuum, or exit from inflation, involved some complicated and still poorly understood physics. The transition is thought to be a “phase change” analogous to the freezing of water. Like freezing water, the Universe actually cooled below the nominal phase-change temperature, but in this case by a much larger amount. The energy that was stored up in the vacuum tumbled out as the vacuum gave way, like water bursting through a dam. This freely available flood of energy spawned all the matter and energy that we see in today's Universe. By creating space filled with matter and photons, inflation was the original “nourishing mother” of our Universe, or, as Alan Guth has described it, the ultimate “free lunch.”

3) What spawned the density ripples? Students of galaxies like myself can also credit inflation with mothering the density ripples needed to kick off galaxy formation. An inflating universe literally expands faster than light in the sense that particles very close to you are swept off and accelerated to speeds faster than light. This is rather like particles falling into a black hole except that here they fall outwards to the rest of the universe rather than into the black hole. Analogous to the hole, every observer in an inflating universe is surrounded by an “event horizon,” which marks the boundary where accelerating particles reach the speed of light and disappear from view. Event horizons emit “Hawking radiation,” a bath of thermal (black-body) radiation, which in the case of black holes causes them eventually to evaporate. The Hawking radiation energy of an inflating universe is not quite uniform but varies slightly from place to place - this is the origin of the tiny energy-density ripples.

An alternative way of looking at the ripples is also instructive. High-energy physics tells us that vacua, including that of inflation, are busy places. According to the Heisenberg uncertainty principle, “virtual” pairs of photons and matter-anti-matter particles are spontaneously created out of nothing and annihilating one another even in so-called “empty” space. This microscopic seething of the vacuum normally goes unnoticed because the fluctuations are short-lived: pairs appear and disappear quickly and on average have no measurable effect. Circumstances are essentially altered in inflation, however; now pairs are torn apart by the rapid expansion of space and, once separated, cannot find one another to annihilate. They therefore must become “real,” frozen into the fabric of the Universe for all time. Their associated energy fluctuations are the tiny ripples - seized by inflation and blown up to what will ultimately become, in our day, galaxies and superclusters.

This whole scenario for the birth of structure can be summed up breathtakingly as follows: the Milky Way and all other galaxies, clusters, and superclusters, were born as weak, microscopic quantum fluctuations some 10-35 to 10-32 seconds after the Big Bang. Pumped up quickly by inflation, they continued to expand with the Universe until gravity corralled their expansion. As galaxies collapsed, stars began to be born within them, and galactic beacons visible across billions of light years switched on. Gravity continued to shepherd the flight of galaxies, weaving a lacy filigree of voids and superclusters that is now spangled over hundreds of millions of light years across the Universe. Simply put, galaxies and large-scale structure are the quantum noise of the Big Bang writ large - surely one of the most remarkable insights of human science.

Contributed by: Dr. Sandra Faber

Cosmic Questions

Did the Universe Have a Beginning? Topic Index
Standard Big Bang Cosmology: The Big Bang Really Happened

A Big Bang with Inflation

The Big Bang as Scientific Fact
The Birth of Big Bang Cosmology
A Bare-Bones Big Bang Model
A Hot Big Bang
A Hot Big Bang with Density Ripples
The Steady-State Universe


Sandra Faber

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