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I've often heard the phrase "physical laws break down at the big bang".

Why is this? Divide by zero?

Please provide the mathematics.

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Here is a link to the equations whose solutions lead to the model of the expanding universe from an initial discontinuity called Big Bang.

The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity.

The article gives the equations derived from General Relativity, whose solutions provide the functions for modeling the BB cosmological model.

A simplified form can be found here.

Here is another link for solutions of the equations leading to a big bang model. For example time is in the denominator in this solution for the density $\rho$, giving infinity at time $t=0$. $$\rho(t)=\frac{1}{32\pi G t^2}$$

One sees that as t=0 is approached the matter density blows up. General Relativity tells us that in the region of high masses the physical laws we have studied and modeled in flat space change and may not hold in the form we know them (for example conservation of energy). The flat space approximation does not hold. Approaching zero time where the density tends to infinity is even worse, indeterminacy in masses means also indeterminacy in the laws governing space time.

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is the breakdown at 0 for rho the divide by zero indeterminate form? –  user24341 May 13 '13 at 3:19
yes, the value tends to infinity –  anna v May 13 '13 at 4:01
is the breakdown that rho(0) tends to infinity or is indeterminate? would you mind explaining why which is the problem? –  user24341 May 13 '13 at 4:13
Physical laws are not made to deal with infinities. I know that there exists many mathematical infinities but I have not seen them to be useful in mathematical physical models. Physical laws are already modified in the region of large masses. As density tends to infinity the distortions of spacetime can no longer be approximated by flat space, where our physical laws are determined so the physical laws become indeterminate too. –  anna v May 13 '13 at 4:18
There's also the issue that physics at the Planck scale is not fully understood –  kleingordon May 13 '13 at 7:00

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