The cosmic microwave background radiation appears to us to be not quite uniform in temperature or intensity in all directions; that is, it is not isotropic. Why is this?

Answer 1

I don't think this is a perfect answer, let's just say it's ok as a first approximation.

The universe was obviously much smaller in the very early universe (I mean billionths of billionths of seconds). At this scale, density and "temperature" fluctuations were random and quantum physics predominated.

The remarkable similarity in the temperature of the cosmic microwave background radiation (CMBR) is explained by the process of inflation, which saw the Universe expand explosively in a fraction of a second, flattening out these variations but not removing them.

Even though the variations we observe are extremely small—less than one part in 10,000—they still need to be explained, and quantum physics and inflation appear to be the most promising theories at this time.

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Answer 2

It is believed that the small fluctuations in the density of the early universe that ultimately resulted in the formation of galaxies and large-scale structures are mainly caused by quantum fluctuations that were amplified during cosmic inflation, a period of rapid expansion in the early universe.

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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.

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.

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.

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.

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