The Klein-Gordon equation at background level for a scalar field φ is given by (found in image below) where H is the Hubble parameter, V the potential of the scalar field, and V′ = dV/dφ. Assume a flat Friedmann-Robertson-Walker universe, dominated by the scalar field. i) State the conditions for slow-roll inflation. Write down the Friedmann equation and the Klein-Gordon equation valid for slow-roll inflation. ii) For a scalar field potential V =1/2m^2φ^2, where m is the mass of the field, calculate the time evolution of the field φ in the case of slow-roll inflation.
Stellar evolution
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Red Shift
It is an astronomical phenomenon. In this phenomenon, increase in wavelength with corresponding decrease in photon energy and frequency of radiation of light. It is the displacement of spectrum of any kind of astronomical object to the longer wavelengths (red) side.
The Klein-Gordon equation at background level for a scalar field φ is given by
(found in image below)
where H is the Hubble parameter, V the potential of the scalar field, and V′ = dV/dφ.
Assume a flat Friedmann-Robertson-Walker universe, dominated by the scalar field.
i) State the conditions for slow-roll inflation. Write down the Friedmann equation and the
Klein-Gordon equation valid for slow-roll inflation.
ii) For a scalar field potential V =1/2m^2φ^2, where m is the mass of the field, calculate the
time evolution of the field φ in the case of slow-roll inflation.
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