Inflationary universe?

Matter and radiation are gravitationally attractive, so in a maximally symmetric spacetime filled with matter, the gravitational force will inevitably cause any lumpiness in the matter to grow and condense. That's how hydrogen gas turned into galaxies and stars. But vacuum energy comes with a high vacuum pressure, and that high vacuum pressure resists gravitational collapse as a kind of repulsive gravitational force. The pressure of the vacuum energy flattens out the lumpiness, and makes space get flatter, not lumpier, as it expands.
So one possible solution to the flatness problem would be if our Universe went through a phase where the only energy density present was a uniform vacuum energy. If this phase occurred before the radiation-dominated era, then the Universe could evolve to be extraordinarily flat when the radiation-dominated era began, so extraordinarily flat that the lumpy evolution of the radiation- and matter-dominated periods would be consistent with the high degree of remaining flatness that is observed today.

This type of solution to the flatness problem was proposed in the 1980s by cosmologist Alan Guth. The model is called the Inflationary Universe. In the Inflation model, our Universe starts out as a rapidly expanding bubble of pure vacuum energy, with no matter or radiation. After a period of rapid expansion, or inflation, and rapid cooling, the potential energy in the vacuum is converted through particle physics processes into the kinetic energy of matter and radiation. The Universe heats up again and we get the standard Big Bang.
So an inflationary phase before the Big Bang could explain how the Big Bang started with such extraordinary spatial flatness that it is still so close to being flat today.A magnet cut in half still has two poles.

Inflationary models also solve the horizon problem. The vacuum pressure accelerates the expansion of space in time so that a photon can traverse much more of space than it could in a spacetime filled with matter. To put it another way, the attractive force of matter on light in some sense slows the light down by slowing down the expansion of space itself. In an inflationary phase, the expansion of space is accelerated by vacuum pressure from the cosmological constant, and light gets farther faster because space is expanding faster.
If there were an inflationary phase of our Universe before the radiation-dominated era of the Big Bang, then by the end of the inflationary period, light could have crossed the whole Universe. And so the isotropy of the radiation from the Big Bang would no longer be inconsistent with the finiteness of the speed of light.

The inflationary model also solves the magnetic monopole problem, because in the particle physics that underlies the inflationary idea, there would only be one magnetic monopole per vacuum energy bubble. That means only one magnetic monopole per Universe.
That's why the inflationary universe theory is still the favored pre-Big Bang cosmology among cosmologists.
But how does Inflation work?

The vacuum energy that drives the rapid expansion in an inflationary cosmology comes from a scalar field that is part of the spontaneous symmetry breaking dynamics of some unified theory particle theory, say, a Grand Unified Theory or string theory.

This field is sometimes called the inflaton. The average value of the inflaton at temperature T is the value at the minimum of its potential energy at that temperature. The location of this minimum changes with temperature, as is shown in the animation to the right.
For temperatures T above some critical temperature Tcrit, the minimum of the potential is at zero. But as the temperature cools, the potential changes and a second minimum develops in the potential at a nonzero value. This signals something called a phase transition, like when steam cools and condenses into water. For water the critical temperature Tcrit where this phase transition happens is 100°C, or 373°K.
The two minima in the potential represent the two possible phases of the inflaton field, and of the Universe, at the critical temperature. One phase has the minimum of the field f=0, and the other phase represents the vacuum energy if the ground state has f=f0.
According to the inflationary model, at the critical temperature, spacetime starts to under go this phase transition from one minimum to the other. But it doesn't do it smoothly, it stays in the old "false" vacuum too long. This is called supercooling. This region of false vacuum expands exponentially fast, and the vacuum energy of this false vacuum is the cosmological constant for the expansion. It is this process that is called Inflation and solves the flatness, horizon and monopole problems.

This region of false vacuum expands until bubbles of the new broken symmetry phase with f=f0 form and collide, and eventually end the inflationary phase. The potential energy of the vacuum is converted through to kinetic energy of matter and radiation, and the Universe expands according to the Big Bang model already outlined.
A testable prediction?

It's always good to have testable predictions from a theory of physics, and the inflation theory has a distinct prediction about the density variations in the cosmic microwave background. A bubble of inflation consists of accelerating vacuum. In this accelerating vacuum, a scalar field will have very small thermal fluctuations that are nearly the same at every scale, and the fluctuations will be have a Gaussian distribution. This prediction fits current observations and will be tested with greater precision by future measurements of the cosmic microwave background.

So are all the problems solved?

Despite the prediction above, inflation as described above is far from an ideal theory. It's too hard to stop the inflationary phase, and the monopole problem has other ways of resurfacing in the physics. Many of the assumptions that go into the model, such as an initial high temperature phase and a single inflating bubble have been questioned and alternative models have been developed.
Today's inflation models have evolved beyond the original assumption of a single inflation event giving birth to a single Universe, and feature scenarios where universes nucleate and inflate out of other universes in the process called eternal inflation.
There is also another attempt to solve the problems of Big Bang cosmology using a scalar field that never goes through an inflationary period at all, but evolves so slowly so that we observe it as being constant during our own era. This model is called quintessence, after the ancient spiritual belief in the Quinta Essentia, the spiritual matter from which the four forms of physical matter are made.
So where does string theory fit in all of this? That's the next topic.

Light travels on geodesics paths through spacetime. When those geodesic paths cross the event horizon of a black hole, they never come back out. Interestingly, in a Universe where the energy density is never negative, this behavior of light leads mathematically to two very crucial properties of black holes:

* The surface area of the event horizon of a black hole can only increase, never decrease. This also means that although two black holes can join to make a bigger black hole, one black hole can never split in two.
* The pull of gravity at the event horizon is constant; it has the same value everywhere on the event horizon.

???????????????????? Note that according to the first property, it is impossible for black holes to decay and go away, because a black hole cannot get smaller or split into smaller black holes. This is going to be changed when we add quantum mechanics to the theory in the next section.