a) The energy density and the pressure for a scalar field with potential V are given by c² P = √1²+V P = (1²-V) = 2² (3½ 60² - v). Derive the Klein-Gordon equation at background level for a scalar field using the energy conservation equation given in the appendix. 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/dx. 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 = X64, where X is a constant, calculate the time evolution of the field in the case of slow-roll inflation. iii) Inflation ends when the following condition is satisfied, 1 = V 2 where mpl is a constant (the Planck mass). Calculate the value of the field at the end of inflation for a scalar field potential V = X64.

a) The energy density and the pressure for a scalar field with potential V are given by c² P = √1²+V P = (1²-V) = 2² (3½ 60² - v). Derive the Klein-Gordon equation at background level for a scalar field using the energy conservation equation given in the appendix. 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/dx. 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 = X64, where X is a constant, calculate the time evolution of the field in the case of slow-roll inflation. iii) Inflation ends when the following condition is satisfied, 1 = V 2 where mpl is a constant (the Planck mass). Calculate the value of the field at the end of inflation for a scalar field potential V = X64.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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