The cosmological constant is always dimensional less?

In summary, in the Randall-Sundrum models, the tension of the brane is given by the equation T=24M^3_5 \sqrt{\frac{-\Lambda}{24M^3_5}}, where the sub index of M represents the number of dimensions of space-time and the superscript is the power. The Planck scales M_4 and M_5 have units of mass, while the tension T is dimensionless. This equation can be derived from the cosmological constant and has units of mass squared in every dimension.
  • #1
alejandrito29
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the cosmological constant is always dimensional less?

in the randall sundrum models the tension of our brane is

[tex]T=24M^3_5 \sqrt{\frac{-\Lambda}{24M^3_5}}[/tex]...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 [tex]M_4[/tex] and [tex]M_5[/tex]?...and then...¿whats units have the tension [tex]T[/tex]?
 
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  • #2


alejandrito29 said:
the cosmological constant is always dimensional less?

in the randall sundrum models the tension of our brane is

[tex]T=24M^3_5 \sqrt{\frac{-\Lambda}{24M^3_5}}[/tex]...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 [tex]M_4[/tex] and [tex]M_5[/tex]?...and then...¿whats units have the tension [tex]T[/tex]?

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

where did you get this equation for T from?
 

Related to The cosmological constant is always dimensional less?

1. What is the cosmological constant?

The cosmological constant is a term in the equations of general relativity that represents the energy density of the vacuum of space. It was first introduced by Albert Einstein as a way to explain the observed expansion of the universe.

2. Why is the cosmological constant always dimensionless?

The cosmological constant is always dimensionless because it is a ratio of two quantities with the same units. In the case of the cosmological constant, it is the ratio of the energy density of the vacuum to the energy density of matter. Since both of these quantities have the same units, the cosmological constant is dimensionless.

3. How does the cosmological constant affect the expansion of the universe?

The cosmological constant plays a major role in the expansion of the universe. It is responsible for the accelerated expansion of the universe, which was confirmed by observations of distant supernovae in the late 1990s. Without the cosmological constant, the expansion of the universe would eventually slow down and potentially even reverse.

4. Is the value of the cosmological constant constant?

Despite its name, the value of the cosmological constant is not constant. It can vary over time and is affected by the energy density of the universe. In fact, the current value of the cosmological constant is much smaller than what was predicted by early theories, leading to the need for new explanations such as dark energy.

5. How does the cosmological constant relate to dark energy?

The cosmological constant is often referred to as a form of dark energy. This is because it is a mysterious force that is thought to be responsible for the observed accelerated expansion of the universe. However, the cosmological constant is just one possible explanation for dark energy and there is still ongoing research to understand its nature and effects on the universe.

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