Science > Physics > cosmology homework; density of a universe filled with x-matter
| Topic: |
Science > Physics |
| User: |
"Johan Lans" |
| Date: |
01 Apr 2007 09:41:55 AM |
| Object: |
cosmology homework; density of a universe filled with x-matter |
Hi, I've got this homwork question, and I just need to know if I'm
on the right track. I hope it's ok to write the equations in latex
code. Here it is: Consider a flat $(k=0)$ universe filled up with
X-matter, with an equation of state: $p_X/c^2=w\rho_X$, where
$-1<w<1$. Find the expressions for the evolution of density
$\rho_X(a),a(t) \text{ and } \rho(t)$, where a is the evolving scale
factor.
I have the two equations:\\
$\left ( \frac{\dot{a}}{a} \right ) ^2 = \frac{8 G \pi
\rho}{3}-\frac{k}{a^2} \\
\dot{\rho}=-3 \frac{\dot{a}}{a}(\rho + p)$
I started by solving $\left ( \frac{\dot{a}}{a} \right ) ^2 =
\frac{8 G \pi \rho}{3}-\frac{k}{a^2}$, which gives me: $a=Ce^{\pm
\sqrt{\frac{8 G \pi \rho}{3}}t}$. Now I have a(t), and should be
able to get $\rho(t)$ by solving the second equation. But this one
has the two a's in it, which are time dependant, and this gives me a
pretty tricky equation to solve. So, is this the right approach, or
is there a better way? I only want hints, not a solution.
/Johan
.
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| User: "Hagar" |
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| Title: Re: cosmology homework; density of a universe filled with x-matter |
01 Apr 2007 10:35:50 AM |
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"Johan Lans" <nospam@nospam.com> wrote in message
news:d9de7$460fc4c1$50d8bcf9$1688@news.chello.se...
Hi, I've got this homwork question, and I just need to know if I'm
on the right track. I hope it's ok to write the equations in latex
code. Here it is: Consider a flat $(k=0)$ universe filled up with
X-matter, with an equation of state: $p_X/c^2=w\rho_X$, where
$-1<w<1$. Find the expressions for the evolution of density
$\rho_X(a),a(t) \text{ and } \rho(t)$, where a is the evolving scale
factor.
I have the two equations:\\
$\left ( \frac{\dot{a}}{a} \right ) ^2 = \frac{8 G \pi
\rho}{3}-\frac{k}{a^2} \\
\dot{\rho}=-3 \frac{\dot{a}}{a}(\rho + p)$
I started by solving $\left ( \frac{\dot{a}}{a} \right ) ^2 =
\frac{8 G \pi \rho}{3}-\frac{k}{a^2}$, which gives me: $a=Ce^{\pm
\sqrt{\frac{8 G \pi \rho}{3}}t}$. Now I have a(t), and should be
able to get $\rho(t)$ by solving the second equation. But this one
has the two a's in it, which are time dependant, and this gives me a
pretty tricky equation to solve. So, is this the right approach, or
is there a better way? I only want hints, not a solution.
/Johan
Hint:
Change the Time Dependency to "Furlongs per Fortnight".
.
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| User: "Johan Lans" |
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| Title: Re: cosmology homework; density of a universe filled with x-matter |
01 Apr 2007 11:28:32 AM |
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Hagar skrev:
"Johan Lans" <nospam@nospam.com> wrote in message
news:d9de7$460fc4c1$50d8bcf9$1688@news.chello.se...
Hi, I've got this homwork question, and I just need to know if I'm
on the right track. I hope it's ok to write the equations in latex
code. Here it is: Consider a flat $(k=0)$ universe filled up with
X-matter, with an equation of state: $p_X/c^2=w\rho_X$, where
$-1<w<1$. Find the expressions for the evolution of density
$\rho_X(a),a(t) \text{ and } \rho(t)$, where a is the evolving scale
factor.
I have the two equations:\\
$\left ( \frac{\dot{a}}{a} \right ) ^2 = \frac{8 G \pi
\rho}{3}-\frac{k}{a^2} \\
\dot{\rho}=-3 \frac{\dot{a}}{a}(\rho + p)$
I started by solving $\left ( \frac{\dot{a}}{a} \right ) ^2 =
\frac{8 G \pi \rho}{3}-\frac{k}{a^2}$, which gives me: $a=Ce^{\pm
\sqrt{\frac{8 G \pi \rho}{3}}t}$. Now I have a(t), and should be
able to get $\rho(t)$ by solving the second equation. But this one
has the two a's in it, which are time dependant, and this gives me a
pretty tricky equation to solve. So, is this the right approach, or
is there a better way? I only want hints, not a solution.
/Johan
Hint:
Change the Time Dependency to "Furlongs per Fortnight".
Thanks for the hint.
Could you give me an example on how to do this?
/Johan
.
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| User: "Phineas T Puddleduck" |
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| Title: Re: cosmology homework; density of a universe filled with x-matter |
01 Apr 2007 03:12:26 PM |
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On 1/4/07 15:41, in article d9de7$460fc4c1$50d8bcf9$1688@news.chello.se,
"Johan Lans" <nospam@nospam.com> wrote:
Hi, I've got this homwork question, and I just need to know if I'm
on the right track. I hope it's ok to write the equations in latex
code. Here it is: Consider a flat $(k=0)$ universe filled up with
X-matter, with an equation of state: $p_X/c^2=w\rho_X$, where
$-1<w<1$. Find the expressions for the evolution of density
$\rho_X(a),a(t) \text{ and } \rho(t)$, where a is the evolving scale
factor.
I have the two equations:\\
$\left ( \frac{\dot{a}}{a} \right ) ^2 = \frac{8 G \pi
\rho}{3}-\frac{k}{a^2} \\
\dot{\rho}=-3 \frac{\dot{a}}{a}(\rho + p)$
I started by solving $\left ( \frac{\dot{a}}{a} \right ) ^2 =
\frac{8 G \pi \rho}{3}-\frac{k}{a^2}$, which gives me: $a=Ce^{\pm
\sqrt{\frac{8 G \pi \rho}{3}}t}$. Now I have a(t), and should be
able to get $\rho(t)$ by solving the second equation. But this one
has the two a's in it, which are time dependant, and this gives me a
pretty tricky equation to solve. So, is this the right approach, or
is there a better way? I only want hints, not a solution.
Just some clarification
You're happy with deriving \rho_x(a) and a(t) right?
So why the issue with \rho(t)?
--
Painius admits he cannot answer a single question to NB:
"Yes, you're right of course, NB. And they get very useless very quickly.
I shall do my best to ignore them, as you wish."
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