Cosmology and astrophysics

The Big Bang model and Hubble’s law

On sufficiently large nearby-universe scales, a galaxy’s average recession speed is proportional to distance. Redshift is an observational signature, not an explosion from a center.

v ≈ H₀ d; z=(λobs−λém)/λém. At small z, v≈cz.

Definition: Hubble constant H₀

H₀ is today’s expansion rate, commonly expressed in km s⁻¹ Mpc⁻¹. The linear relation v≈H₀d is a local approximation; at large distances one uses cosmological models and redshift.

Adjust parameters to explore the physical relation. The illustration is schematic, not to astronomical scale.

Model and observations

H₀ is today’s expansion rate, commonly expressed in km s⁻¹ Mpc⁻¹. The linear relation v≈H₀d is a local approximation; at large distances one uses cosmological models and redshift.

Example: A quick estimate

Use the relation above to predict the trend when one parameter changes, then check it in the simulation.

Solution

Hold other quantities fixed and apply the equation. The simulation illustrates a trend; it does not replace real data or uncertainty analysis.

In an FLRW model, the comoving distance $\chi$ of an ideal galaxy stays fixed while its proper distance is $D(t)=a(t)\chi$ . Its recession speed from expansion is therefore $v_{\rm rec}=H(t)D$ , not motion through space from an explosion center. At small redshift, combining $v\simeq cz$ with Hubble’s law estimates distance; at large redshift one must integrate the expansion history and distinguish coordinate recession from a convention-dependent inferred speed.

Evidence for the Big Bang is a network of independent tests: observed expansion, the CMB’s near-blackbody spectrum, light-element abundances, and the growth of structure. Hubble measured the redshift–distance relation in galaxies; Einstein supplied the general-relativistic framework for cosmological models. The cosmic age is not simply $1/H_0$ : it depends on the full history $H(a)$ , the matter content, and spatial curvature. An $H_0$ measurement must therefore be interpreted within a model and compared with independent methods.

Quick check

What is the best use of the simulation or equation?

What should be considered when drawing conclusions about an astronomical phenomenon?

References

Bradley W. Carroll and Dale A. Ostlie (2017). An Introduction to Modern Astrophysics