Hubble expansion across time dimension?

The expansion of the universe, as described by the Hubble's law, refers to the expansion of space itself. This expansion is observed in the three spatial dimensions (length, width, and height), rather than in the time dimension.

According to the theory of general relativity, the fabric of spacetime can be influenced by the distribution of matter and energy. On large scales, such as the scale of the universe, the expansion of space itself can occur. This means that the distances between galaxies are increasing over time, leading to the observed phenomenon of the expanding universe.

The expansion of the universe is often visualized using the analogy of an expanding balloon. As the balloon inflates, the dots on its surface (representing galaxies) move away from each other. However, it's important to note that this analogy is limited and doesn't fully capture the complexities of the universe's expansion.

While the expansion of the universe is described in terms of space,is there implication on observed properties of light and thus the passage of time?

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Commented May 17, 2023 at 17:40
• Time is fundamentally different than space in actual physical terms. Time is that which the clocks show. Clocks are local systems with an energy reservoir and a mechanism that disperses this energy evenly over all of space. In contrast a distance measurement involves a spatially extended system. So whereas extended space measurements can depend on spatial expansion, local time measurements can not. We could break relativity by making cosmological time T global and by introducing a scaling constant dt_local=a*dT or something alike, but it will probably clash with observed local physics. Commented May 17, 2023 at 19:27
• Did ChatGPT or a similar product write the first three paragraphs of this question? That's not allowed here. Commented May 18, 2023 at 20:37
• @benrg I just asked Bing's chatbot a trivial physics question. It gave me a false answer. I told it that the answer is false and asked it to try again. It then terminated the conversation, claiming that I wasn't sufficiently well behaved. Microsoft's nerds have a lot to learn about proper human behavior, I am afraid. They can't even admit that their toys are wrong and are currently blaming the user. Commented May 19, 2023 at 0:21

The FLRW metric used in cosmology is given, in one parametrization, by $$ds^2 = dt^2 + a(t)^2\left[\frac{dr^2}{1-kr^2} + r^2d\Omega^2\right].$$ The first term, $$dt^2$$, tells you about time, and the second term, the one multiplied by the scale factor $$a(t)^2$$, tells you about space. The fact that the universe is expanding is captured in the scale factor $$a(t)$$, and so we can see from the metric that the expansion of the universe is acting only on space and not on time $$t$$ (though there are parametrizations of this metric in terms of "conformal time" $$\tau$$, so that the scale factor multiplies the whole metric).