Understanding the Role of a(t)*dr in Calculating Actual Distance

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SUMMARY

The discussion focuses on the calculation of proper distance in cosmology, specifically the role of the term a(t)*dr, which represents the elementary length along the radial direction that varies with time. It emphasizes that proper distance changes over time due to the expansion of the universe, causing objects to move further apart. The integration of a(t)*dr and dr is highlighted as a method to determine actual distance at a specific time, with a reference to a detailed breakdown of distance measures in cosmology provided in an external paper.

PREREQUISITES
  • Understanding of cosmological principles and the expansion of the universe.
  • Familiarity with the concept of proper distance in cosmology.
  • Knowledge of mathematical integration techniques.
  • Basic grasp of the terms a(t) and dr in the context of radial distance calculations.
NEXT STEPS
  • Study the integration of a(t)*dr and dr in cosmological models.
  • Explore the implications of the universe's expansion on distance measurements.
  • Review the detailed breakdown of distance measures in the provided arXiv paper.
  • Investigate the differences between proper distance and comoving distance in cosmology.
USEFUL FOR

Astronomers, cosmologists, and physics students interested in understanding the calculations of distances in an expanding universe.

Apashanka Das
actually I want to clarify that is the proper distance a(t)*dr is the elementary length along the radial direction which is changing with respect to time and if integrating a(t)*dr and dr ,which may be considered the actual distance
 
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Apashanka Das said:
actually I want to clarify that is the proper distance a(t)*dr is the elementary length along the radial direction which is changing with respect to time and if integrating a(t)*dr and dr ,which may be considered the actual distance
What is done in these coordinates is to fix the calculation to be at a specific time. The proper distance will be different at different times because the universe is expanding, meaning objects within the universe are getting further apart.

Anyway, if you want a good, detailed breakdown of the distance measures used in cosmology, this is a good summary:
https://arxiv.org/pdf/astro-ph/9905116.pdf
 
actually what is the difference between dr and a(t)*dr in terms of distance?Which shall be considered the exact distance between two points say at time t?
 
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