1.2 The Theory of Inflation Review

summary

The inflationary theory helps to explain many unanswered questions that arise in the standard Big Bang model.

- Observations establish that the universe is homogeneous. In the conventional Big Bang theory, we must assume the universe was this homogeneous from the very beginning.
- The standard Big Bang theory provides no insight into the “bang” itself—why space began expanding in the first place.
- The inflationary theory remedies this by arguing that the “bang” arose from
*gravitational repulsion*. This outward push explains why space began expanding while also offering insight into how the observable universe homogenized.

According to general relativity, certain exotic substances can result in repulsive gravity.

- A gravitational field can be created by pressures, as well as energy or mass densities.
- Positive pressure contributes an attractive gravitational field; negative pressure contributes a repulsive gravitational field.
- For those who are following the mathematics: the equation describing how $a(t)$, the scale factor for the universe, evolves in time is $$\frac{d^2 a}{dt^2} = -4 \pi G \left(\rho + \frac{3p}{c^2}\right) a $$ where $G = $ Newton’s constant, $\rho = $ mass density, $p = $ pressure, and $c =$ the speed of light.
- Notice from the equation that when $p$ is positive, it contributes to the deceleration of spatial expansion, as does positive energy density $\rho$. Also notice that negative pressure contributes to the acceleration of spatial expansion, that is, it yields gravitational repulsion.

Examining the equation of state of a quantum field can tell us about the sign of the gravitational field it contributes.

- According to modern particle physics, certain configurations of quantum fields have sufficient negative pressure to create gravitational repulsion.
- When the total energy of a quantum field is dominated by the
*potential energy*, then $$p = -\rho c^2$$ - Notice from the equation for $a(t)$ that this pressure is sufficiently negative to ensure that the scale factor’s growth accelerates. That is, expansion gets faster over time, the hallmark of gravitational repulsion.

Einstein used this concept in the form of the

*cosmological constant*to build a static model of the universe.- Introduced by Einstein in 1917, the cosmological constant $\Lambda$ was an addition to the general theory of relativity.
- Repulsive gravity of the cosmological constant balanced the attractive gravity of ordinary matter to yield an unchanging cosmos—the accepted view at the time.
- Later, Einstein called the idea his “greatest blunder” after Hubble discovered that all galaxies were moving away from us, implying an expanding universe.