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I know that the cosmological constant was developed as an addition to the Einstein Field Equation as an anti-gravity force: $$R_{\mu \nu} - \frac{1}{2} R g_{\mu \nu} + \Lambda g_{\mu \nu} = \frac{8 \pi G}{c^4} T_{\mu \nu}$$

so that he could get a static universe. But later it was discarded. And now it is related to dark energy.

But what exactly does the cosmological constant mean. Is it a measure of the amount of dark energy? If so, how can we measure it? Please note that I want to know the physical meaning of the constant in our universe (but some mathematical exposure can be helpful anyway)

NOTE: The answer given here: What does the 'cosmological constant' represent? is more inclined towards the fact that the cosmological constant was developed as a tool to keep the universe static, or that it represents curvature where $T_{\mu \nu} = 0$, but what I am looking for is what do we think of the cosmological constant today? I am not asking how or why it crops up in the EFE, or why it was developed to make sense of a solution to the EFE, but simply what it really is, physically?

PNS
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The cosmological constant is a measure of the (uniform) energy density associated with space: it is how much "intrinsic energy" each parcel of space has, just matter has an energy associated with it due to its mass. Because of how the equation is typically written, it is not directly given in units of energy density, however

$$\rho_0 = \frac{c^2 \Lambda}{8\pi G}$$

is in units of energy density. For the empirically measured value of $\Lambda \approx 1.1056 \times 10^{-52}\ \mathrm{m^{-2}}$, $\rho_0 \approx 5.9238 \times 10^{-27}\ \mathrm{J/m^3}$ or if you like, $5.9238\ \mathrm{J/Gm^3}$. Thus, each cubic gigameter (a cube of roughly similar volume to our Sun) of space holds a bit less than six joules of inherent energy simply due to its being space itself.

The_Sympathizer
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