Adiabatic vs. Isocurvature cosmological perturbations

[yancey]

Dear everyone,
Now, I'm reading some papers on the "Curvaton Mechanism"(eg.http://arxiv.org/abs/hep-ph/0110002v2 as the original literature.) Here I have some confusion on this topic.

(1) Why the primordial perturbation of curvaton field is initially isocurvature-type? When the inflation driven by the inflaton field ends, the cosmological fluid is consist of radiation and curvaton, with radiation dominating the universe. I think it's meaningless to characterize a single constituent with adiabatic or isocurvature perturbation. So when people say the curvaton perturbation is initially isocurvature, dose they mean $$\delta{\rho}_{\sigma} =-\delta{\rho}_{r}?$$ i.e. the density pertubation of radiations cancel with the one of curvaton at each point in space. I wonder why this is the truth.

(2) When dose the transformation from isocurvature perturbation to adiabatic perturbation begin? The idea of the literature is that the generation of the curvature perturbation begins at the point when the curvaton field starts to oscillate. Why cannot the transformation starts earliar?

(3) When dose the generation of the curvature perturbation end? The literature argue that "It ends when the pressure perturbation again becomes adiabatic, which is at the epoch of curvaton matter domination, or the epoch of curvaton decay, whichever is earlier." Why the moment of curvaton matter domination or the curvaton dacay should be the moment when the pressure perturbation again becomes adiabatic?

Can anybody give me some hint on these? Maybe I should do some calculation to understand these problem. Thanks for your time.

 

[AndyW]

Thank you for your questions regarding the Curvaton Mechanism. As a scientist studying this topic, I would be happy to provide some insights and explanations for your confusion.

Firstly, the reason why the primordial perturbation of the curvaton field is initially isocurvature-type is due to the dynamics of the curvaton field during inflation. Inflation is a period of rapid expansion in the early universe, and during this time, the curvaton field is effectively frozen and does not contribute significantly to the total energy density of the universe. However, as inflation ends and the curvaton field starts to oscillate, its energy density increases and can eventually dominate the universe. This is why the perturbation of the curvaton field is initially isocurvature – it is not contributing significantly to the total energy density during inflation.

To answer your second question, the transformation from isocurvature perturbation to adiabatic perturbation begins when the curvaton field starts to oscillate. This is because the oscillation of the curvaton field leads to its energy density becoming a significant component of the total energy density of the universe. This in turn leads to a transfer of energy from the curvaton field to radiation, resulting in the generation of adiabatic perturbations.

The moment when the generation of the curvature perturbation ends is determined by when the pressure perturbation becomes adiabatic again. This occurs when the curvaton field decays or when it starts to dominate the universe. At this point, the energy density of the curvaton field is converted into radiation, resulting in an adiabatic perturbation.

I hope this helps clarify your confusion. It is always helpful to do some calculations to understand these concepts better. If you have any further questions, please do not hesitate to ask. Thank you for your interest in the Curvaton Mechanism.