# Attractive higgs force and inflation

Inflation was the extreme accelerating expansion of the universe, see here: http://en.wikipedia.org/wiki/Inflation_(cosmology) It worked in a similar way to dark energy but was so strong it would easily tear atoms apart (if it wasn't far to hot for atoms to form in the first place).

The weird thing about inflation and dark energy is that they are under tension.

[Optional reading]: Explanation of how pressure works backwards in general relativity

In general relativity, pressure itself is attractive. This is not because it takes energy to compress materials, the energy put in to compressing something simply shows up as extra mass. This is an extra effect.

Suppose you dive deep into a (non-rotating) neutron star (pretend the center is liquid) and measure the central density (as a swimmer would gauge the inertial resistance of water). You then move 1mm away from the core, release a pellet of dark matter (which goes right through everything so it has no buoyancy), and measure the acceleration towards the center (because of the shell theorem and the slow maximum speed of the pellet (~10 m/s), you can assume newtonian gravity in the local vicinity).

The measured acceleration will be greater than the calculated acceleration, up to almost twice as much. This is a consequence of light bending twice as much as "expected" and can be derived from special relativity using a reference frame with constant acceleration.

Pressure is equivalent to an exchange of fast-moving particles. These "virtual" particles "bend more" toward a mass and conversely the mass is pulled back more toward it. The inflation field was under enormous tension, which is the exchange of negative mass particles, and it created a repulsion. Another effect is that work must have been done on the inflation energy as space expanded, just as it energy is added to a rubber band when you pull on it. This work showed up as more inflation energy, and meant that it does not dilute when space expands. Eventually, the pressure/density ratio, (equation of state) went above the critical value of -1 and the field began to dissipate. The -1 "critical value" also causes that the fluid to be Lorentz invariant, which means there is no preferred reference frame.

The question itself

The Higgs particle is a purely attractive force, see here:

http://profmattstrassler.com/articles-and-posts/particle-physics-basics/the-known-forces-of-nature/the-strength-of-the-known-forces/

Could the Higgs force create a strong enough tension (perhaps with help from other forces?) to overwhelm the positive pressure effects of quantum degeneracy and heat and leave enough tension to cause inflation? If so you would not need GUT or TOE speculations for the mechanism of inflation. Furthermore, you could quantify it's strength and the nature of it's eventual decay.

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I think there is another forum for this sort of question. –  DWin Jul 17 '14 at 23:50

## 1 Answer

You are slightly misinterpreting some words by Prof Matt Strassler. He says that the force mediated by the exchange of the Higgs bosons – the "Higgs force" – is attractive, much like gravity between two ordinary positive-mass objects.

But that doesn't mean that "everything" in the presence of a Higgs field is attractive. Indeed, the Higgs potential contributes a term to the stress-energy tensor that is proportional to $g_{\mu\nu}$, and it therefore includes a negative pressure whose magnitude is equal to the energy density.

At this qualitative level, the Higgs field behaves just like the inflaton. The negative pressure acts in a "repulsive" way and may cause the exponentially accelerating expansion of the Universe.

However, the detailed shape of the potential and the energy scale associated with the Higgs field and the Higgs boson is generally different than what one needs for inflation, so the general expectation is that the ordinary Higgs field known from its 125 GeV Higgs bosons isn't capable of producing inflation. This viewpoint is (or would be) strengthened by the discovery of the primordial gravitational waves by BICEP2 which would indicate that the energy density during inflation was huge, near the GUT scale, and therefore much higher than the energy densities expected from the relatively light 125 GeV Higgs boson's field.

On the other hand, there are semirealistic models that use the ordinary Higgs field as an inflaton, too. They typically add some new coupling of the field to the curvature. See e.g.

http://arxiv.org/abs/0710.3755

and its references and followups. Such models could be very economical when it comes to the field content but this attractive feature is compensated by the awkward interactions one has to add. Moreover, there are other reasons to think that new physics does occur at the GUT scale so particle physicists generally don't view GUT as a liability at all. Grand unification helps (or would help) to explain and unify many other things in physics.

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Thanks for the thorough answer, and the experimental results that show a GUT scale inflation. –  Kevin Kostlan Jul 18 '14 at 13:06