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Cambridge 0625 IGCSE  ·  Topic E6.7

E6.7 Cosmology: Redshift, CMBR, the Hubble Constant, and Expanding Space

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Cosmology is the scientific study of the origin, evolution, and ultimate fate of the Universe. Observational discoveries over the past century—specifically galactic redshift and cosmic microwave background radiation—have transformed theoretical cosmology into a quantitative physical science within Cambridge IGCSE Physics.

01 — Explanation

Core Principles of Cosmological Expansion

The Universe is not static; it is undergoing metric expansion. Space itself is stretching, causing galaxies that are not gravitationally bound together to move away from one another.

Galactic Redshift

When light emitted by distant galaxies is analyzed using spectroscopy, characteristic absorption line patterns are shifted toward longer, redder wavelengths relative to laboratory reference spectra on Earth. This phenomenon is known as redshift.

Redshift occurs because as electromagnetic waves travel through expanding space, the wavelength (λ\lambda) of the photons is stretched during transit:

Redshift z=λobserved−λemittedλemitted\text{Redshift } z = \frac{\lambda_{\text{observed}} - \lambda_{\text{emitted}}}{\lambda_{\text{emitted}}}

The greater the redshift observed in a galaxy's spectrum, the faster that galaxy is receding from Earth.

02 — Explanation

Detailed Breakdown and Cosmological Mathematics

1. Hubble's Law

In 1929, Edwin Hubble discovered a direct linear relationship between the recession velocity (vv) of a distant galaxy and its distance (dd) from Earth:

v=H0dv = H_0 d

where H0H_0 is the Hubble Constant. The Hubble constant measures the rate of expansion of the Universe.

  • The currently accepted value for the Hubble Constant in SI units is:
H0≈2.2×10−18 s−1H_0 \approx 2.2 \times 10^{-18}\text{ s}^{-1}

2. Estimating the Age of the Universe

If the Universe has been expanding at a uniform rate since its inception, tracing the motion of receding galaxies backward in time indicates that all matter in the Universe was concentrated at a single point (a gravitational singularity) at time t=0t = 0.

Using v=H0dv = H_0 d, the time tt elapsed since the Big Bang (the age of the Universe) can be calculated as:

t=dv=1H0t = \frac{d}{v} = \frac{1}{H_0}

Substituting H0=2.2×10−18 s−1H_0 = 2.2 \times 10^{-18}\text{ s}^{-1}:

t=12.2×10−18 s−1≈4.55×1017 s≈13.8 billion yearst = \frac{1}{2.2 \times 10^{-18}\text{ s}^{-1}} \approx 4.55 \times 10^{17}\text{ s} \approx 13.8 \text{ billion years}

3. Cosmic Microwave Background Radiation (CMBR)

The Big Bang Theory is further confirmed by Cosmic Microwave Background Radiation (CMBR).

  • CMBR is isotropic microwave radiation filling all points in space around us.
  • It represents thermal remnant radiation emitted roughly 380,000 years after the Big Bang when the Universe cooled sufficiently for neutral atoms to form (recombination).
  • Originally emitted as high-energy gamma and ultraviolet radiation, the wavelengths of these photons have been stretched by a factor of 1100 over 13.8 billion years of spatial expansion into the microwave region, matching a blackbody spectrum at T≈2.725 KT \approx 2.725\text{ K}.

03 — Explanation

Real-World Context and Astronomical Instrumentation

Modern cosmological measurements rely on space telescopes such as the James Webb Space Telescope (JWST) and the Planck satellite. JWST observes deep-space galaxies in high-resolution infrared to detect ultra-high redshift light (z>10z > 10) emitted over 13 billion years ago, allowing astronomers to observe the earliest galaxy formations following the Big Bang.

04 — Explanation

Key Terms and Definitions

TermSymbol / UnitDefinition
Redshift (zz)DimensionlessLengthening of light wavelengths caused by spatial expansion.
Hubble Constant (H0H_0)s−1\text{s}^{-1} (2.2×10−18 s−12.2 \times 10^{-18}\text{ s}^{-1})Ratio of a galaxy's recession speed to its distance from Earth.
Age of Universe (tt)Second (s), YearsEstimated as t=1/H0≈13.8 billion yearst = 1/H_0 \approx 13.8\text{ billion years}.
CMBRMicrowave spectrumThermal remnant radiation from the early Universe filling all space.

05 — Explanation

Conclusion

Galactic redshift and Cosmic Microwave Background Radiation provide compelling empirical proof of an expanding Universe. Utilizing Hubble's Law (v=H0dv = H_0 d) allows physicists to calculate the Hubble constant and accurately estimate the age of the cosmos at 13.8 billion years.