What are the equations used to define energy density and pressure in inflation driven by vector field?
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Hey mate!✌✌
⏩ In QFT, energy density and pressure can be defined from Noether current due to Poincare translation invariance. What if we are considering a system at finite temperature?
⏩ For a scalar field, we have
ρ=12ϕ˙²+V0(ϕ and p=12ϕ˙²−V0(ϕ).
⏩ After considering temperature, we can naively replace V0 with temperatuer-corrected potential energy VT. This is what I assumed at first. Then from some cosmology textbooks, there is a relation: Tdp(T)dT=ρ(T)+p(T).
⏩ I don't see why this relation is satisfied for ρρ and pp defined earlier. Actually Kolb & Turner in "The early universe" mention that p=−VT and ρ=−p+Tdp(T)dT . So I am confused about how to define ρρ and pp.The definition in Kolb&Turner does not account for the kinetic energy in scalar field. Also, I always thought ρρ and pp should be obtained from stress energy tensor in order to satisfy equation like Friedman equations in cosmology.
Thanks for the question!
♥♥♥
⏩ In QFT, energy density and pressure can be defined from Noether current due to Poincare translation invariance. What if we are considering a system at finite temperature?
⏩ For a scalar field, we have
ρ=12ϕ˙²+V0(ϕ and p=12ϕ˙²−V0(ϕ).
⏩ After considering temperature, we can naively replace V0 with temperatuer-corrected potential energy VT. This is what I assumed at first. Then from some cosmology textbooks, there is a relation: Tdp(T)dT=ρ(T)+p(T).
⏩ I don't see why this relation is satisfied for ρρ and pp defined earlier. Actually Kolb & Turner in "The early universe" mention that p=−VT and ρ=−p+Tdp(T)dT . So I am confused about how to define ρρ and pp.The definition in Kolb&Turner does not account for the kinetic energy in scalar field. Also, I always thought ρρ and pp should be obtained from stress energy tensor in order to satisfy equation like Friedman equations in cosmology.
Thanks for the question!
♥♥♥
Answered by
0
ஜ۩۩ஜ ӇЄƳƛ MƛƬЄ ஜ۩۩ஜ
₳nswer :
The vector field takes the use of all the particles that makes the effect of the all elements
нσρє нєℓρѕ !❤️❤️
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