# Why is the temperature of the cosmic background radiation not perfectly isotropic?

Mar 20, 2016

Primordial fluctuations in matter density (which form the seed for the present days structures like galaxies and galaxy cluster) will manifest as anisotropies in CMBR.

#### Explanation:

CMBR anisotropies are due to the following reasons:

1. Relative motion of solar system with respect to the rest frame of CMBR gives rise to a dipole anisotropy of about $4 \setminus \quad m K$,
2. Emissions from milky-way galaxy is dominant on the equatorial plane.
3. Primordial perturbations in matter density which form the seed for cosmic structures like galaxies and galaxy clusters,

If the anisotropies due to the first two are filtered out we are still left with anisotropies of magnitude $200 \setminus \quad \setminus \mu K$. This is because of the fluctuations in matter density (the primordial seed perturbations). While the average temperature of CMBR is $\setminus \overline{T} = 2.725 \setminus \quad K$, the temperature at a given direction could be up to $200 \setminus \quad \setminus \mu K$ above or below this value.

Higher temperature indicates higher matter density. There is direct relation connecting the two which can be deduced from the fundamental principles.

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

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.