The Friedmann equation for a spatially flat Universe is given by(adsbygoogle = window.adsbygoogle || []).push({});

$$\Big(\frac{\dot R}{R}\Big)^2=\frac{8 \pi G}{3}\rho$$

where ##R(t)## is the proper radius of some spherical volume with us at its center.

Let us assume that there is a mass ##M## inside this spherical volume of radius ##R##. The density ##\rho## is then given by

$$\rho=\frac{M}{(4/3)\pi R^3}.$$

Substituting the above expression for the density ##\rho## into the Friedmann equation gives

$$\Big(\frac{\dot R}{R}\Big)^2=\frac{2 G M}{R^3}.$$

Now let us consider a Universe with a maximum density ##\rho##. The maximum density in a spherical volume of radius ##R## is realized by a Black hole whose Schwarzschild radius is equal to ##R##. Therefore we have the relationship

$$\frac{GM}{R}=\frac{c^2}{2}.$$ If we substitute the above relationship into the Friedmann equation we obtain

$$\Big(\frac{\dot R}{R}\Big)^2=\frac{c^2}{R^2}$$

which has the linear solution

$$R=c\ t.$$

Therefore it seems that a Universe with a maximum density ##\rho## expands linearly rather than exponentially as would be expected for a de Sitter Universe with a constant Planck scale density.

Is this reasoning correct?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Argument that a maximum density Universe expands linearly

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads for Argument maximum density |
---|

I Does space have its own density? |

I How does flux density scale with redshift? |

I Don Page - cosmological doomsday argument |

B Relationship Between Density and the Hubble parameter |

**Physics Forums | Science Articles, Homework Help, Discussion**