Well for one thing, the Inflaton field needs to be turned off somehow (since inflation ended), but as far as I know there is no way to turn the Higgs field off.
Or, perhaps the inflaton field is turned off by the Higgs field turning on. For it seems the more mass the universe has the more tendency there would be to contract instead of expand. Could it all be one field whose value reverses?
I think people also think the inflaton mass in something like 10^11-10^13 GeV, so the Higgs is too light. I forget the exact reasoning here though.
There are people who believe they are one and the same. See the link below:
Are the 3 generations of mass for electrons, muon, and tau, for example, due to a difference in how the Higgs field interacts with the an electron? And is the decay of the tau to the muon to an electron due to how the higgs mechanism to a base particle?
I'm not quite sure I understand this. Inflation is caused by any field that is sufficiently dominated by its potential (vacuum energy). This is true of the Higgs field in its false vacuum state. The present universe, however, is not in the Higgs false vacuum, but in some true vacuum that breaks the electroweak symmetry. In this sense, the Higgs field is very much "off", its nonzero VEV notwithstanding. From a conceptual point of view, then, there is nothing wrong with considering the Higgs as a model inflaton: the field starts in the false vacuum during which time the universe inflates, and then rolls down to the true vacuum, at which time the universe stops inflating.
The electroweak Higgs was originally eyed as a potential inflaton candidate, but it doesn't give the right CMB fluctuations. There is much present interest in adding gravitational couplings and non-standard kinetic terms to the electroweak Higgs sector to render a Higgs field viable for inflation.
Hmmm... perhaps I had misunderstood the problem then.
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