GR & The Cosmological Constant

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Discussion Overview

The discussion revolves around the relationship between the cosmological constant and the dimensionality of spacetime in the context of General Relativity (GR). Participants explore whether the cosmological constant must be adjusted when considering calculations in higher dimensions, as well as the implications of such adjustments.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions if the cosmological constant needs to change when working with higher dimensions in relativity, indicating a curiosity about dimensionality in calculations.
  • Another participant clarifies that GR is set in four-dimensional spacetime and states that the cosmological constant does not depend on the number of dimensions used in calculations.
  • Some participants agree that the cosmological constant is independent of the number of dimensions, emphasizing that GR operates within a four-dimensional framework due to observational limits.
  • A different viewpoint suggests that while the Einstein-Hilbert action can be defined in more than four dimensions, it is uncertain whether the cosmological constant remains unchanged, noting that interpretations of its nature may vary in higher dimensions.

Areas of Agreement / Disagreement

There is some agreement that the cosmological constant does not depend on the number of dimensions in spacetime. However, there is disagreement regarding the implications of higher dimensions on the nature of the cosmological constant and whether it remains unchanged.

Contextual Notes

Participants express uncertainty about the implications of defining the cosmological constant in higher dimensions and the potential changes in interpretations that may arise from such considerations.

General_Relativity21
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When we approach a calculation in relativity, do we have to change the cosmological constant in order to work with bigger dimensions? Because i know we are limited to seeing 1, 2 and 3 dimensions, i was just curious if you wanted to figure out an answer using an equation based on a bigger dimension in relativity, i was guessing that the cos constant had to change also? :confused:
 
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Welcome to Physics Forums General_Relativity21!

This is an interesting question, and seems to relate strongly to GR, so I am moving the thread to the S&GR section, where I think you will quickly get a good answer.
 
The setting of GR is four-dimensional spacetime. It is possible to work with fewer then four dimensions, but not more then four (in General Relativity).

The cosmological constant does not depend on the number of dimensions in which you are calculating.
 
Agreed, the cosmological constant has nothing to do with the number of dimensions in space-time. We work with 3 spatial dimensions and one time dimension in GR because that's what we see. Because space and time can "intermix" depending on the observer, we say that in GR we work with a 4-dimensional "space-time continuum".
 
As far as I know you can define the Einstein-Hilbert action (which leads to general relativity) in more than 4 dimensions. I don’t know whether the cosmological constant remains unchanged or not, but it is for sure that possible interpretations of its nature change in such a case. May be this is a question for the string forum.
 

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