# I'd like to know your interpretation.

1. Dec 18, 2011

### EhsanZ

With Hobson's notation:

H=(da/dt)/a

dH/dt = ((d2a/dt2)/a) - ((da/dt)/a)2

If ((d2a/dt2)/a) is negative, (dH/dt) is certainly negative.
But if ((d2a/dt2)/a) is positive, (dH/dt) can be positive or negative.

2. Dec 18, 2011

### mathman

dH/dt = ((d2a/dt2)/a) - ((da/dt)/a)2

Above is incorrect. Should be:

dH/dt = (d2a/dt2)/a - (da/dt)/a2

3. Dec 18, 2011

### I like Serena

No, it is correct.
I think you're forgetting the application of the chain rule.

I also think EhsanZ's interpretation is correct, although I do not know what "Hobson's notation" is.
I couldn't find it with google, except for in this thread. ;)

4. Dec 18, 2011

### BillSaltLake

Actually I think the only thing wrong with second eq. is a lack of superscripting of the 2s:

dH/dt = ((d2a/dt2)/a) - ((da/dt)/a)2

5. Dec 18, 2011

### George Jones

Staff Emeritus
$d^2 a/dt^2 > 0$ and $dH/dt < 0$ means that the expansion of the universe is accelerating while the Hubble constant is decreasing. We think that this is happening today.
This (I presume) refers to the notation used in the book General Relativity: An Introduction for Physicists by Hobson, Efstathiou, and Lasenby.

EhsanZ, play around with the spatially flat, matter-only Lemaitre model given on page 406 and in problem 15.23. This a good analytic approximation to our universe.

6. Dec 18, 2011

### Chronos

George is correct. If you look at the equations dispassionately, it is obvious the result can never be negative.

7. Dec 19, 2011

### mathman

8. Dec 20, 2011

### EhsanZ

No my friend! U made a mistake.

9. Dec 20, 2011

### EhsanZ

Doesn't matter! Everybody makes mistakes.

10. Dec 20, 2011

### EhsanZ

I meant the notation that Hobson had used in his book named "General Relativity: An Introduction for Physicists ".

11. Dec 20, 2011

### EhsanZ

Yes, you're right my friend. I should've written it more carefully.
Thanks