The same physical reality in Two Higgs doublet model (2HDM) can be described by different Lagrangians. We study this property called by the reparametrization invariance (in space of Lagrangians). We consider the Z2-symmetry of the Lagrangian, which prevents a \phi 1\leftrightarrow \phi 2 transitions, and the different levels of its violation, soft and hard. We argue that softly Z2 violated 2HDM is a natural model in the description of EWSB. We consider different vacua in the 2HDM. We find simple condition for a CP violation in the Higgs sector. In the Model II for Yukawa interactions we obtain the set of relations among the couplings to gauge bosons and to fermions which allows one to analyse different physical situations (including CP violation) in terms of these very couplings, instead of the parameters of Lagrangian. We discuss possible interaction of Higgs fields of the SM or 2HDM with the inflatory scalar field describing an exponential expansion of Universe after Big Bang.
PACS numbers: 14.80.Cp, 12.60.Fr
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