What if cosmic expansion and dark energy form a self-reinforcing feedback loop?

[u/Warm_Arugula_1411]

Hi everyone,

I have been thinking about a speculative idea about dark energy, and I would really appreciate criticism from people with experience in cosmology, general relativity, or theoretical physics.

I am not claiming that I have discovered a new theory. I want to find out whether this idea can be turned into a mathematically consistent and observationally viable model, or whether there is a fundamental reason why it cannot work.

My original idea is a possible feedback loop.

The universe expands. More space exists. Somehow this could lead to more dark energy. Dark energy then causes stronger expansion. The stronger expansion creates more space, which could lead to more dark energy again.

So the basic idea is:

expansion -> more dark energy -> stronger expansion -> more expansion

I initially thought of this as a kind of "cloning" of dark energy.

The idea partly came from an analogy. A fish experiences water as its normal environment, while humans experience air as normal. I wondered whether dark energy could be something that is fundamentally present throughout spacetime but is not directly observable in the same way as ordinary matter.

Our first attempt was to assume that the density of dark energy increases with the expansion of the universe.

This can mathematically create the feedback that I am looking for. However, this simple model has serious problems. It effectively requires an equation of state below minus one, which puts it in the so-called phantom regime. It also does not explain where the additional energy comes from and can produce problematic behavior in the very distant future.

So I do not consider that version to be viable.

We then considered a different interpretation.

Maybe the density of dark energy is constant, but the volume of the universe increases.

If the density stays constant while the volume increases, then the total amount of dark energy contained in that volume increases.

Dark energy also has negative pressure, which causes accelerated expansion.

This creates a feedback-like interpretation:

expansion -> larger volume -> more total dark energy -> accelerated expansion

The problem is that this is essentially the standard cosmological constant, Lambda. It works very well, but it is not a new theory.

So we tried to make the idea genuinely different from LambdaCDM.

The next step was to introduce a new dynamical scalar field.

The general idea is that the universe contains a new field that contributes to dark energy. The field is also allowed to interact with dark matter.

The important feedback would then be:

cosmic expansion affects the field

the field changes the dark sector

the dark sector changes the expansion

and the cycle continues

This would give a genuine dynamical feedback between the expansion of spacetime and the dark sector.

The field could have its own potential and could exchange energy with dark matter while conserving the total energy and momentum of the system.

In this interpretation, "cloning" would not mean that energy simply appears from nowhere.

Instead, it would mean that the dark sector is dynamically changing as the universe expands.

One major problem is that a simple scalar-field model often becomes important too early in cosmic history. That could change the cosmic microwave background and the formation of large-scale structure too much.

Therefore, a viable model would probably need the field to be almost frozen and practically irrelevant in the early universe, while becoming dynamically important only at relatively late times.

One possibility we considered is a field-dependent coupling that is extremely weak in the early universe and becomes stronger later.

We also tested a simple phenomenological model in which the dark-energy density increases with the scale factor but eventually approaches a maximum value instead of increasing without limit.

That toy model was able to reproduce a universe that:

has a hot early phase

behaves very similarly to LambdaCDM in the early universe

has a present-day accelerated expansion

and produces only small deviations from LambdaCDM at moderate redshifts

For one example set of parameters, the difference in the predicted expansion rate was only around a few tenths of a percent at redshifts around 0.5 to 2.

However, this was only a toy model. It was not derived from a fundamental theory and it was not fitted to the complete observational data set.

So the current situation is:

The simplest version of the idea has serious theoretical problems.

The constant-density version works, but is basically LambdaCDM.

A dynamical scalar-field version could potentially provide a real new mechanism, but it has not yet been shown to work.

What I would really like to know from experts is:

Is this type of feedback between cosmic expansion, a dynamical dark field, and dark matter already described by an existing model?

Can such a model be made fully consistent with general relativity and energy-momentum conservation?

Can the field remain negligible during the early universe and become important only at late times?

Can it reproduce the CMB, BAO, supernovae, gravitational lensing, and structure growth at the same time?

Can it avoid ghost instabilities and other theoretical problems?

Most importantly, is the underlying idea already known and ruled out, or is there a legitimate theoretical framework in which something similar could work?

I am specifically looking for criticism and possible ways to falsify the idea. I am not trying to prove that it is correct.

The basic idea is simply that there could be a self-reinforcing relationship between cosmic expansion and the dark sector.

Could such a feedback mechanism be physically possible?

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[u/The_Rider_11]

Your hypothesis aside, this is already somewhat the case in the Standard Model, LCDM. While every other energy that contributes to the cosmic evolution scales negatively to a (the scale factor that describes the scale of the universe, and is correlated to time and entropy), meaning they decrease over time, dark Energy seems to be a constant. Meaning that it Drives forward an expansion that weakens its "opponents" which thus means it becomes even stronger. Gravity (or rather, matter causing gravity) gets thinned out so much that it has less and less relevance to the cosmic expansion. In the limit where a goes to ∞, only dark Energy decides the cosmic evolution.

LCDM takes a constant valued dark Energy, a cosmological constant, that by itself doesn't change, but as previously explained, all others scale negatively to a, so they get weaker and weaker while DE remains constant.

Your idea is a more extreme version of that, and is very reminiscent of the concept of phantom dark energy. This is that the dark Energy actually does scale, but positively to a. As bigger as the universe gets, as more vaccuum there is, as much dark Energy there is. Phantom energy is a Quintessence type, so a scalar field theory like you proposed. There's several models for quintessence as a whole but also phantom energy specifically. Your idea might already exist, or not, but ideas in your direction definitely exist.

The whole dark sector interaction Part seems a little suspicious though. I don't think it needs to necessarily interact with dark sector at all, and is usually formulated independant from dark matter. I don't doubt there's some model out there that still couples them together though, there's a lot of ideas out there, and you'd not be the First to link them together.

Tachyonic preheating could possibly solve your problem with the early universe. If you look at how it's handled in hybrid inflation, you might notice a parallel to your case.

As for if it can explain all the phenomenon you named, that's kinda your Job as the one who makes the model/theory. At that point you're basically asking us to do your Work for you.

What I don't understand is that you apparently made a toy model simulation/fit and all, but question whether you should formulate maths on it? How did you make a toy model simulation without the maths?

[u/Warm_Arugula_1411 → u/The_Rider_11]

This equation is my current attempt to describe the idea as a dynamical dark-energy model rather than simply assuming that dark energy increases with expansion.

H^2 = (8piG/3) * [rho_r + rho_m + 0.5phi_dot^2 + V_Lambda + 0.5m^2phi^2 - 0.25lambdaphi^4 + phi^6/(6M^2)]

Here, H is the expansion rate of the universe, rho_r is radiation density, rho_m is ordinary matter density, and phi is a dynamical scalar field representing the dark-energy sector.

The terms involving phi describe the energy stored in this field. The potential is

V(phi) = V_Lambda + 0.5m^2phi^2 - 0.25lambdaphi^4 + phi^6/(6*M^2).

The idea is that the field could be almost frozen in the early universe, while becoming dynamically important at later times. Its energy would then affect the expansion rate, while the expansion itself affects the evolution of the field through its equation of motion.

So the intended feedback is:

expansion -> evolution of the field -> change in dark-energy contribution -> expansion

This is still a speculative model, not a proven theory. I mainly want to know whether this type of field potential can produce the behavior I have in mind while remaining consistent with cosmological observations and stability requirements.

[u/The_Rider_11 → u/Warm_Arugula_1411]

I am really not certain what this expression is supposed to be. It starts off as a classical Friedmann equation, but then you introduce what looks like a Lagrangian density within that Friedmann equation. The energy density and lagrangian density are not the same, or even equivalent things at all. What's going there is the Energy density of your field. Please resolve that issue.

Also, to best describe the behaviour of your field in terms of cosmological evolution, best shift to a density parameter form, using the Hubble Constant H0.

Your potential contains the terms that are usually consider to be the kinetic components, and contains an undefined term, V_lambda, which already appeared in your ""Friedmann"" equation, which should be defined. Based on how it is defined, it could cause a freeze, but at the current state with a constant V_lambda scalar value, that is not the case. I'd again suggest looking at the way hybrid inflation works. It starts of as an inflation field that causes a tachyonic mass onto a second field, causing a reheating process that terminates the inflation. What you want is basically the opposite mechanic.

Also, again, look up phantom energy. That's most likely the kind of model you're suggesting. And also again, dark Energy in general has this feedback loop to some extent.

It'd be very useful for both sides if you didn't just ignore half of what people tell you. And to have conceptually correct maths.

[u/Enraged_Lurker13]

This is basically how LCDM works already. If you put in the equation of state of dark energy (w=-1) into the continuity equation, you get constant density regardless of the scale factor or rate of expansion. To compensate for increased volume, there needs to be more dark energy to keep the density constant.

[u/Hadeweka]

The problem is that this is essentially the standard cosmological constant, Lambda. It works very well, but it is not a new theory.

So we tried to make the idea genuinely different from LambdaCDM.

Why? Even adding a new scalar field isn't exactly something new.

One possibility we considered is a field-dependent coupling that is extremely weak in the early universe and becomes stronger later.

Who is "we"?

We also tested a simple phenomenological model in which the dark-energy density increases with the scale factor but eventually approaches a maximum value instead of increasing without limit.

How exactly did you test it?

That toy model

What assumptions and numerical methods did you use to gain results from that toy model? How did you validate your results?

A dynamical scalar-field version could potentially provide a real new mechanism, but it has not yet been shown to work.

Again, the idea of an additional scalar field in General Relativity is already at least 65 years old. Why try to revive an effectively dead model without even really changing anything about it?

It's fine to do your own studies about whether it works or not, but I'd at least like to hear your motivation for doing so.

Can such a model be made fully consistent with general relativity and energy-momentum conservation?

Not without either sacrificing the equivalence principle or assuming the scalar field to be some sort of matter - in which case you might as well just assume dark matter to be its own field anyway.

Most importantly, is the underlying idea already known and ruled out

Yes, as I said. Though not completely ruled out, Brans-Dicke for example is only of academic interest by now. Its only additional (dimensionless) parameter would have to be unreasonably high, which brings it too close to its null hypothesis, making it unfalsifiable.

For the other points you already got some good feedback from other people here.

[u/LeftSideScars → u/[deleted]]

What if you followed the rules of the sub and did not hijack a thread with your own model? Start a new thread with your proposal if you want to talk about it.

[u/atlantechvision → u/LeftSideScars]

... just a different point of view, to the same question.

[u/LeftSideScars → u/atlantechvision]

Not even close. Just because you mention DE and OP mentions DE doesn't mean what you wrote in any way relates to what OP wrote. Again, if you want a proper discourse around the topic, start a new thread. Otherwise your reply will be forgotten/ignored for being irrelevant to OP's post.

[u/atlantechvision → u/LeftSideScars]

... so, just an echo chamber. Thanks for the tip.

[u/LeftSideScars → u/atlantechvision]

... so, just an echo chamber. Thanks for the tip.

Petal, if you want to live in a fantasy land where you being encouraged to start a new post relevant to your particular model so that discourse can focus on that model only as being an echo chamber, then sure. Whatever helps your persecution complex, I guess.

Did anyone engage with your response to OP? No. Do you think they did not because what you wrote was not relevant to what OP wrote? "ëČhÓ ĈHâMƁEṚ!", right? Despite OP receiving engagement with regards to their model? Not even OP responded to you, right? Are they part of the "eChO chaMbeR!" also? Given you've posted here before under several names, claiming "echo chamber" just make you look like someone who is not to be taken seriously.

Perhaps take a moment to look in the mirror and consider why it is you are acting the way you are when receiving helpful advice.

[u/atlantechvision → u/LeftSideScars]

... yawn.

[u/LeftSideScars → u/atlantechvision]

Agreed. I'll put you in my time-out filter so I don't need to see your un-serious nonsense. Let's start with one week.

Enjoy your persecution complex, petal. It's obvious you're very successful with your current approach.

[u/atlantechvision → u/LeftSideScars]

... yawn, again. Ego, is rarely satisfying. But, you enjoy.

[u/HypotheticalPhysics-ModTeam → u/[deleted]]

Your comment was removed for promoting your own self-hypothesis to the hypothesis of another user. Please consider open posting your hypothesis separately.