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In this chapter, we will discuss the anisotropy of CMB Radiation and COBE, i.e., Cosmic Background Explorer.

To understand the observations from space and the primary anisotropies in the Cosmic Microwave Background Radiation, let us take the following equations and understand it as shown below.

$$n_{\gamma,0} = \frac{Total \: energy \: density}{Characteristic \: energy \:of \:Photons}$$

$$n_{\gamma,0} = \frac{aT_0^4}{k_BT_0}$$

Where $k_B$ is **Boltzmann Constant** and $T_0$ is the **present temperature of the universe**.

Using the present temperature $(T_0)$ as 2.7 K, we get the current CMB photon number density as 400 cm^{−3}.

The cosmic stellar photon number density is much smaller (∼= 10^{−3} cm^{−3}) over large scales.

If the stellar contributions from galaxies, which get mixed with CMB, are negligible, the baryon to proton ratio is −

$$\eta = \frac{n_{b,0}}{n_{\gamma,0}}$$

The present value is ∼5 × 10^{−10}. Since both photon and baryon number densities are proportional to **a ^{−3}**, then

As opposed to the number density, the matter energy density is more dominated than photon energy density at present.

The Energy density of baryonic matter = $\rho_{b,0}c^2 = 0.04\rho_cc^2 = 2 × 10^{−9} ergcm^{−3}$. While, the Energy density of radiation = $aT_0^4 = 4 \times 10^{−13}ergcm{−3}$.

**Penzias** and **Wilson** found the CMB to be isotropic within the limits of observations. The limits are low angular resolution and sensitivity of instruments. They made observations from earth, due to this, observations cannot be made through all the spectrum as water vapor in the atmosphere absorbs many wavelengths ranging from 1mm to 1m. So, CMB can’t be asserted as a spectrum.

The CMB is thought to be rotationally invariant (isotropic). Since there existed a time when matter and radiation were in equilibrium, then the formation of structures in the universe is unexplainable. Since the distribution of matter is not isotropic but is clumped together like a cosmic web with huge voids in between, CMB is thought to have an extragalactic origin.

But, as the observations from the space began, anisotropies in the CMB were found, which lead to the reasoning that these anisotropies in matter lead to the formation of structures.

The main satellites which were launched to observe the CMB were −

**Cosmic Microwave Background Explorer**(COBE, 1989)**Wilkinson Microwave Anisotropy Probe**(WMAP, 2001) and**Planck**(2009).

COBE mainly had two instruments. They were **Far InfraRed Absolute Spectrometer** (FIRAS) and **Differential Microwave Radiometers** (DMR Antennas). FIRAS measures intensity of the CMB as a function of wavelength along any specific direction. Whereas, DMR has 3 antennas to measure the difference in intensity of CMB from three different directions. The following pointers give us some more information on FIRAS and DMR.

CMB observations from FIRAS show that the CMB radiation corresponds to black body spectrum at T = 2.72528±0.00065 K.

The DMR measures three frequencies (31.5 GHz, 53 GHz, 90 GHz) in all directions in the sky.

The “red batman symbol” in the DMR observations is noise from foreground emission (galactic diffused synchrotron emission).

The intensity variations in the observations correspond to temperature variations. The presence of hot and cold spots proves that the CMB radiation is anisotropic.

This anisotropy must be present at decoupling time as there are no distortions in CMB. So, matter should have some pockets with higher density than that of the others.

The CMB spectrum (intensity as a function of energy) is nearly a perfect black body corresponding to T = 2.7 K. The specific intensity of the CMB radiation is nearly the same for all directions. Confirmation that universe is isotropic at large scales (validates our assumption of cosmological principle).

Analysis of the data showed that there are temperature anisotropies (“fluctuations”) in the CMB spectrum at the resolution of COBE (DMR).

**Resolution of COBE, WMAP, Planck**

The DMR instrument on-board COBE had a limiting (maximum) spatial resolution of ∼ 7 degrees.

Wilkinson Microwave Anisotropy Probe (WMAP) had an average resolution of ∼ 0.7 degrees.

Planck satellite has an angular resolution of ∼ 10 arc-minute.

Cosmic stellar photon number density is much smaller than the CMB photon number density.

We live in a matter dominated universe, since matter energy density is higher than the photon energy density.

COBE, WMAP, Planck are efforts to measure and quantify anisotropies in the CMB.

The formation of structure in the universe is a result of CMB anisotropies.

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