Cosmological Calculator

Explore the expansion history of the universe and calculate key cosmological parameters

Adjust parameters to explore different universe models

km/s/Mpc
Current value: 67-74 km/s/Mpc
Includes dark matter and baryonic matter
Cosmological constant/dark energy
Measure of cosmic expansion
Age of Universe
13.8
Billion years
Critical Density
8.7e-27
kg/m³
Lookback Time
7.7
Billion years
Luminosity Distance
6,700
Megaparsecs (Mpc)
Hubble Time
13.9
Billion years
Hubble Length
4,300
Megaparsecs (Mpc)
Curvature Density
0.00
Ωₖ
Radiation Density
9e-5
Ωᵣ
Cosmological Principles

The Lambda-CDM model is the standard model of Big Bang cosmology:

  • Homogeneity: The universe is uniform at large scales
  • Isotropy: The universe looks the same in all directions
  • Cosmic Expansion: The universe is expanding
  • Dark Energy: Responsible for accelerated expansion
  • Dark Matter: Explains galactic rotation curves
  • Cosmic Microwave Background: Remnant radiation from the Big Bang
Cosmological Formulas
H(z) = H₀ √[Ωₘ(1+z)³ + Ωᵣ(1+z)⁴ + Ωₖ(1+z)² + ΩΛ]
t = ∫ dz / [H(z) (1+z)]
ρ_c = 3H² / (8πG)
D_L = (1+z) c ∫ dz / H(z)
Where:
H(z) = Hubble parameter at redshift z
H₀ = Hubble constant
Ωₘ = Matter density parameter
Ωᵣ = Radiation density parameter
Ωₖ = Curvature density parameter
ΩΛ = Dark energy density parameter
ρ_c = Critical density
D_L = Luminosity distance
Cosmic Timeline
Event Time Redshift (z) Temperature
Big Bang 0 ∞ 10³² K
Inflation 10⁻³⁶ s 10²⁶ 10²⁷ K
Quark Formation 10⁻⁶ s 10¹³ 10¹³ K
Nucleosynthesis 3 min 10⁹ 10⁹ K
Recombination 380,000 yr 1100 3000 K
First Galaxies 400 million yr 20 60 K
Today 13.8 billion yr 0 2.7 K
Key Experiments

Our understanding of cosmology comes from key experiments:

  • Hubble's Law (1929): Discovered cosmic expansion
  • CMB Discovery (1965): Confirmed Big Bang theory
  • COBE Satellite (1992): Measured CMB anisotropies
  • Supernova Surveys (1998): Discovered dark energy
  • Planck Satellite (2013): Precise CMB measurements
  • LIGO/Virgo (2015): Detected gravitational waves

Universe Composition

Component Percentage Density
Dark Energy 68.3% 6.9×10⁻²⁷ kg/m³
Dark Matter 26.8% 2.7×10⁻²⁷ kg/m³
Baryonic Matter 4.9% 4.9×10⁻²⁸ kg/m³
Radiation 0.005% 5×10⁻³¹ kg/m³

Frequently Asked Questions

Redshift occurs when light is stretched to longer wavelengths as objects move away from us, indicating expansion.

Blueshift occurs when light is compressed to shorter wavelengths as objects move toward us, indicating approach.

In astronomy, redshift is much more common due to the expansion of the universe.

Redshift is highly accurate for measuring relative distances to distant galaxies:

  • For nearby galaxies (z < 0.1), accuracy is within 5-10%
  • For distant galaxies (z > 1), accuracy depends on Hubble constant value
  • At cosmological distances, factors like dark energy affect accuracy

Redshift remains the most reliable method for measuring distances beyond our local galactic group.

Yes, redshift measurements are crucial for determining the age of the universe:

  • The highest redshift objects provide information about the early universe
  • CMB radiation at z≈1100 gives us a snapshot of the universe at 380,000 years old
  • By combining redshift data with cosmic expansion models, scientists estimate the universe is 13.8 billion years old

Redshift measurements of distant supernovae also helped discover the accelerating expansion of the universe.

The current record holders for highest observed redshift:

  • GN-z11 galaxy: z = 11.1 (observed by Hubble Space Telescope)
  • HD1 galaxy: z ≈ 13 (candidate observed by Subaru Telescope)
  • Cosmic Microwave Background: z ≈ 1100 (not a single object but the entire universe)

With the James Webb Space Telescope, astronomers expect to find galaxies at z > 15, corresponding to when the universe was less than 300 million years old.

Dark energy significantly impacts redshift measurements and interpretation:

  • Dark energy causes the acceleration of the universe's expansion
  • At high redshifts (z > 1), the expansion was slowing due to gravity
  • At lower redshifts (z < 1), dark energy dominates and causes acceleration
  • This transition is visible in redshift-distance relationships

The discovery of dark energy came from observing that distant supernovae at z ≈ 0.5 were fainter (thus farther) than expected in a decelerating universe.

Hubble Constant Measurements

Method Value (km/s/Mpc) Year
Hubble (1929) 500 1929
Baade (1952) 250 1952
Sandage (1958) 75 1958
HST Key Project 72 2001
Planck Satellite 67.4 2018
SH0ES Project 73.2 2021