I Time Space Fabric: Malleability & Extension Explored

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Spacetime is often mischaracterized as a "fabric" with properties like malleability and extension, which is misleading. Instead, spacetime is a complex concept in physics that does not behave like a physical material. For a deeper understanding of its properties, studying general relativity through textbooks is recommended. Online resources, such as Sean Carroll's lecture notes, provide valuable insights into the nature of spacetime. Engaging with scientific literature is essential for grasping these advanced concepts accurately.
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What is space time fabric is it have properties like malleability or extension because I was watching cosmos in discovery they said "time space is very flexible flexible than we thought."
Can you suggest some mathematics about time space fabric
 
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You should not be trying to learn actual science from pop science sources. Spacetime is not a "fabric" and does not have properties like those of a fabric. To learn about the actual properties of spacetime, I suggest a textbook on relativity. A good online source is Sean Carroll's lecture notes:

https://www.preposterousuniverse.com/grnotes/
 
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Thanku sir
 
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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