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

Answer 1

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.

Anisotropies in CMBR are caused by the following:

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

Elevated temperature corresponds to increased matter density. This is a direct relationship that can be inferred from basic principles.

#(\delta\rho)/\rho \propto (\delta T)/T#

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

Temperature Contrast Field: Fluctuations in CMBR temperature are quantified by the temperature contrast field #(\deltaT)/T# #(\deltaT)/T\equiv\frac{T-\bar{T}}{\bar{T}}#, where #\bar{T}# is the average temperature and #\deltaT# is the fluctuations about this average.

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Answer 2

Ariana Acosta

Cosmic microwave background radiation temperature fluctuations are attributed to variations in the early universe's density, which are believed to have originated from quantum fluctuations during the inflationary period, which resulted in small temperature variations across the sky.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.