# Gravity and the Higgs Field

1. Jul 14, 2012

### FesterCluck

Can anyone speak to what effects gravity would have on the Higgs field or vice versa? As I understand, the Higgs field exists as a non-zero base energy field. A second assumption is being passed around that this field is "constant value across the entire universe", which simply doesn't compute well with our current observations on gravity.

I'm refraining from layman speculation, and I'll ask those who respond to do the same. While we may not have experimental examples yet, I'm also very interested in mathematical conclusions which have been reached.

2. Jul 14, 2012

### tom.stoer

The Higgs field behaves exactly the same way as other quantum fields w.r.t. gravity.

Today we are simply not able to calculate the vacuum energy density of quantum fluctuations correctly; in some sense the energy density has to be set to zero by hand. We have some procedures like subtracting a constant like in classical field theory, normal ordering of operators, renormalization ... So basically in QFT we always subtract a constant term such that the energy density in vacuum is exactly zero. We can do this w/o changing e.o.m. or any other prediction of the theory. Think about a particle moving in a potential V(x); now subtract V(x)-const.; the particle will move in exactly the same way b/c it feels the same force. So in QFT we chose 'const' such that the vacuum energy density is zero everywhere. And we can change this 'const' for energy w/o affecting the vacuum value of the field.

Therefore we know the vacuum value of the Higgs field (its responsible for its mass and the mass of other particles), we know its energy density (zero), and therefore we can expect that vacuum does not "produce any gravity", regardless whether there is a Higgs or not.

But there is indeed one interesting question, namely how to calculate this "const" from a quantum field theory or in the context of quantum gravity. Unfortunately today we are not able to do this; we either get infinite results - or finite results which are nonsense physically. So calculating the vacuum energy density - which may be related to the cosmological constant and dark energy - is an unsolved problem today.

3. Jul 14, 2012

### Eonic

If I understand your question correctly, you want gravity to pull at the Higgs field resulting in 'more field' around massive objects and 'less field' in empty space.

Two reactions:
1) The Standard Model is the same at every point in space: particles have the same properties and follow the same laws at every point. The Standard model also determines the value of the Higgs field and it does not allow spacial variations. The masses of particles also depend on the value of the Higgs field and those are the same everywhere.

2) The energy of the Higgs field is not a reality on the cosmological scale. Cosmologically the observed vacuum energy is much much smaller than the total Standard Model prediction.