1. The effect of the thermal vacuum on the power spectrum of inflation is examined by using the thermal field dynamics. The thermal effect influences the CMB anisotropy at large length scale. After removing the divergence using the holographic cutoff, we observe that the thermal vacuum explains well the observational CMB result at low multipoles.
Temperature Effect on the Power Spectrum in Inflation Shaoyu Yin, Bin Wang, and Ru-Keng Su Physics Letters B 675 (2009) pp
Physics Department, Fudan University, 220 Handan Road, , Shanghai, China
History of Universe: Inflation Starts at very High Temperature
The initial fluctuation, which became the seed for large scale structure, imprints on the anisotropy of the cosmic microwave background (CMB) radiation. The finite temperature effect on the initial state must be considered.
Theoretical frame of the Thermo Field Dynamics
Conclusion: The temperature effect and the holographic cutoff should be both considered in the study of inflation.
Power Spectrum
consider temperature
zero temperature
divergence at k=0
Adiabatic vacuum with temperature effect
In holographic principle, the UV cutoff and IR cutoff is related by
So the momentum cutoff
Holographic Principle