Cosmology Lecture 23

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Quantum Field Quickie

To understand inflation, we need Quantum Field Theory. Fields are generalizations of classical particles. Here are some properties of classical particles and their generalizations as fields:

where , repeated indices are summed over, and is the metric tensor defined by:

Inflation

Quantum Field Theory is relevant to inflation because the scalar field contributes energy to the universe. Including the energy density associated with this field in the Friedmann Equation:

We can express the energy density for the scalar field as the (0,0) component of the energy momentum tensor:

where we used . The pressure associated with is given by:

where in this case the ’s are not summed over. Note the negative sign on . For a slowly varying, spatially homogeneous :

Then using that , we find that:

So we have a very viable candidate for dark energy . If , then we have exponential expansion. Next time we’ll investigate , which will aid us in understanding why this exponential expansion should dominate for the very beginning of the universe.