rede96 said:
So if the expansion rate is decreasing, why do people say that universe is accelerating? That's really confusing!
Yes, this is confusing at first. I see we even have a featured thread in the cosmology section about this very subject and how to avoid this confusion.
In any case, there are two distinct things being mixed up here: the rate of expansion, which is by what fraction all distances increase every time unit, and the change in distances between actual objects carried by the expansion of space. The first is decreasing at an ever slowing rate, the latter increasing at an accelerated rate.
A very handy analogy to use here that may illuminate the difference is the analogy with a savings bank account. I know marcus is also fond of using it, and perhaps he even already did (the lazy me only skimmed the thread).
As you know, when you put a given amount of money on the account, it'll usually be made to grow at some specified yearly or monthly rate.
If you were to think about the amount of money as analogous to distances between some objects in the universe, and the percentage rate at which your money grows as the Hubble parameter, you'll get a pretty good picture.
Turns out, you can make the amount of money on your account grow at an accelerated pace, even though the percentage rate by which it grows may be decreasing.
Imagine you've got an account in a bank that makes your deposited money grow by (1+1/n)%, where n is the number of months since deposit. You get 2% increase after the first month, 1.5% after the second, 1.3% after the third and so on. The farther away in time you go, the less the rate decreases, but it
never stops decreasing.
The first months, when the drop in the percentage rate was significant, will make the amount of money grow at a slowing pace, but after a while when the rate flattens out and asymptotically approaches 1%, you'll get an accelerated, or even exponential growth of money.
Try it out on paper. Imagine you've got 10000 bucks or so deposited. The first month, you get 200 bucks. The second month, 153 bucks - the rate is going down, and the 'speed' at which you're gaining money is going down as well.
But if it's, say a 10th month, and you have at that time say, 1 000 000 bucks, on the tenth month you'll get 1.1% of 1 000 000 = 11000$, the next, eleventh month, 1.09% of 1 011 000 = 11020$. So your money (distances) are already accelerating in their growth.
Here, I believe in visual aids. marcus' numbers can be plotted:
The above is the graph of evolution of the Hubble parameter, or expansion 'rate' with time (analogous to percentage rate on your account)
while the following one:
Shows the increase of distances between given objects (i.e. the 'scale factor'; the total amount of money in the analogy) over the same period of time.
You should be able to easily see that the first is always going down, while the second always increases (i.e. universe expands, your savings grow), but at first the curve was sloping down (decelerating expansion, or less money gained every month), while after a while it begun curving up (accelerating expansion).
). Moreover according to the standard cosmic model everybody uses it is slated to continue declining.