a) State the problems of the Hot Big Bang model in cosmology, and briefly explain how infla tion solves these problems. b) The Klein-Gordon equation at background level for a scalar field is given by 4 +3H + V' = 0, where H is the Hubble parameter, V the potential of the scalar field, and V' = dv/dy. Assume a flat Friedmann-Robertson-Walker universe, dominated by the scalar field.
a) State the problems of the Hot Big Bang model in cosmology, and briefly explain how infla tion solves these problems. b) The Klein-Gordon equation at background level for a scalar field is given by 4 +3H + V' = 0, where H is the Hubble parameter, V the potential of the scalar field, and V' = dv/dy. Assume a flat Friedmann-Robertson-Walker universe, dominated by the scalar field.
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Transcribed Image Text:a) State the problems of the Hot Big Bang model in cosmology, and briefly explain how infla-
tion solves these problems.
b) The Klein-Gordon equation at background level for a scalar field is given by
+3H +V' = 0,
where H is the Hubble parameter, V the potential of the scalar field, and V' = dV/dp.
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 = m²p2, where m is the mass of the field, calculate the
time evolution of the field in the case of slow-roll inflation.
c) The inflationary slow-roll parameters (p) and n(y) are given by
2
1
<(x) = 2/₁² (2) ².
€
a²
* ( ).
V
n(x) =
where a is a constant.
i) Calculate (4) and n(y) for the scalar field potential V= / m² p².
ii) Inflation ends when €(p) = 1. Calculate the value of the field at the end of inflation.
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