# On the WMAP image of the cosmic microwave background radiation, are the higher density irregularities the brighter bits or the darker bits?

Mar 2, 2016

The colour code shows fluctuations of CMBR temperature about its mean value of $\setminus \overline{T} = 2.725 \setminus \quad K$. The pixels coloured red / deep blue represent points that are $200 \setminus \quad \setminus \mu K$ above/below the average value. Higher temperature indicates higher concentration of matter .

#### Explanation:

The averaged CMBR temperature is $\setminus \overline{T} = 2.725 \setminus \quad K$

Given below is a map of temperature fluctuations about this average value, created from the 9 year data of WMAP. In this map the temperature fluctuations about the average value are shown in a scale of $\setminus \pm 200 \setminus \mu K$.

Colour Code:

The pixels in red represent temperatures that are $200 \setminus \mu K$ above the average. i.e $T - \setminus \overline{T} = + 200 \setminus \quad \setminus \mu K$

The pixels in dark blue represent temperature that are $200 \setminus \mu K$ below the average. 1.e. $T - \setminus \overline{T} = - 200 \setminus \quad \setminus \mu K$

What do they mean?: Higher temperature indicates higher matter density.

Density Contrast Field: Fluctuations in mass density are quantified by the density contrast field $\frac{\setminus \delta \setminus \rho}{\setminus} \rho$.
$\frac{\setminus \delta \setminus \rho}{\setminus} \rho \setminus \equiv \setminus \frac{\setminus \rho - \setminus \overline{\setminus \rho}}{\setminus \overline{\setminus \rho}}$, where $\setminus \rho$ is the density at a point and $\setminus \overline{\setminus \rho}$ is the average matter density.

Temperature Contrast Field: Fluctuations in CMBR temperature are quantified by the temperature contrast field $\frac{\setminus \delta T}{T}$
$\frac{\setminus \delta T}{T} \setminus \equiv \setminus \frac{T - \setminus \overline{T}}{\setminus \overline{T}}$, where $\setminus \overline{T}$ is the average temperature and $\setminus \delta T$ is the fluctuations about this average.

There is direct relation connecting the two which can be deduced from the fundamental principles:

$\frac{\setminus \delta \setminus \rho}{\setminus} \rho \setminus \propto \frac{\setminus \delta T}{T}$