Introduction to neutrino decoupling temperature
This neutrino decoupling calculator turns two early-universe inputs into a freeze-out temperature, then carries that temperature through the page’s redshift and time scaling. It is designed for quick comparisons: adjust g* or GF, click Compute, and see how the estimated decoupling epoch shifts.
Neutrino freeze-out is controlled by both weak-interaction strength and the radiation content of the primordial plasma. A larger g* slightly raises the freeze-out temperature by making the universe expand faster at a given temperature. A larger GF, by contrast, keeps neutrinos coupled longer and pushes decoupling to a lower temperature.
The discussion below explains what this estimate means, how to choose sensible inputs, how the formula is assembled, and how to read the output without confusing this streamlined calculation with a full cosmology code.
What neutrino decoupling question does this calculator answer?
The central neutrino decoupling question is: at what temperature do weak interactions become too slow to keep neutrinos in thermal equilibrium with the primordial plasma? At that point, neutrinos stop tracking the bath temperature in the same way and begin to free-stream through the expanding universe.
You can also use the page for scenario comparisons. For example, test how a different g* changes freeze-out, how the inferred cosmic time moves, or whether a changed GF moves the result from the standard band into an early- or late-decoupling label.
How to use the neutrino decoupling temperature calculator
Start by entering the effective relativistic degrees of freedom, g*, and the Fermi constant, GF, in the units printed beside the fields. Then select Compute to refresh the temperature, redshift, cosmic time, and classification. When comparing cases, change one quantity at a time and keep a note of the values used; that makes the direction of each physical effect much easier to see.
The defaults provide a useful standard-era starting point, but they are not a guarantee that every plasma model should use the same assumptions. Make sure that the g* value and weak-interaction constant describe the same early-universe scenario before drawing conclusions from a comparison.
Inputs for a neutrino decoupling estimate: choosing g* and GF
For a neutrino decoupling estimate, the form asks only for quantities that directly enter the freeze-out relation. The effective relativistic degrees of freedom, g*, represents the radiation content of the plasma. It affects the expansion rate, so a plasma with more relativistic species expands a little more quickly at the same temperature.
The Fermi constant GF, expressed in GeV⁻², represents the weak-interaction strength used in this approximation. Units are particularly important here: enter a value already expressed in GeV⁻², rather than mixing conventions from another source. If you are uncertain, begin with the defaults and vary one field at a time. A modest g* adjustment usually shifts the output gently, whereas a changed GF can have a more pronounced effect.
Formulas for neutrino decoupling: from expansion rate to freeze-out
The neutrino decoupling calculation follows the freeze-out scaling used by the script. It sets the weak interaction rate against the expansion rate in a radiation-dominated universe. The resulting decoupling temperature grows with g* to the one-sixth power and falls with GF to the two-thirds power, which explains why the weak constant has the stronger sensitivity.
In practical terms, the calculator combines the relativistic degrees of freedom, weak coupling, and Planck mass into a temperature in GeV, then converts it to MeV for display. It maps the same temperature into redshift and cosmic time using the page’s temperature ratio and radiation-era scaling. These deterministic steps make the calculator especially useful for relative comparisons.
A higher decoupling temperature corresponds to a larger redshift and a much earlier cosmic time. A lower temperature points to a later moment in the same radiation-dominated epoch. The three displayed outputs belong together, so a plausible result should move consistently across all of them.
Worked example: neutrino decoupling with the default values
This worked example uses the defaults already placed in the neutrino decoupling form: g* = 10.75 and GF = 1.1663787e-5 GeV⁻². With these assumptions, the calculator returns Tdec ≈ 1.49 MeV, redshift z ≈ 6.33×109, and cosmic time ≈ 3.33×10-1 s. The built-in classification is standard, meaning the estimate falls between this page’s deliberately simple late- and early-decoupling thresholds.
The number is not meant to be a sacred universal value. Its value as an example is that it gives you a clear baseline. Raise g* slightly and the temperature should rise modestly; strengthen GF and the temperature should fall more sharply. If a tiny input change produces an unexpectedly enormous shift, check units and decimal placement before inferring new physics.
Sensitivity check: how neutrino decoupling responds to g* and GF
The live outputs provide the most useful sensitivity check for this neutrino decoupling model. Since Tdec scales as g*1/6 and GF-2/3, increasing g* nudges the temperature and redshift upward while making the inferred freeze-out time earlier. Increasing GF does the opposite: weak interactions remain effective longer, the freeze-out temperature decreases, and the inferred cosmic age increases.
Because redshift and time are derived from the calculated temperature, they should always track it coherently. Higher Tdec means higher redshift and shorter time; lower Tdec means lower redshift and later time. This simple cross-check is a helpful guard against a mistaken interpretation of the scale.
How to interpret a neutrino decoupling result
The result panel presents a compact early-universe snapshot: temperature, redshift, cosmic time, and a descriptive band. Read the label as a quick orientation rather than a detailed physical diagnosis. A late-decoupling result is below the page’s 0.5 MeV threshold, while an early-decoupling result is above 2 MeV; values between those limits are called standard by this calculator.
For several runs, copy the displayed values into notes or a spreadsheet with the g* and GF assumptions beside them. Comparing temperature, redshift, and time together is more informative than comparing any one output alone, and it makes a unit or transcription error easier to spot.
Limitations and assumptions for neutrino decoupling estimates
This neutrino decoupling calculator is a transparent first-pass freeze-out estimate, not a replacement for a detailed numerical cosmology treatment. It captures the central dependence on g* and GF, but it does not model every species threshold, entropy-transfer effect, non-standard particle component, or precision correction that can matter in a research-grade calculation.
Display rounding can also create small differences from a hand calculation. Use the result to bracket a likely decoupling regime, test the direction of a proposed parameter change, and prepare inputs for a fuller model when the physics demands one. That is where a compact estimate is most useful: it makes the core scaling visible before more complicated corrections are introduced.