Calculator Inputs
Plotly Graph
After calculation, the graph shows how Ωm(z) evolves with redshift and compares the major input densities.
Example Data Table
| Model | H0 (km/s/Mpc) | ρb (kg/m^3) | ρcdm (kg/m^3) | ΩΛ0 | Ωk0 | z | Approx Ωm0 |
|---|---|---|---|---|---|---|---|
| Concordance-like | 67.4 | 4.20e-28 | 2.24e-27 | 0.685 | 0.000 | 0.50 | 0.313 |
| Higher matter case | 70.0 | 4.80e-28 | 2.90e-27 | 0.650 | 0.000 | 1.00 | 0.394 |
| Open model sample | 65.0 | 3.90e-28 | 1.90e-27 | 0.620 | 0.060 | 2.00 | 0.312 |
These values are illustrative. They help test layout, exports, and graph behavior.
Formula Used
Critical density: ρc = 3H² / (8πG)
Present matter density parameter: Ωm0 = ρm / ρc
If split densities are entered: ρm = ρb + ρcdm
Expansion function: E(z)² = Ωm0(1 + z)³ + Ωr0(1 + z)⁴ + Ωk0(1 + z)² + ΩΛ0
Redshift-scaled matter parameter: Ωm(z) = Ωm0(1 + z)³ / E(z)²
This page uses SI units internally. H0 is converted from km/s/Mpc to s⁻¹ before calculating the critical density.
How to Use This Calculator
- Enter the Hubble constant in km/s/Mpc.
- Choose either split matter densities or direct total matter density.
- Provide redshift and any cosmological density parameters you want included.
- Press the calculate button to show the result above the form.
- Review Ωm0, Ωm(z), closure residual, and the graph.
- Use the CSV and PDF buttons to export results or the example table.
FAQs
1. What does the matter density parameter represent?
It measures how much matter exists relative to the critical density needed for a spatially balanced universe at the present epoch.
2. Why is critical density important?
Critical density provides the normalization reference. Without it, raw matter density values are harder to compare across cosmological models.
3. What is the difference between Ωm0 and Ωm(z)?
Ωm0 is the present-day normalized matter density. Ωm(z) is the normalized matter share at a chosen redshift after expansion effects are applied.
4. Should I use split or direct matter density mode?
Use split mode when baryons and dark matter are known separately. Use direct mode when only the total matter density is available.
5. Why can the closure residual differ from zero?
The entered Ω terms may not sum to one. That can be intentional, approximate, or a sign that one cosmological component needs revision.
6. Can this calculator model non-flat universes?
Yes. Enter a nonzero curvature parameter Ωk0. The expansion term then includes curvature when scaling matter with redshift.
7. Why is radiation included?
Radiation is usually small today, but it can matter more at high redshift. Including Ωr0 keeps the redshift scaling more complete.
8. Are the outputs suitable for research publication?
They are useful for checking scenarios and learning concepts. For publication, confirm assumptions, units, and parameter sources independently.