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Universe Expansion Scenario Model — result sheet
Integrate a bounded dimensionless scale-factor scenario from present time using matter, radiation, curvature, dark-energy fractions, and a chosen Hubble constant.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: E(a)=√(Ωr/a⁴+Ωm/a³+Ωk/a²+ΩΛ); da/dt=aH₀E(a), integrated from a(0)=1 with H₀ converted to Gyr⁻¹; redshift z=1/a−1.
This page is an educational numerical scenario, not a precision cosmology calculator. It evolves a normalized scale factor from today under a user-entered four-component Friedmann-style model and reports the scale factor, implied redshift, and instantaneous expansion rate at the selected time.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Elapsed time from today — Gyr; minimum -13.7; maximum 100
- Hubble constant — km/(s·Mpc); minimum 1.0E-6; maximum 1000
- Matter density fraction Ωm — fraction; minimum 0; maximum 5
- Radiation density fraction Ωr — fraction; minimum 0; maximum 5
- Dark-energy fraction ΩΛ — fraction; minimum 0; maximum 5
- Curvature fraction Ωk — fraction; minimum -5; maximum 5
Worked example
| Input | Value |
|---|---|
| Elapsed time from today | 5 |
| Hubble constant | 67.4 |
| Matter density fraction Ωm | 0.315 |
| Radiation density fraction Ωr | 0 |
| Dark-energy fraction ΩΛ | 0.685 |
| Curvature fraction Ωk | 0 |
Five billion years into the future, the model gives a scale factor of about 1.383, redshift about −0.277, and an instantaneous Hubble rate of about 60.4 km/(s·Mpc).
Assumptions and limits
- The four density fractions must sum to one so the entered Hubble constant is the present-day rate at a=1.
- The model uses a homogeneous and isotropic background with matter, radiation, curvature, and a constant dark-energy term; it omits local gravitational motion and detailed cosmological parameter inference.
- The integration starts at a=1 today and uses a bounded fourth-order Runge–Kutta stepper with a fixed maximum resolution.
- Negative elapsed time is interpreted as a look-back scenario and positive time as a future scenario; the result is rejected if the numerical path reaches a nonpositive scale factor.
- The displayed redshift is the simple background relation z=1/a−1 and is not a distance, a spectroscopic fit, or a prediction for a particular galaxy.
- Use published cosmological data and specialist software for research, observation planning, or any result that requires uncertainty analysis.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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