Cosmology Suite Calculator

The simple v = H₀d / d = cz form only holds at low redshift, where the universe's expansion rate hasn't changed much since the light was emitted. At higher z the expansion rate E(z) = √(Ωm(1+z)³ + ΩΛ) varies significantly over the light's travel time, so this calculator numerically integrates 1/E(z) with Simpson's rule across 1,000 subdivisions to get an accurate comoving distance instead of relying on the linear shortcut, which would understate distances at larger redshifts.

The mode checks your entered time-since-Big-Bang against thirteen threshold boundaries — from the Planck Epoch through Galaxy Formation Era — because each era in the standard cosmological model is defined by which physics dominated then, not by a continuous formula. Alongside the epoch name, it still computes a continuous temperature from T ∝ 1/a using your scale factor input, since photon temperature genuinely does scale smoothly with expansion even though the named eras are discrete categories.

It sums your three density inputs (Ωb + Ωdm + ΩΛ) into Ωtotal and checks it against 1: with dark energy present and Ωtotal ≥ 1 it reports accelerating expansion, with no dark energy and Ωtotal > 1 it reports a Big Crunch, and with Ωtotal < 1 it reports an open, eternally expanding universe. It also computes a deceleration parameter q₀ = (Ωm+Ωdm)/2 − ΩΛ, where a negative value confirms acceleration is currently underway — matching current cosmological measurements.

At zero spin the calculator uses the plain Schwarzschild formulas, but a nonzero spin parameter switches it to the Kerr solution, where r₊ = GM/c² × (1 + √(1 − a²)) shrinks the event horizon compared to a non-spinning hole of the same mass. The innermost stable circular orbit shifts too — the code's iscoFactor ranges continuously from 1 up toward 9 (times GM/c²) depending on spin direction and magnitude, versus the fixed 6× factor used for a non-rotating (Schwarzschild) black hole.

All modes default to H₀ ≈ 70 km/s/Mpc, a commonly used round-number value, but real measurements disagree — Planck's cosmic microwave background analysis gives about 67.4, while local supernova-based (SH0ES) measurements give about 73.0. This unresolved gap is the "Hubble tension," and because H₀ appears directly in distance, age, and lookback-time calculations throughout every mode, swapping between these values will meaningfully shift your results, especially at higher redshift.