Introduction to Cosmology: Expansion, Scale Factors, and Critical Density

This set of vocabulary flashcards covers fundamental concepts of cosmology, including the cosmological principle, expansion mechanics, the scale factor, and density parameters for the fate of the universe.

Cosmology

The study of the universe as a whole, rather than individual objects like galaxies or stars.

Cosmological Principle

The combination of two fundamental assumptions in cosmology: that the universe is both isotropic and homogeneous on the largest scales.

Isotropic

The property that the universe looks the same regardless of which direction you look in the sky.

Homogeneous

The property that the universe is smooth and lacks clumpy clustering on the largest scales, looking the same everywhere.

Occam's razor

The philosophical principle that the simplest explanation is usually the correct one.

Scale factor ($r$)

A dimensionless number that describes the expansion of the universe, where the distance at any time $t$ is related to the current distance $d_0$ by the formula $d(t) = r(t) \times d_0$. By convention, $r = 1$ at the current time ($t_0$).

Physical coordinates

A coordinate system based on current measurements that maps the movement of space as it expands.

Co-moving coordinates

A coordinate system that moves along with the expansion of space, meaning the coordinates of objects do not change unless the object itself is actually moving through space.

Hubble constant ($H_0$)

The current rate of change of the scale factor ($\frac{\triangle r}{\triangle t}$), representing the slope of the velocity-distance relationship in Hubble's law.

Redshift ($z$)

The fractional change in the wavelength of light defined as $z = \frac{\text{lambda}_{obs} - \text{lambda}_0}{\text{lambda}_0}$. It is related to the scale factor by the equation $1 + z = \frac{1}{r_{em}}$.

Hubble parameter ($H(t)$)

The fractional rate of change of the scale factor at any given time, defined as $H(t) = \frac{1}{r} \times \frac{\triangle r}{\triangle t}$. It equals the Hubble constant at the current time when $r = 1$.

Critical density ($\rho_{crit}$)

The mass density of the universe required for the kinetic energy of expansion to exactly equal the gravitational potential energy, defined by the formula $\rho_{crit} = \frac{3 H_0^2}{8 \text{pi} G}$.

Omega ($\text{Omega}$)

A symbol used to express the actual density of the universe as a fraction or multiple of the critical density ($\text{Omega} = \frac{\rho}{\rho_{crit}}$).

Open universe

A universe where the total density ($\text{Omega}_{total}$) is less than one, meaning kinetic energy exceeds potential energy and the universe expands forever.

Closed universe

A universe where the total density ($\text{Omega}_{total}$) is greater than one, meaning potential energy exceeds kinetic energy, eventually causing the universe to stop expanding and recollapse.