A Trying to plot a graph of energy densities for radiation and PBHs

AI Thread Summary
The discussion revolves around modeling a plot of energy density relations for radiation and Primordial Black Holes (PBHs), with the user seeking assistance due to inaccuracies in their current model. They assume PBHs decay into a Planck relic instantaneously and question whether conservation laws apply to their plots. The user notes that the model breaks down for smaller beta values and is open to providing more details or formulas if needed. They are advised to use the PF LaTeX feature for posting equations instead of images. The thread highlights the complexities involved in accurately representing these energy densities in a graph.
di_a_tonic17
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So a bit of context, I've been trying to model a plot of energy density relation for radiation and Primordial BH, but it is not right. Would someone be able to help me out? This is what I have so far. I am assuming the PBHs decay into a Planck relic, and the decay is instantaneous. Does the conservation law not follow through for the 2nd, 3rd, and 4th plots? Also, it completely breaks down for smaller values of beta. I'm attaching my calculation breakdown in the images below.


Any help would be appreciated.


If any more details are required, I'd be happy to provide them
 

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Including the formulas used would be helpful.
 
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di_a_tonic17 said:
I'm attaching my calculation breakdown in the images below.
Images for equations are not acceptable here. Please use the PF LaTeX feature to post equations directly. There is a "LaTeX Guide" link at the bottom left of each post window.
 

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