Is the Cosmological Arrow of Time Linked to the Thermodynamic Arrow of Time?

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The cosmological arrow of time is considered a specific instance of the thermodynamic arrow of time, particularly when viewing the universe as an isolated system. Sean Carroll's blog post on Cosmic Variance provides a detailed explanation of this relationship. It addresses the complexities of the cosmological arrow of time and the initial low entropy state of the universe. The discussion emphasizes the interconnectedness of these concepts in understanding time's directionality. Overall, the link between the two arrows of time is affirmed as a significant aspect of cosmological theory.
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Is the cosmological arrow of time just a special case of the thermodynamic arrow of time, where the universe is the isolated system?
 
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short answer: yes

the longer answer is nicely summed up in this post by Sean Carrol on the blog Cosmic Variance

http://cosmicvariance.com/2006/08/01/boltzmanns-anthropic-brain/

Its not an overly long read and helps to explain a lot of the issues surrounding the cosmological arrow of time and how our Universe could have started in such a low entropy state.
 
https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.
Why was the Hubble constant assumed to be decreasing and slowing down (decelerating) the expansion rate of the Universe, while at the same time Dark Energy is presumably accelerating the expansion? And to thicken the plot. recent news from NASA indicates that the Hubble constant is now increasing. Can you clarify this enigma? Also., if the Hubble constant eventually decreases, why is there a lower limit to its value?
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