Can Non-Adiabatic Perturbations Arise After Single-Field Inflation?

It is shown that non-adiabatic cosmological perturbations cannot appear during the period of reheating following inflation with a single scalar inflaton field. Electronic address: [email protected] According to a widely adopted picture [1], the perturbations to the Robertson– Walker cosmology arose from the quantum fluctuations in a slowly rolling scalar “inflaton” field during a period of inflation, then became classical as their wavelength was stretched beyond the horizon, and subsequently were imprinted on the decay products of the inflaton during a period of “reheating.” One of the attractions of this picture (and in particular the assumption that there is just one inflaton field) is that it has generally been thought to lead only to adiabatic perturbations, in agreement with current observations [2]. A recent preprint [3] has raised the question, whether it is possible for non-adiabatic cosmological perturbations to arise during reheating even after inflation with a single inflaton field. This would be very important if true, for then observational limits on non-adiabatic fluctuations in the cosmic microwave background would provide some constraints on the otherwise mysterious era of reheating, and indeed on the whole history of the universe between inflation and the present. However, there are very general grounds for expecting that single-field inflation can only produce adiabatic fluctuations, whatever happens in reheating or subsequently. It has been shown [4] that, whatever the constituents of the universe, the differential equations for cosmological perturbations in Newtonian gauge always have a solution which for wavelengths outside the horizon (that is, for physical wave numbers that are much less than the cosmological expansion rate) are adiabatic, in the sense that a quantity ζ [5] is conserved: ζ = −Ψ− δρ/3(ρ̄+ p̄) , (1) where δρ is the perturbation to the total energy density in Newtonian gauge; ρ̄ and p̄ are the unperturbed total energy density and pressure; the perturbed metric is given by ds = −(1 + 2Φ)dt + a(1− 2Ψ) dx ; (2) and as usual H ≡ ȧ/a. (Reference [4] dealt mostly with a quantity [6]