Friedmann Equation Calculator: Universe Expansion & Pressure Dynamics

Calculate Cosmic Acceleration Using the Friedmann Equation

kg/m³
Input the total mass-energy density of the universe (e.g., critical density approx. 9.9e-27 kg/m³).
Pa
Input the total pressure in Pascals. For a dust-dominated universe, P≈0. For radiation, P = ρc²/3.

Unravel the mysteries of cosmic evolution with our Friedmann Equation Calculator based on pressure. This advanced tool allows you to quantify the universe's acceleration by considering its total mass-energy density and pressure. Gain insights into how pressure influences the cosmos, vital for cosmology and astrophysics research.

Formula:

Friedmann Acceleration Equation

The Friedmann acceleration equation, incorporating pressure, is a fundamental equation in physical cosmology that describes the acceleration of the universe's expansion. It is given by:

\[ \frac{\ddot{a}}{a} = - \frac{4\pi G}{3} \left( \rho + \frac{3P}{c^2} \right) \]

  • ä/a: Cosmic acceleration (inverse seconds squared, s⁻²). A negative value indicates deceleration, positive indicates acceleration.
  • G: Gravitational Constant (approximately 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻²)
  • c: Speed of Light in vacuum (approximately 2.998 × 10⁸ m/s)
  • ρ (rho): Total Mass-Energy Density of the universe (kg/m³)
  • P: Total Pressure within the universe (Pascals, Pa or N/m²)

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