Re: [Phys-l] cosmology question

[David Bowman <David_Bowman@georgetowncollege.edu>]

Regarding Brian W's response:

> On 5/25/2011 9:07 AM, David Bowman wrote:
> > x*(dx/dt)2/H_02  = [Omega]_m + (1 - [Omega]_m -
> > [Omega]_lambda)*x + [Omega]_lambda*x3
> Alpha offers this in response:
>
> x(t) = (zeta|-> integral_1^zeta xi/(_lambda xi^3 omega-_lambda xi 
> omega-_m xi omega+_m omega+xi) dxi)^(-1)(c_1+(3 t)/4)
>
> Quite!      :-)
>
> Brian W

Who or what is Alpha, & how does his/her/its response follow from what I wrote?  I cannot parse the response.  Please translate it into  something readable.

For some reason Brian stripped the ^ symbols from my version of the Friedmann equation, which ought to have been copied above as:

x*(dx/dt)^2/H_0^2 = [Omega]_m + (1 - [Omega]_m - [Omega]_lambda)*x + [Omega]_lambda*x^3 .

Brian's comment suggests to me that maybe some readers may not understand my notation as far as reducing mathematical equations into an ASCII form.
So here is a dictionary of my notation:

* = multiply by.

/ = divide by.

+ = add to.

- = subtract from (when a binary operation) or negate (when a unary operation).

^ = raised to the power of (i.e. what immediately follows is a right side superscript on what immediately preceeds the symbol).

_ = lower right susbscript (what immediately follows is a right side subscript on what immediately preceeds the symbol).

[greek letter] = the corresponding symbol for the greek letter named in [...], (e.g. [Omega] = capital letter omega, [pi] = lower case letter pi).

dx/dt = the derivative of x with respect to t.

(...) = parentheses indicating a pending operation is to be performed on the whole evaluated value of of whatever expression ... is inside them.

^ and _ symbols take precedence over * and / symbols which, themselves, take precedence over + and - symbols.

BTW, when raising a subscripted quantity to a power the whole quantity is raised to the power, not just the subscript.  So in the above Friedmann equation H_0^2 = (H_0)^2 = the square of the Hubble parameter, H_0, rather than an H with a subscript which is the square of zero.

So could Brian please translate Alpha's response into a notation compatible with the above scheme?

Thanks.

David Bowman