Starting with the Robertson-Walker metric(adsbygoogle = window.adsbygoogle || []).push({});

[itex] \large ds^2 = -dt^2 + a^2(t) [ \frac{dr^2}{1-kr^2} + r^2(d\theta^2+\sin^2\theta d\phi^2] [/itex]

Consider a light ray emitted at the Big Bang travelling radially outwards from our position.

Therefore we have:

[itex] ds = 0 [/itex]

[itex] d\theta = d\phi = 0 [/itex]

Substituting into the above metric we have

[itex] dt = a(t) \frac{dr}{\sqrt{1-kr^2}} [/itex]

Integrating both sides and assuming [itex]a(0)=0[/itex] we have

[itex] t = a(t) \int{\frac{dr}{\sqrt{1-kr^2}}} [/itex]

Thus we must have a linear cosmology

[itex] a(t) \propto t [/itex]

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

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

# Simple argument for a linear cosmology

Loading...

Similar Threads - Simple argument linear | Date |
---|---|

I Don Page - cosmological doomsday argument | Jun 30, 2017 |

I Entropy of a simple universe | May 3, 2017 |

Simple explanation of the Boltzmann Brain paradox | Jul 8, 2015 |

Simple no-pressure cosmic model gives meaning to Lambda | Apr 3, 2015 |

Phi squared inflation | Feb 10, 2015 |

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