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In an alternative universe the energy conservation equation is given by p+4- + = 0, a c2 and the Friedmann equation takes the form 2 a 8πG = p², 3 where all variables have their usual meaning, and a, p, and P depend on time t only. Assume this alternative universe is dominated by a fluid with equation of state P = c² wp, where the equation of state parameter w is a constant (with w -1). a) Calculate p(a), the dependence of the energy density p on the scale factor a. b) Calculate the time evolution of the scale factor a(t).

In an alternative universe the energy conservation equation is given by p+4- + = 0, a c2 and the Friedmann equation takes the form 2 a 8πG = p², 3 where all variables have their usual meaning, and a, p, and P depend on time t only. Assume this alternative universe is dominated by a fluid with equation of state P = c² wp, where the equation of state parameter w is a constant (with w -1). a) Calculate p(a), the dependence of the energy density p on the scale factor a. b) Calculate the time evolution of the scale factor a(t).

College Physics
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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In an alternative universe the energy conservation equation is given by p+4- + = 0, a c2 and the Friedmann equation takes the form 2 a 8πG = p², 3 where all variables have their usual meaning, and a, p, and P depend on time t only. Assume this alternative universe is dominated by a fluid with equation of state P = c² wp, where the equation of state parameter w is a constant (with w -1). a) Calculate p(a), the dependence of the energy density p on the scale factor a. b) Calculate the time evolution of the scale factor a(t).
Transcribed Image Text:In an alternative universe the energy conservation equation is given by p+4- + = 0, a c2 and the Friedmann equation takes the form 2 a 8πG = p², 3 where all variables have their usual meaning, and a, p, and P depend on time t only. Assume this alternative universe is dominated by a fluid with equation of state P = c² wp, where the equation of state parameter w is a constant (with w -1). a) Calculate p(a), the dependence of the energy density p on the scale factor a. b) Calculate the time evolution of the scale factor a(t).
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