How can an inflaton field maintain its energy while expanding without diluting?

[_PJ_]

In the general descriptiopns of Inflation Theories, they mainly rely on the inflaton field having a property by which it is 'non-diluting'
Can anyone explain just how anything can be non-diluting?

Is energy simply condensed from "somewhere" to propagate the field and maintain it's energy as it expands?
By what mechanism can a field such as this maintain such a specific energy despite having a finite, but extremely dynamic size, all the while obeying principles of conservation of energy?
If the energy is condensed or otherwise a result of some asymmetry, how is this maintained throughout the expansion yet also befitting the smooth exit?

 

[Orodruin]

all the while obeying principles of conservation of energy?

Energy is not conserved in GR.

 

[_PJ_]

Energy is not conserved in GR.

Thanks for a rather brief response.
And...? Inflationary theory is a QFT theory. Energies are conserved.

 

[Orodruin]

Thanks for a rather brief response.
And...? Inflationary theory is a QFT theory. Energies are conserved.

No they are not. In an expanding universe you lose time-translation invariance, which is directly related to the conservation of energy through Noether's theorem. Inflationary theory is not a field theory in flat space-time.

 

[_PJ_]

No they are not. In an expanding universe you lose time-translation invariance.

Okay, so that must mean the field itself must definitely be expanding? Which further makes it harder for me to understand the notion that it does not dilute...

 

[Orodruin]

Okay, so that must mean the field itself must definitely be expanding?

This statement makes no sense. A field is an object which has a value at each event in space-time. It does not make sense to talk about a field expanding - it fills space-time by definition.

Energy non-conservation is nothing particular for inflation, it is already there in cosmology when the universe is matter or radiation dominated.

 

[_PJ_]

I apologise for my bad description, I'm never good at explaining what I mean.

What I am trying to ask, is that, given space is expanding, and, as you say a field fills the entirety of space, as space expands the field must still fill all of space - I admit I was wrong to ay 'expanding' also, but my issue is still the same, and unanswered, that given an amount of net energy in the field at time zero, and then a later time, the spatial extent has increased, but the field is non-diluting, then the net energy in the field must be the same proportional to the region considered?
I accept that the energy is not conserved as you say - but that's not relevant to my main problem:

GR describes the gravitational force as responsible for the topography of the spacetime. Therefore, it is a gravitational force that powers the inflation, ovbviously just opposite to the attractive gravity we usually associate.
Gravitational energy pushing the universe outwards (i.e. expansion) is negative to the attractive gravitational energy - yet the inflationary field is non-diluting - so where is this energy from? If it's not conserved, surely there is a universal gravitational deficit?

in which case, how is this reconcilable with any smooth exit?

 

[George Jones]

As Orodruin says, there is not global conservation of energy for the universe. It is possible to talk about local quantities.

In many inflation models, the local energy density of the inflation field has a kinetic term and a potential term. In popular models, the potential term starts in a plateau that dominates the kinetic term. Consequently, during this plateau the local energy density is almost constant, i.e., non-diluting. The field does, however, slowly roll down from the plateau. During the plateau period, the inflation field acts like a cosmological constant on steroids.

 

[_PJ_]

Thank you George, that really helps a lot.
I am relieved that you mention "almost constant" and that there is still a decline from 'potential' to 'kinetic' which is where I was mistaken in my understanding!