- #1

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- I
- Thread starter timmdeeg
- Start date

- #1

- #2

- 1,254

- 141

For Open and Closed cases, you play around with ##\Omega##. I have used the http://jorrie.epizy.com/docs/index.html?i=1 version, which has more liberal range limits than the approved Github version.

- #3

timmdeeg

Gold Member

- 1,306

- 176

Ah, great, thanks for your advise!

One question, how can I show only one of these curves?

One question, how can I show only one of these curves?

Last edited:

- #4

- 1,254

- 141

- #5

timmdeeg

Gold Member

- 1,306

- 176

Got it, thanks.

- #6

Bandersnatch

Science Advisor

- 3,300

- 2,567

- #7

- 1,254

- 141

As a matter of fact it seems to crash if I set Lambda to 0.001 and Omega to 1.5. Will have to investigate that.

I recall that I have previously simulated a zero lambda situation with collapse on older, less accurate versions, but it will take some searching to find that.

- #8

George Jones

Staff Emeritus

Science Advisor

Gold Member

- 7,599

- 1,477

This graph shows ##H## as a function of time related to the L-CDM model. Do we (@Jorrie) have similar graphs e.g. for ##\Lambda=0##; ##k=-1## critical, ##\Lambda=0##; ##k=0## open, ##\Lambda=0##; ##k=+1## closed?

@Jorrie is there a way for the calculator to show recollapse?

In a closed matter-only (dust) FLRW univers, parametric expessions for the scale factor ##a## and cosmological time ##t## as functions of conformal time ##η## are (from Ryden)

$$\begin{align}

a\left(\eta\right) &= \frac{1}{2} \frac{\Omega_0}{\Omega_0 - 1} \left( 1 - \cos\eta \right) \\

t\left(\eta\right) &= \frac{1}{2H_0} \frac{\Omega_0}{\left( \Omega_0 - 1 \right)^{3/2}} \left( \eta - \sin\eta \right),

\end{align}$$

with ##0<\eta<2\pi##, and with ##\Omega_0>1## the present density relative to critical density.

The Hubble parameter is given by (with abuse of notation)

$$H\left(\eta\right) = \frac{1}{a} \frac{da}{dt} = \frac{1}{a}\frac{\frac{da}{d\eta}}{\frac{dt}{d\eta}} = \frac{2H_0 \left( \Omega_0 - 1 \right)^{3/2}}{\Omega_0} \frac{\sin\eta}{\left( 1 - \cos\eta \right)^2}.$$

Ii is easy to put ##\eta##, ##t\left(\eta\right)## , and ##H\left(\eta\right)## into three columns of a spreadsheet, and to use these to plot ##H\left(\eta\right)## versus ##t\left(\eta\right)## for ##0<\eta<2\pi##.

- #9

Bandersnatch

Science Advisor

- 3,300

- 2,567

Yeah, but that requires ME to do some work, instead of somebody else ;)Ii is easy to

For those interested, here's the graph for ##\Omega_0=1.5## and ##H_0=67.74##

And the spreadsheet

(make a copy if you want to change the parameters)

The behaviour tracks what Jorrie's calc outputs for early periods, so it's probably typed in alright.

The switcheroo towards collapse happens around 100 Gyrs for 1.5x critical density; for 2x density it's about 45 Gyrs; 800 Gyrs for 1.1 - which are the time scales I wanted to get a sense of.

Share:

- Replies
- 8

- Views
- 823

- Last Post

- Replies
- 2

- Views
- 1K

- Replies
- 49

- Views
- 2K

- Replies
- 1

- Views
- 666

- Last Post

- Replies
- 4

- Views
- 604

- Last Post

- Replies
- 4

- Views
- 1K

- Replies
- 6

- Views
- 1K

- Last Post

- Replies
- 8

- Views
- 1K

- Replies
- 20

- Views
- 449

- Last Post

- Replies
- 14

- Views
- 636