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Physically the cosmological constant may correspond to a mysterious energy field filling the entire universe. With a proper choice of the cosmological constant , the universe was static, neither expanding nor contracting.
It's not mysterious at all. It's simply virtual bosons, mostly virtual light, i.e. photons off-mass-shell both inside and outside the classical light cone.
Subsequently, the redshifts of extragalactic nebulae were reinterpreted as due to the motion of the nebulae. That is, the nebulae, recognized as galaxies outside our galaxy the Milky Way, were flying away from us, causing a redshift of light. Over time, the astronomer Edwin Hubble was able to show that the dimmer the galaxy and therefore presumably the farther away (at least on average) the galaxy, the larger the redshift and thus the faster the galaxy appeared to be running away from the Earth. This rather peculiar observation could be easily explained if the universe was expanding as predicted by the original General Theory of Relativity without the cosmological term (the cosmological constant was either zero or nearly zero).
The cosmological term at large scales is the inverse area of our future event horizon and is, therefore, direct evidence for the holographic principle of 'tHooft and Susskind