That would be like the H that applies in that picture, but the ratio of the height you are now to the height in that picture depends on more than just the rate you were growing in that picture. It would be a bit like if you were using your height to talk about your age, and you look at a picture of yourself at 4 feet tall, and say you were growing two inches a year when you were that tall. What's more, the z we get from a given measurement reflects all the expansion, so all the H's, since that light was emitted, not just the value of that H at that z. So in that sense, the answer is "yes," but be careful- we also think of z as a measure of how far away the objects are, and H does not depend on location it depends on age. What the Hubble constant really depends on is how old was the universe at the time, but if you have a dynamical model of the universe, you can map that into z and come up with a function H(z).
Since everything but dark energy dilutes with increasing $a$, $H(a)$ will asymptotically converge to a value $H_0\sqrt/a$, multiplying by the scale factor shows the acceleration $da/dt$: The value is given by the Friedmann equation:Īre the fractional energy densities in radiation, matter, curvature, and dark energy, respectively.įor instance, you can solve the above equation at $z=0.1$ and find that the expansion rate was 5% higher than today.
It's more or less the norm to use the term Hubble constant $H_0$ for the value today, and Hubble parameter $H(t)$ or $H(a)$ for the value at a time $t$ or, equivalently, a scale factor $a = 1/(1+z)$, where $z$ is the redshift. The Hubble constant describes the expansion rate of the Universe, and the expansion may, in turn, may be decelerated by "regular" matter/energy, and accelerated by dark energy.
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