By using particle physics natural units with ##\hbar=c=1## so that Planck's length ##l_P=(8\pi G)^{1/2}## we can express Einstein's field equations as(adsbygoogle = window.adsbygoogle || []).push({});

$$G_{\mu\nu}=l_P^2\ T_{\mu\nu},$$

where ##G_{\mu\nu}## has dimension ##[\hbox{proper length}]^{-2}##, ##l_P## has dimension ##[\hbox{proper length}]##, ##T_{\mu\nu}## has dimension ##[\hbox{proper length}]^{-4}##.

In cosmology we assume the expanding FRW metric. If we assume flat space for simplicity and cartesian coordinates then we have the following line element

$$ds^2=-dt^2+a^2(t)\left(dx^2+dy^2+dz^2\right).$$

Therefore an interval of proper length in the x-direction for example is given by

$$ds=a(t)dx$$

If ##l_P## is a proper length then should it expand with the scale factor ##a(t)## or should it remain constant?

In order for it to remain constant then its corresponding comoving interval ##dx \sim 1/a## which seems unnatural to me.

Therefore I think that as ##l_P## is a proper length it should expand with the scale factor ##a(t)##.

Does this make sense?

**Physics Forums - The Fusion of Science and Community**

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 Does the Planck length expand in a FRW universe?

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Does Planck length | Date |
---|---|

I Does space have its own density? | Mar 11, 2018 |

B Why does the multiverse theory have only 4 levels? | Dec 24, 2017 |

How/Why does GR break down in Planck Epoch? | Sep 20, 2015 |

Does the Planck length grow with the scale factor? | Jul 5, 2008 |

**Physics Forums - The Fusion of Science and Community**