# how is cosmological constant used in equations? [closed]

People say that they use cosmological constant in an equation to remove a non required value. For example, the cosmological constant $\Lambda$ appears in Einstein's field equation in the form of:

$$R_{\mu \nu} -\frac{1}{2}R\,g_{\mu \nu} + \Lambda\,g_{\mu \nu} = {8 \pi G \over c^4} T_{\mu \nu}$$

But then how can we just put a value in an equation and remove some other value like in the case of the cosmological constant?

For example, if I build a house and after building I notice that the dimensions of a certain room in the building is not right I just cant write in my blue print that my dimensions are wrong. I have to actually go and make it correct. But here we are just putting a value and eliminating some other value. So if anyone can tell me how this thing happens I will really appreciate that.

## closed as unclear what you're asking by Ben Crowell, Brandon Enright, JamalS, ACuriousMind♦, NeuneckNov 14 '14 at 14:02

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• "...*remove some other value like in the case of the cosmological constant*": what do you believe has been removed here? – WetSavannaAnimal Nov 14 '14 at 10:47

Einstein's equation is a mathematical model devised to provide an approximate description of the universe. We know it's approximate because it generically predicts singularities that we believe to be unphysical, and it takes no account of quantum mechanics.

So the question is whether the equation:

$$R_{\mu \nu} -\frac{1}{2}R\,g_{\mu \nu} + \Lambda\,g_{\mu \nu} = {8 \pi G \over c^4} T_{\mu \nu} \tag{1}$$

is a better approximation to the real world than the equation:

$$R_{\mu \nu} -\frac{1}{2}R\,g_{\mu \nu} = {8 \pi G \over c^4} T_{\mu \nu} \tag{2}$$

The only way to tell which is the better approximation is by experiment. Prior to the observation of cosmic acceleration equation (2) seemed to be a perfectly good description of the universe, but once the acceleration had been measured equation (1) is a better approximation than equation (2).

Your analogy of the house is misleading because a blueprint is used to construct the house, but Einstein's equation wasn't used to construct the universe. A better analogy would be to make a plan of an existing house. Suppose you make a plan of a house, but a bit later you notice that the size of a room on the plan isn't the same as the size of the actual room. Obviously you made a mistake when drawing up the plan, so you change the plan. You can think of Einstein's equation as a plan of the universe. When cosmic acceleration was observed this showed the plan was wrong so we had to modify it by adding the cosmological constant.

• The cosmological constant is not a constant value, it's what we use to describe the propulsion effect of dark energy on the expansion of the universe, in comparison to the gravity pulling the universe back together. Dark energy itself may be a form of energy that has it's own gravity, changing the equations for how much propulsion it takes to overcome what amount of gravity, all forms of propulsion have limits, and it is impossible to know how much dark energy there is, because if there was more, there would also be more gravity, and the only reason we know it's there at all, is it must be. – rowanman28 Mar 3 '15 at 4:56