0
$\begingroup$

Disclaimer The question below is based on a vague knowledge, and hence, statements can be potentially wrong or misleading.

An important quantity in Cosmology is the density fluctuation of matter quantified in terms of the ratio $$\frac{\delta\rho(\textbf{x})}{\bar{\rho}}=\frac{\rho(\textbf{x})-\bar{\rho}}{\bar\rho}\tag{1}$$ where $\bar{\rho}$ is the average density. If I understand it correct, the information of CMB anisotropies enables us to predict the density fluctuations at the time of recombination.

Question $1$ Is it meaningful to talk about density fluctuations $\frac{\delta\rho(\textbf{x})}{\bar{\rho}}$ for the present universe?

Question $2$ If yes, how can it be measured and what is its present value, and can it be related to its primordial value?

$\endgroup$

1 Answer 1

1
$\begingroup$

The term that you are referring to is called density contrast.

$$\delta = \frac{\delta\rho(\textbf{x})}{\bar{\rho}}$$ Usually its denoted as $\delta$. However some books uses different notations such as in Longair its denoted as $\Delta$.

Now for galaxies, the present $\delta$ can be found by

$$\delta_{galaxy} = \frac{\rho_{galaxy}}{\rho_{cric}}$$ where $\rho_{crit} = 10^{-26}~~kg/m^3$$(Equivalent to the critical energy density)

For a galaxy which has an average density, this is equal to $\delta_{galaxy} \approx 10^{6}$

For a cluster $\delta_{cluster} \approx 10^3$

Since the $\rho$ (average matter density) changes as $(1+z)^3$ for $z \approx 100$ the $\delta_{galaxy} \approx 1$.

For more information, Longair, Galaxy Formation, 2nd Ed, (Chp 11. Page 312)

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.