# Thread: Why is the cosmological constant a constant?

1. ## Why is the cosmological constant a constant?

Why is the cosmological constant a constant? Is it only to not affect the energy conservation law?

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It's not constant if the cosmological expansion is accelerating.

It's not constant if the cosmological expansion is accelerating.
Not quite. It can still be a constant with the accelerating expansion, it just can't be zero. Whether the cosmological constant is really constant determines whether the rate of that acceleration is changing. (It's a poor example, but think about the value of g, the acceleration due to gravity on the Earth's surface. It's constant, yet objects accelerate, because it's not zero.)

As far as tommac's question goes, we don't know if it's constant or not. There are a number of models proposed, some of which treat it as constant and some of which assume it can vary. At this point, we just don't have sufficient data to determine which of those models might be better.

It's not constant if the cosmological expansion is accelerating.

The cosmological constant is that term which appears as the greek letter Lambda in the two Friedmann Equations. Being constant, then as the expansion scale factor "a(t)" changes in time, it remains constant (unlike the mass-energy density and pressure terms). Another way of looking at it: the ratio energy/volume remains constant for this term, regardless of the value of a(t). Thus its name.

If it dominates the negative term on the RHS of the second Friedmann Equation, then the expansion has a net positive acceleration. In the limit that the Lambda term completely dominates over the negative (pressure and mass-energy density) term in the second Friedmann Equation, then the Hubble Parameter approaches a constant value (counter-intuitive, yet true).

We do not know that the mechanism responsible for the observed accelerated expansion actually behaves as a cosmological constant, but so far this hypothesis is consistent with the observations.

5. Originally Posted by Spaceman Spiff

The cosmological constant is that term which appears as the greek letter Lambda in the two Friedmann Equations. Being constant, then as the expansion scale factor "a(t)" changes in time, it remains constant (unlike the mass-energy density and pressure terms). Another way of looking at it: the ratio energy/volume remains constant for this term, regardless of the value of a(t). Thus its name.

If it dominates the negative term on the RHS of the second Friedmann Equation, then the expansion has a net positive acceleration. In the limit that the Lambda term completely dominates over the negative (pressure and mass-energy density) term in the second Friedmann Equation, then the Hubble Parameter approaches a constant value (counter-intuitive, yet true).

We do not know that the mechanism responsible for the observed accelerated expansion actually behaves as a cosmological constant, but so far this hypothesis is consistent with the observations.
But it is constant because we believe that the acceleration of universal expansion is not changing. However, this is not deduced from Einsteins Field Equations correct?

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That the cosmological constant is a constant is to some extent an accident of history.

In the 1890s, Hugo von Seeliger and C. Neumann both introduced (in different ways) a constant to Newtonian mechanics to create a static model of the universe.

Einstein followed something similar to Seeliger's approach and introduced a generalization to the field equations governing gravity in the form of another term that included the cosmological constant. Now one could have added some function in the place of that constant; adding a constant is simpler than adding a function, and the constant will approximate the action of many functions to some degree of accuracy.

Additionally, to model a static universe, the factor would be unchanging even if this additional factor was the product of a function.

7. Originally Posted by tommac
But it is constant because we believe that the acceleration of universal expansion is not changing.
More precisely, because we don't have evidence that it's changing. But we also know that we don't have as much data as we'd like, so we know that it would be a bit early to suggest that we know for sure that it's constant.

Originally Posted by tommac
However, this is not deduced from Einsteins Field Equations correct?
Einstein added a constant term to his equations. As Kwalish Kid points out, that's the simplest way to add such a term; the most general would be to add an arbitrary function. It makes sense to start with modeling it as a constant term, and then if we find that isn't possible, we can look at the more general option.

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Thanks to each of you for clarifying my perception. I was interchanging the Hubble parameter with the cosmological constant.

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