Why is it necessary to hypothesize a new scalar field, the inflaton field, in order to explain the inflation? In what way, does it differ from the Standard model Higgs field?
The Big Bang cosmological model is based on all the particle physics knowledge up to now, the nuclear physics, thermodynamics etc in order to describe the history of the universe. It is a model based on General Relativity, and General Relativity is a classical, not a quantized theory.
Partly in response to the problems in cosmological models known as the "flatness problem" and the "horizon problem", Alan Guth proposed a period of extraordinary inflation at an early stage of the "Big Bang" expansion of the universe.
An effective quantization of gravity is assumed for that very early period in the history of the universe.
Triggered by the symmetry breaking that separates off the strong force, models suggest an extraordinary inflationary phase in the era 10^-36 seconds to 10^-32 seconds. More expansion is presumed to have occurred in this instant than in the entire period ( 14 billion years?) since.
Already one is discussing an extension of the standard model of particle physics, into GUT, Grand unified theories. Such an extension will certainly have a larger number of Higgs mesons.
The reason one is talking of an inflaton instead of a Higgs is because it is an effective quantization of gravity that is proposed, not of particle physics. It may be if and when a unified theory is developed for all four forces, the infaton may be a type of Higgs, but at the moment this is a matter of research. Certainly if one is in the energy range of symmetry breaking of the strong force, one is beyond the standard model .
Quantization of gravity is successful in string theories, and also the embedding of the standard model symmetries. It may be that further research in this field will shed light on the need or not of a separate inflaton field. At the moment it seems to be assumed as necessary . This review may help.