Writing series
A four-part series on time, gauge, and geometry in inflationary cosmology.
In cosmology, time is not handed to you. General covariance turns the Hamiltonian into a constraint, the lapse becomes pure gauge, and choosing a clock becomes a gauge choice. This series follows that idea from a clean constraint analysis of the flat FLRW scalar field all the way to the contact geometry of the reduced dynamics, and to what happens when that reduced picture is pushed past where it holds.
The running example is a single inflaton. Part 1 fixes the vocabulary; Part 2 walks the menu of clocks; Part 3 finds the rigid contact geometry hiding in the e-fold gauge; and Part 4 follows the clock to where it stops, at a zero-energy vacuum, and shows how to give the Hubble rate back.
why, in cosmology, time is a gauge choice
A full constraint analysis of the flat FLRW scalar field: the Friedmann equation is the Hamiltonian constraint, the lapse is pure gauge, and so choosing a clock is a gauge choice.
the same universe, told by different clocks
The menu of clocks - cosmic, conformal, and the e-fold gauge in which the inflaton dynamics becomes autonomous and its velocity is bounded - and what each one makes manifest or hides.
when the inflaton's trajectories foliate, and the contact geometry that decides it
Reducing the constrained system yields a contact geometry; when the inflaton's trajectories foliate, that rigid structure is what decides the dynamics.
a zero-energy vacuum, and how to give the Hubble rate back
At a zero-energy vacuum the field kinates and the contact picture degenerates - not a failure of physics but a gauge-and-reduction choice run past its domain. The cure is to un-reduce and give the Hubble rate back.