LETTER: Warm Inflation: Towards a Realistic COBE Data Power Spectrum for Matter and Metric Thermal Coupled Fluctuations

I consider the COBE data coarse–grained field that characterize the now observable universe for a model of warm inflation which takes into account the thermally coupled fluctuations of the scalar field with the thermal bath. The power spectrum for both, matter and metric fluctuations are analyzed. I find that the amplitude for the fluctuations of the metric during the horizon entry should be very small for the expected values of temperature.