Re: Does Hubble's Constant change with distance.
- From: brian@xxxxxxx (Brian Tung)
- Date: Thu, 19 Apr 2007 00:18:52 -0700 (PDT)
anandsr wrote:
I just had a thought we always relate the hubble's constant with the
age of the universe.
But if it so then the farther we look we must see it change.
Does it really change? Because I don't remember there being any
mention of it's relation with time. It is always stated as a constant.
Now if it is really a constant then we cannot relate it with the age
of the universe or else some other parameter eg light speed must
change to keep it a constant.
Does this make sense? I am no physicist.
Your question does make sense. The Hubble constant does change with
time, but very slowly. If you have not seen any mention of its relation
with time, you haven't looked in the right places--papers that deal with
cosmic evolution over large time scales, billions of years. On those
time scales, the variability of the Hubble "constant" is as fundamental
to the development of the universe as the curvature of the Earth is to
long plane flights. On shorter times scales--say, tens of millions of
years--the Hubble constant is, for most intents and purposes, constant.
I suspect your intuition is correct. As you may have noticed, the
Hubble constant, now estimated to be about 70 km/s per megaparsec, is
essentially in units of s^-1--hertz, in other words. You can think of
it as the instantaneous doubling frequency--how many times the universe
doubles in scale per second. Obviously, this frequency is very small.
In fact, since there are 3.1 x 10^19 km in each megaparsec, the doubling
rate is about 2.3 x 10^-18 Hz--the Hubble constant. Each second, the
universe doubles in size a minucule 2.3 billionths of a billionth times.
But early in the universe's history, it must have been doubling much
faster. Two objects separated by, say, 100 megaparsec are now moving
apart at a relative speed of 7000 km/s. But there must have been a time
when those objects were much closer together--say, just 7000 km. If
they were moving also at 7000 km/s at that time, the Hubble constant
would have been 7000 km/s per 7000 km, or 1 megaparsec/s per megaparsec.
The doubling frequency would have been 1 Hz.
As it happens, the two objects were probably moving apart even faster
than that, so the Hubble constant would have been correspondingly
higher.
However, with the untrue but convenient fiction that the objects were
always moving apart at the same speed, we can interpret the Hubble
constant in yet another way--we can think of it as the inverse, the
reciprocal, of the time since the Big Bang. If you take the reciprocal
of 2.3 x 10^-18 Hz, you get 4.3 x 10^17 seconds, which is about 13.6
billion years. That is indeed the estimated age of the universe.
Again, it's clear that if this is to remain consistent, the Hubble
constant must increase the further back in time you go. About 12.2
billion years ago, for instance, when the universe was a tenth as old as
it is now, the Hubble constant should have been about 10 times greater.
This analysis is simplistic, based on our notion that expansion is
constant. The prevailing model has a varying expansion rate, for
reasons that are beyond the scope of this post (mostly because I don't
know the details!).
--
Brian Tung <brian@xxxxxxx>
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html
.
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