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mysearch

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Hi,

I am trying to understand the general status of Lambda-CDM model of cosmology and specifically how it is thought to explain the expansion of the universe for the first 7 billion years. Rather than replicate too many equations, this http://en.wikipedia.org/wiki/Friedmann_equations" outlines the standard forms of the Friedmann, Fluid and Acceleration equations. However, I believe it is possible, and acceptable, to express these equations purely in terms of the respective component mass-energy density

[tex] \rho_M[/tex] matter energy density

[tex] \rho_R[/tex] radiation energy density

[tex] \rho_D[/tex] dark matter energy density

[tex] \rho_K[/tex] space curvature energy density

[tex] \rho_\Lambda[/tex] dark energy density

If so, it would seem that the 3 basic equations of Friedmann cosmology can be presented as follows, although the details are again omitted, the weightings are believed to reflect the equation of state for each density variable:

[1] [tex] H^2 = \frac{8}{3} \pi G(\rho_M + \rho_R + \rho_D + \rho_K + \rho_\Lambda ) [/tex]

[2] [tex] \dot{\rho} = -H(3 \rho_M + 4 \rho_R + 3 \rho_D + 2 \rho_K + 0 \rho_\Lambda ) [/tex]

[3] [tex] \frac{\ddot{a} }{\dot{a}} = \frac{4}{3} \pi G(1 \rho_M + 2 \rho_R + 1 \rho_D - 0 \rho_K - 2 \rho_\Lambda ) [/tex]

By way of information, the 1st attached graph suggests that the various energy density components are a function of time. This graph was produced as an extension of the following equation, which appears to be the basis of many of the on-line http://www.astro.ucla.edu/~wright/ACC.html" , e.g. Ned Wright.

[4] [tex]H=H_0 \sqrt{\frac{\rho_1}{\rho_0}} = H_0 \sqrt{ \frac{ \Omega_M}{a^3} + \frac{ \Omega_R}{a^4} + \frac{ \Omega_D}{a^3} + \frac{ \Omega_K}{a^2} + \frac{ \Omega_\Lambda}{a^0} } [/tex]

On review of the 1st graph, the earlier universe appears to be dominated by radiation, e.g. +97%, but its density falls as a power of 4 as the universe expanded. In contrast, dark energy appears to have been negligible in the early universe, but its density is thought to have been unaffected by expansion. As such, today, dark energy is thought to represent 73% of the energy density followed by 23% dark matter, 4% baryon matter and radiation being virtually zero. The energy density associated with space curvature, based on [k=0], is thought not to have been a factor on the larger scale of the universe.

The 2nd attached graph shows a plot of acceleration against time, which is based on the energy-density effects that result from equation [3] above and the equations of state implicit in the weighting applied to each. From my perspective, the most logical way to orientated the sign of acceleration is to assume that it reflects the direction with respect to the velocity [v] of expansion, as implied by the Hubble constant [H]. However, equation [1] does not seem to explain why [H=v/d] should be associated with an expanding velocity [v]. This said, the acceleration equation [2] is assumed to imply that the expansion of the universe was slowing down in the first 7 billion years, but subsequently started to speed up due to the growing effect of dark energy. However, what I am struggling to understand is:

I have attached some additional questions regarding inflation in post #2 as this idea seems to encompass a range of hypotheses and appears to be somewhat of an add-on to the general L-CDM model. However, I would appreciate any knowledgeable clarifications of any of the issues raised. Thanks

I am trying to understand the general status of Lambda-CDM model of cosmology and specifically how it is thought to explain the expansion of the universe for the first 7 billion years. Rather than replicate too many equations, this http://en.wikipedia.org/wiki/Friedmann_equations" outlines the standard forms of the Friedmann, Fluid and Acceleration equations. However, I believe it is possible, and acceptable, to express these equations purely in terms of the respective component mass-energy density

[tex] \rho_M[/tex] matter energy density

[tex] \rho_R[/tex] radiation energy density

[tex] \rho_D[/tex] dark matter energy density

[tex] \rho_K[/tex] space curvature energy density

[tex] \rho_\Lambda[/tex] dark energy density

If so, it would seem that the 3 basic equations of Friedmann cosmology can be presented as follows, although the details are again omitted, the weightings are believed to reflect the equation of state for each density variable:

[1] [tex] H^2 = \frac{8}{3} \pi G(\rho_M + \rho_R + \rho_D + \rho_K + \rho_\Lambda ) [/tex]

[2] [tex] \dot{\rho} = -H(3 \rho_M + 4 \rho_R + 3 \rho_D + 2 \rho_K + 0 \rho_\Lambda ) [/tex]

[3] [tex] \frac{\ddot{a} }{\dot{a}} = \frac{4}{3} \pi G(1 \rho_M + 2 \rho_R + 1 \rho_D - 0 \rho_K - 2 \rho_\Lambda ) [/tex]

By way of information, the 1st attached graph suggests that the various energy density components are a function of time. This graph was produced as an extension of the following equation, which appears to be the basis of many of the on-line http://www.astro.ucla.edu/~wright/ACC.html" , e.g. Ned Wright.

[4] [tex]H=H_0 \sqrt{\frac{\rho_1}{\rho_0}} = H_0 \sqrt{ \frac{ \Omega_M}{a^3} + \frac{ \Omega_R}{a^4} + \frac{ \Omega_D}{a^3} + \frac{ \Omega_K}{a^2} + \frac{ \Omega_\Lambda}{a^0} } [/tex]

On review of the 1st graph, the earlier universe appears to be dominated by radiation, e.g. +97%, but its density falls as a power of 4 as the universe expanded. In contrast, dark energy appears to have been negligible in the early universe, but its density is thought to have been unaffected by expansion. As such, today, dark energy is thought to represent 73% of the energy density followed by 23% dark matter, 4% baryon matter and radiation being virtually zero. The energy density associated with space curvature, based on [k=0], is thought not to have been a factor on the larger scale of the universe.

The 2nd attached graph shows a plot of acceleration against time, which is based on the energy-density effects that result from equation [3] above and the equations of state implicit in the weighting applied to each. From my perspective, the most logical way to orientated the sign of acceleration is to assume that it reflects the direction with respect to the velocity [v] of expansion, as implied by the Hubble constant [H]. However, equation [1] does not seem to explain why [H=v/d] should be associated with an expanding velocity [v]. This said, the acceleration equation [2] is assumed to imply that the expansion of the universe was slowing down in the first 7 billion years, but subsequently started to speed up due to the growing effect of dark energy. However, what I am struggling to understand is:

*What caused the expansion of the universe for the 1st 7 billion years?*I have attached some additional questions regarding inflation in post #2 as this idea seems to encompass a range of hypotheses and appears to be somewhat of an add-on to the general L-CDM model. However, I would appreciate any knowledgeable clarifications of any of the issues raised. Thanks

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