The cosmological constant is always dimensional less?

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SUMMARY

The discussion centers on the dimensionality of the cosmological constant within the context of Randall-Sundrum models. It is established that the tension T of the brane is expressed as T=24M^3_5 √(-Λ/24M^3_5), where M represents the dimensionality of spacetime. The cosmological constant Λ is confirmed to have dimensions of mass squared across all dimensions, specifically under the conditions where c and ħ are set to 2. The inquiry into the units of the Planck scales M_4 and M_5, as well as the tension T, is also addressed.

PREREQUISITES
  • Understanding of Randall-Sundrum models
  • Familiarity with cosmological constants and their properties
  • Knowledge of Planck scales M_4 and M_5
  • Basic grasp of dimensional analysis in physics
NEXT STEPS
  • Research the implications of the cosmological constant in modern cosmology
  • Study the derivation and applications of the Randall-Sundrum models
  • Explore the relationship between tension and dimensionality in theoretical physics
  • Investigate the significance of Planck units in quantum gravity theories
USEFUL FOR

The discussion is beneficial for theoretical physicists, cosmologists, and students of advanced physics who are exploring the implications of the cosmological constant and brane-world scenarios.

alejandrito29
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the cosmological constant is always dimensional less?

in the randall sundrum models the tension of our brane is

T=24M^3_5 \sqrt{\frac{-\Lambda}{24M^3_5}}...the sub index of M is the number of dimension of space time and the supercript is the power.

¿whats units have the Planck scales M_4 and M_5?...and then...¿whats units have the tension T?
 
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alejandrito29 said:
the cosmological constant is always dimensional less?

in the randall sundrum models the tension of our brane is

T=24M^3_5 \sqrt{\frac{-\Lambda}{24M^3_5}}...the sub index of M is the number of dimension of space time and the supercript is the power.

¿whats units have the Planck scales M_4 and M_5?...and then...¿whats units have the tension T?

The cosmological has dimensions of mass squared in every dimension(units c= hbar=2)

where did you get this equation for T from?
 

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