Cosmology

by Steven Weinberg

invariant under arbitrary changes in the spatial coordinates, so we can evaluate it just as well in co-moving Robertson–Walker coordinates. This can be done directly, using Eq. (1.1.13), but to save work, suppose we adopt a spatial coordinate system in which the particle position is near the origin x i = 0, where g˜ij = δij + O(x 2 ), and we can therefore ignore the purely spatial components  i jk of the affine connection. General relativity gives the equation of motion d 2 x i dτ 2 = − i µν dx µ dτ dx ν dτ = − 2 a da dt dx i dτ dt dτ . Multiplying with dτ /dt gives d dt  dx i dτ =

larger than the observed dark energy density, V ρ0,crit
10−29 g/cm3 , by a factor of order 10 56 . There are other unknown contributions to the vacuum energy that might cancel this contribution, coming from fluctuations in fields at higher energies or from the field equations themselves, but this cancelation would have to be precise to about 56 decimal places. There is no known reason for this remarkable cancelation. 37 The discovery of dark energy now adds a second problem: why