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However, inflation is just the cosomological paradigm, not a theory! The known field-theoretical mechanisms of inflation use a slow-roll scalar field φ (called inflaton) with proper scalar potential V(φ) (12; 13). The scale of inflation is well beyond the electro-weak scale, ie. is well beyond the Standard Model of Elementary Particles! Thus the inflationary stage in the early universe is the most powerful High-Energy Physics (HEP) accelerator in Nature (up to 1010 TeV). Therefore, inflation is the great and unique window to HEP! The nature of inflaton and the origin of its scalar potential are the big mysteries. Throughout the paper the units ¯ h = c =.

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