How soon can the first stars form?

Question

Introduction

In our universe, the cosmic microwave background was formed approximately 400,000 years after the Big Bang. It was hot, but within a few million years after the Big Bang, it would no longer have consisted significantly of visible light. The first stars formed about 100 million years later, give or take, as larger structures were slowly beginning to form.

In my universe, I'd like to see if I can create a period of overlap, where the first stars form while the CMB is still hot enough to be visible to the naked human eye, and exists at wavelengths suitable for chlorophyll-based photosynthesis. I've found by playing around with the Saha equation that I can keep the CMB hot and visible for a few million years more, but only if I increase the baryon density by a lot.

Therefore, I want to see if I can change my universe's parameters to instead accelerate star formation by a factor of 100 or so. I'm not going to change most fundamental constants like the speed of light; that tends to cause issues later on. The parameters I'm willing to change are the various density parameters for photons, baryonic matter, dark matter, and dark energy: $\Omega_{\gamma}$, $\Omega_M$, $\Omega_D$, and $\Omega_{\Lambda}$. These evolve over time; today, $\Omega_{\Lambda,0}=0.692$, $\Omega_{D,0}=0.258$, $\Omega_{M,0}=0.048$ and $\Omega_{\gamma,0}\approx0$. As the first structures were forming, however, the universe would have been matter-dominated (that is to say, $\Omega_M,\Omega_D\gg\Omega_{\gamma},\Omega_{\Lambda}$).

Structure formation and star formation

Given what I know about star formation in the early universe (see e.g. 1 2, for more information), I think we can break the process down into a couple key stages:

1. Small density fluctuations grow as gravitational instabilities cause perturbations to collapse. These form small dark matter halos rich in primordial gas.
2. This gas cools mainly after molecular hydrogen forms because much of the gas should exist at temperatures less than $\sim10^4\text{ K}$ - the threshold where atomic cooling is important.
3. When clumps in a gas cloud are massive enough (i.e. reach the Jeans mass), they can collapse to form stars, just as they do today.

If I could affect any of the three stages - halo collapse, cooling, or protostellar collapse - I might be able to achieve what I want. The problem is, I don't know how changing my parameters would affect the relevant timescales - if at all.

Existing work

I've done a basic literature search on theoretical work on early structure formation. Much of the existing results are based on numerical simulations (e.g. Abel et al. 2000, Bromm et al. 1999). They assume a universe dominated (at the time) by cold dark matter, i.e. with $\Omega_D\approx0.95$ and $\Omega_M\approx0.05$. Using a couple of different numerical methods, they studied the evolution of clumps through collapse. As it is beyond me to reproduce the simulations, I can't even speculate on how they would behave differently in another universe.

If there are analytical approximations for the timescales involved, I can't find them. I suspect that there's something out there, but I don't know where it is (cosmology is not exactly an area of expertise of mine).

The question

Let's say I want stars to form within the first 2 million years after the Big Bang. What combination of the cosmological parameters ($\Omega_{\gamma}$, $\Omega_M$, $\Omega_D$, and $\Omega_{\Lambda}$) is needed to cause this? (I assume, that $\Omega_M$ and $\Omega_D$ are the ones I should be focusing on.) By simply adjusting the contributions of different types of matter and energy, can I make star formation in this universe begin earlier than it did in ours?

Requirements

I have a couple of requirements:

• The universe needs to be stable, and should eventually evolve to become what it is today: expanding at an accelerated rate and dominated by dark energy.
• Fundamental constants not derived from the density parameters should not change. For instance, increasing the speed of light, lowering the mass of an electron or increasing the gravitational constant are forbidden. I don't want to run into any unfortunate paradoxes or contradictions.
• Please note the hard-science tag on the question. Ideally, an answer would be backed up by either analytical or numerical results. I'm not asking anyone to run simulations . . . but if you did, that could be amazingly helpful.

Notes

The question's remained unanswered for a while. Aside from the fact that simulations of subhalo collapse might be necessary to address the problem in detail, I think the question could be difficult to answer given our current knowledge of the physics behind it all. There are a few possible sticking points:

• I recently got to talk with an astrochemist about Population III star formation in general; it turns out that rate coefficients for the molecular hydrogen cooling reactions are not precisely known.
• There are still some discrepancies between different simulations of halo collapse/early structure formation.
• We don't have a lot of information about Population III stars.

Putting this all together, my question might remain unanswered for a while, but I'm okay with that. If you know of new developments (or old ones) that make this question answerable, and you can apply those properly, please do write an answer. But if we can only speculate - well, I'd rather wait until we can do more than speculate.

Answer 1

Increase the starting density of dark matter.

From OP:

The parameters I'm willing to change are the various density parameters for photons, baryonic matter, dark matter, and dark energy: Ωγ, ΩM, ΩD, and ΩΛ.

From OP:

Given what I know about star formation in the early universe (see e.g. 1 2, for more information), I think we can break the process down into a couple key stages:

Small density fluctuations grow as gravitational instabilities cause perturbations to collapse. These form small dark matter halos rich in primordial gas.

Dark Matter: https://www.pnas.org/content/112/40/12246

The benchmark cosmic baryon mass density and baryon-to-DM mass ratio are

ρb=(4.14±0.05)×10−31 g cm−3, ρb/ρDM=0.183±0.005.

so ρDM= 2.262e-30

The Formation and Fragmentation of Primordial Molecular Clouds https://arxiv.org/pdf/astro-ph/0002135.pdf

3.1. Formation of the First Objects To illustrate the physical mechanisms at work during the formation of the first cosmological object in our simulation, we show the evolution of various quantities in Figure 1... In the first, before a redshift of about 35, the Jeans mass in the baryonic component is larger than the mass of any non-linear perturbation. Therefore, the only collapsed objects are dark-matter dominated, and the baryonic field is quite smooth. (We remind the reader that a change in the adopted cosmological model would modify the timing, but not the nature, of the collapse.) In the second epoch, 23 < z < 35, as the nonlinear mass increases, the first baryonic objects collapse.

This is what we want to do: modify the timing. We want it faster.

So: initial conditions right after the Big Bang have dark matter and baryonic (regular matter) spread smoothly. ρb/ρDM=0.183±0.005 and so baryonic matter is 0.18 as dense as dark matter. The initial perturbations are with dark matter - the "small density fluctuations".

If dark matter is more dense to start with (and I mean absolute density, not relative to baryonic matter), initial perturbations will more quickly form gravitational nuclei that can later pull in the baryonic matter. More dark matter = more gravity.

So we will increase the amount of dark matter in the protouniverse. Collapse of dark matter is the first thing to happen and the more there is the faster it will collapse.

We will make the dark matter 1000000 times more dense. ρDM= 2.262e-24

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The dark matter will collapse faster. If we make it even more dense can it collapse even faster? Those density values are not very dense especially when you consider the density of the stars that need to happen.

I think this answer is within the scope of the hard-to-achieve demands of the question. Increasing baryon density would give a similar result as noted in the OP. I think, though, increasing baryon density would be slower as regards speeding the formation of stars. As I understand it, the primordial baryons are hot and this opposes their clustering. Dark matter is not affected by heat in the same way and that is why it is the first stuff to cluster.

Answer 2

Abraham Loeb has suggested the possibility of an early habitable period between 10-17 million years, with the CMB itself being a potential energy source for habitable planets within this time period

The habitable epoch of the early Universe https://lweb.cfa.harvard.edu/~loeb/habitable.pdf

He also provides a means by which halo collapse could have occurred during this time period.

I realise this is not quite as far back as you need, but it does seem to bring you a lot closer. Maybe there is enough play in this theory to achieve the desired effect by tweaking some of the variables but I haven't spent much time with it yet.

Thoughts on visible light

• Visible light is arbitrarily related to human vision which is only relevant if there are humans around, if you can replace "human visible" with "visible by some creatures who evolved in the early universe" then Loeb's theory may actually fit all the requirements. Just a thought, please disregard if not relevant.

• There are many kinds of chlorophyll, some of which are known to interact with infrared light (https://science.sciencemag.org/content/360/6394/1210) these adaptations seem to have arisen in low light environments, so plants which have evolved in this environment could conceivably photosynthesise directly from the CMB during the above time period.

This is a just a partial answer as it doesn't provide star formation at the time when the CMB is human visible, but it does seem to answer the question "can I make star formation in this universe begin earlier than it did in ours?" (or rather it suggests that star formation could conceivably have happened much sooner in our universe than conventional wisdom dictates)