Comoving Distance Calculator

Formula

The formula to calculate the Comoving Distance (DC) is:

\[ D_C = \frac{c}{H_0} \int_0^z \frac{dz'}{\sqrt{\Omega_M (1+z')^3 + \Omega_\Lambda}} \]

Where:

\( D_C \) is the Comoving Distance
\( c \) is the speed of light
\( H_0 \) is the Hubble Constant
\( z \) is the redshift
\( \Omega_M \) is the density parameter for matter
\( \Omega_\Lambda \) is the density parameter for dark energy

What is Comoving Distance?

Comoving distance is a measure of distance used in cosmology that accounts for the expansion of the universe. It represents the distance between two points in the universe, assuming the universe is not expanding. This distance is useful for comparing the separation of objects at different times in the history of the universe. Comoving distance remains constant over time for objects moving with the Hubble flow, making it a valuable tool for understanding the large-scale structure of the cosmos.

Example Calculation

Let's assume the following values:

Hubble Constant (H0) = 70 km/s/Mpc
Redshift (z) = 2
Density Parameter for Matter (ΩM) = 0.3
Density Parameter for Dark Energy (ΩΛ) = 0.7

Using the formula to calculate the Comoving Distance:

We perform the numerical integration of the integrand from 0 to 2.

Assuming an integral value of approximately 1.759, the comoving distance is:

\[ D_C = \frac{299792.458}{70} \times 1.759 \approx 5182.73 \text{ Mpc} \]

The Comoving Distance is approximately 5182.73 Mpc.