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:
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.