Author Jonathan David
Author Jonathan David
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Particle Physics and Cosmology: The Beginning of Time

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Particle Physics and Cosmology: The Beginning of Time

Citation: The content below is based on the most recent edition of University Physics with Modern Physics.

Important Formulas

  • Planck Energy:

        \[E_p = \sqrt{\frac{\hbar c^5}{G}}\]

  • Hubble’s Law:

        \[v = H_0 d\]

  • Friedmann Equation:

        \[\left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3} \rho - \frac{k}{a^2} + \frac{\Lambda}{3}\]

  • Critical Density:

        \[\rho_c = \frac{3 H_0^2}{8 \pi G}\]

  • Redshift Formula:

        \[1 + z = \frac{\lambda_{\text{observed}}}{\lambda_{\text{emitted}}}\]

  • Cosmic Microwave Background Temperature:

        \[T(t) \propto \frac{1}{a(t)}\]

Key Terms and Definitions

  • Planck Epoch: The earliest period in the universe’s history, from time zero to approximately 10^{-43} seconds, where quantum effects of gravity were significant.
  • Hubble’s Constant (H_0): The proportionality constant in Hubble’s Law that describes the rate of expansion of the universe.
  • Friedmann Equation: A set of equations derived from Einstein’s field equations that describe the expansion of the universe.
  • Cosmic Microwave Background (CMB): The remnant radiation from the Big Bang, providing a snapshot of the universe at approximately 380,000 years old.
  • Redshift (z): The increase in wavelength (and corresponding decrease in frequency) of light from distant galaxies due to the expansion of the universe.
  • Critical Density (\rho_c): The density of matter and energy required for the universe to be flat.

Example

Consider a galaxy located 10^{6} \, \text{Mpc} away. If the Hubble constant is 70 \, \text{km/s/Mpc}, find the galaxy’s recession velocity:

Using Hubble’s Law:

    \[v = H_0 d\]

Substituting values:

    \[v = 70 \, \text{km/s/Mpc} \cdot 10^6 \, \text{Mpc}\]

Result:

    \[v = 7 \times 10^7 \, \text{km/s}\]

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