As inflation began, the size of the universe (the currently...

As inflation began, the size of the universe (the currently visible universe) expanded from about $10^{-30} \mathrm{m}$ to twice that size in $10^{-35}$ sec. Calculate Hubble's constant at that time, converting it to the same units used today. In the next $10^{-35}$ sec the size of this region doubled again. Show that Hubble's constant remains the same.

Key Concepts

Inflation

Inflation refers to the extremely rapid, exponential expansion of the universe that is believed to have occurred a fraction of a second after the Big Bang. This phase of expansion drastically increased the scale of the universe, smoothing out any irregularities and setting universal conditions that influence the large-scale structure observed today.

Hubble's Constant

Hubble's constant, or the Hubble parameter, is a measure of the rate at which the universe is expanding at any given time. It is defined as the ratio of the expansion velocity to the distance (H = v/d) or, equivalently, as the time derivative of the scale factor divided by the scale factor itself. A constant Hubble parameter indicates an exponential expansion of space.

Scale Factor

The scale factor is a variable that quantifies the relative expansion of the universe over time. It is a key component in cosmological models because its evolution determines how distances change across the universe. During inflation, the scale factor increases exponentially, leading to consistent relative increases in distance regardless of the absolute size of the universe.

Exponential Expansion

Exponential expansion is a process whereby the scale factor of the universe grows by a constant multiplicative factor over equal intervals of time. This means that if the universe doubles in size over a fixed time interval, the derived Hubble parameter (as the logarithmic derivative of the scale factor) remains constant, which is a defining feature of inflation.

Transcript

Please give Ace some feedback