Because in the flat space-time (i.e. vacuum or ground state) the cosmological constant is proportional to the T^00. Indeed, according to the Einstein's equation: Lambda g_munu = 8 pi G T_munu / c^4. Thus the expectation of the vacuum energy, i.e. rho^vac= T^00 = Lambda / (8 pi G), where c=1.

The cosmological constant makes a contribution to the Einstein-Hilbert action that is compatible with all symmetries. While its value cannot be predicted within general relativity, it can be measured. The problem is that we do not know how to predict its value theoretically. If we try to *identify* it with the vacuum expectation value of the energy density, computed within the Standard Model, coupled to gravity, the discrepancy between the value computed this way and the value measured is many orders of magnitude; That is one aspect of the problem. One reason we would be tempted to do that is, that in Einstein's equations, the cosmological constant and the energy-momentum tensor both contribute in similar ways. So it's clear that we do not understand many things on this issue and progress is likely to come from trying to find the right questions to ask.

Let's recall that more than a century ago it was proposed that the mass of the electron had a purely electromagnetic origin-and there were many proposals to that effect, that turned out to be wrong. We know now the correct way to frame the question-even though we do not know how to calculate the numerical value of the mass of the electron,itself, yet.

We lack, for the moment, a corresponding insight into the issue of the cosmological constant.

I am writing about essentially what happens when

doing calculations. In a free scalar theory the Hamiltonian

is of the form,

H= int dp w(p) [ a^dagger a + delta(0)/2 ]

here a and a^dagger are raising and lowering operators.

I have suppressed factors of 2 pi. The vacuum is defined as

the state which is destroyed by the lowering operator

a |0>=0

So, has contribution from the second term only

and after integration it diverges. Because we can measure

energy differences only we usually drop second term in the

Hamiltonian which gives rise to infinities.

The problem arises elsewhere, when gravity catches all

masses and energies. In the theory of relativity mass and

energy can be converted to each other. They should contribute

to the RHS of Einstein's equations and contribute to

stress energy tensor. Additional term in the RHS will be

Lambda g_mu nu. Current experimental data says that

Lambda= 10^-12 eV^4

This is much smaller than the scale of VEV of the

Higgs scalar which is 10^11 eV. Thus there is a

large discrepancy. Nobody knows what is the answer.

Stam said "we lack, for the moment, a corresponding insight into the issue of the cosmological constant".

The apparently acute incomprehensibility of the value of the cosmological constant aside, explaining the vacuum energy density is much like the challenge of explaining the value of any other physical constant. There is a need to first understand the nature of the universe.

Mathematical physics has led to no significant insights here. As anyone with a basic familiarity of science should know (even if they are not allowed to say so openly), the anthropic principle is a highly implausible explanation for the biocompatibility of the universe - there are too many examples of fine-tuning that go well beyond the scope of the weak anthropic principle . This civilisation once thought the Earth was literally at the centre of the universe. Now it thinks that human evolution alone can explain the physical constants. It needs to get over this giant ego problem.

What has been lacking for a long time is a non-anthropic explanation for the cosmological constant - not to mention the appetite to hunt for one. So beware, if you are genuinely eager for an answer, you may discover things that do not sit comfortably with the complacent cosmological outlook currently in vogue on this planet.

Article A Non-anthropic Solution to the Cosmological Constant Problem

The answer to the present innocent question is also innocent. One introduces the cosmological constant for a particular reason in order to tweak or control evolution in some realistic sense.

Hence the problem (it is really not a problem, it is much more than a problem) as expressed by Stam:

If we try to *identify* it (the cosmological constant) with the vacuum expectation value of the energy density, computed within the Standard Model, coupled to gravity, the discrepancy between the value computed this way and the value measured is many orders of magnitude.

One way to proceed would be to start with the simplest possible fundamental ansatz, i.e. the Schwarzschild solution (without a cosmological constant) which surprisingly is commensurate with QM observables and their conjugate partners.

This is the original "black hole" item that started modern speculations. Fortunately the modeling does not stop here. One can easily formulate rotational degrees of freedom for black hole objects, cf. molecular rotations in chemical physics.

Adding the richness of a QM compatible black hole formulation is not complicated in itself, the only objection is that cosmologists many times are more at ease in classical modelling of very large spatio-temporal structures, except for Planck scale processes at high energy. The cosmological conundrum finds its place in this environment of incompatibilities.

The problem must be buried very deeply in the sand.

Robin,

You cannot bury absentia.

The cosmological constant can appear on either side of Einstein's field equations. Of course, we know that the universe is definitely not static these days. Nevertheless, there could in principle be two distinct constants - one for each side of the equations. Given the long-standing difficulty of formulating a theory of quantum gravity, it is intriguing that the cosmological constant can be interpreted both in classical and quantum terms, especially since it could be hinting at a potential bridge between the two realms. It is an inescapable prediction of quantum field theory that strong gravitational accelerations should, via the Unruh effect, result in a net influx of energy into the universe. It is difficult to understand this if it does not come at the expense of the vacuum. Some might say that there is nothing of interest here either from a physical or cosmological perspective, but I happen to disagree. When one encounters what is widely regarded as the "worst prediction in all physics" it is hardly appropriate to turn a blind eye. One would hope that a civilisation which openly accepts it does not comprehend 95% of the universe might eventually try heeding the precious clues that nature provides.