Primordial Neutron Stars

This paper proposes a novel cosmological scenario where an initially excessive baryon asymmetry in the early universe triggers the gravitational collapse of Hubble patches into primordial neutron stars with masses as low as 0.1 solar masses, provided that a subsequent large entropy injection later restores the observed baryon asymmetry and preserves standard Big Bang nucleosynthesis predictions.

The Gist

The Big Idea: Baby Neutron Stars

Usually, when we think of a neutron star, we imagine a cosmic heavyweight: the dead, super-dense core of a massive star that exploded. It takes a star the size of our Sun (or bigger) to crush itself down into a tiny, dense ball of neutrons.

This paper proposes a wild new idea: What if neutron stars could be born as "babies" in the very first seconds of the universe?

These "Primordial Neutron Stars" (PNS) wouldn't need a massive star to die first. Instead, they would form directly from the chaotic soup of the early universe, potentially being much smaller and lighter than the neutron stars we see today.

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The Recipe: Three Special Ingredients

To cook up these baby neutron stars, the authors say the early universe needed a very specific, unusual recipe. Think of it like baking a cake that requires three weird ingredients you don't usually find in a standard kitchen.

1. The "Too Much Flour" Problem (Excess Baryons)

In our normal universe, there is a tiny, perfect balance between matter (protons/neutrons) and energy. But for this scenario to work, the universe needed to be overloaded with matter right after it was born.

• The Analogy: Imagine a baker who accidentally dumps a whole sack of flour into a bowl meant for a single cookie. The bowl is now overflowing with dough.
• The Science: The universe had a "baryon asymmetry" (matter vs. antimatter) that was way too high. This meant there was so much raw material packed into a small space that a single "patch" of the universe had enough mass to become a neutron star immediately, without waiting for stars to form and die.

2. The "Squeeze" (Enhanced Density)

Just having extra flour isn't enough; you have to squeeze it together.

• The Analogy: Imagine the universe is a giant, bouncy trampoline. Usually, the fabric is smooth. But in this scenario, someone stomped on a tiny spot, creating a deep, tight crater.
• The Science: The paper suggests that on very small scales, the density of the universe was much higher than usual. These "craters" of matter were so dense that gravity tried to crush them instantly.

3. The "Emergency Brake" (Entropy Injection)

Here is the tricky part. If the universe stays overloaded with matter, it would ruin everything we know about how the universe evolved (like how the first elements formed).

• The Analogy: Imagine you are baking that giant cookie, but you realize, "Oh no! If I bake this now, it will be too big and ruin the recipe for the rest of the batch!" So, you suddenly pour a massive amount of water (steam) into the oven. This doesn't destroy the cookie, but it dilutes the flour-to-water ratio, making the rest of the batch normal again.
• The Science: A mysterious "Early Dark Energy" component acted like a pressure release valve. It expanded rapidly and injected entropy (heat/energy), which diluted the excess matter. This restored the universe to its normal state after the baby neutron stars had already formed, but before the Big Bang Nucleosynthesis (the creation of the first atoms) began.

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The Formation Process: A Cosmic Squeeze Play

Here is how the baby neutron star actually forms, step-by-step:

1. The Crunch: Because of the "Too Much Flour" and the "Squeeze," a patch of the universe collapses under its own gravity.
2. The Near-Miss: Usually, when matter collapses this hard, it turns into a Black Hole (a point of infinite density).
3. The Save: But, as the matter gets squeezed, it hits a "wall." The atoms get so close that they turn into neutrons. Neutrons are like stiff, unyielding marbles; they resist being squished further.
4. The Result: The collapse stops just before it becomes a black hole. The "stiffness" of the neutrons acts as a brake. Instead of a black hole, you get a Primordial Neutron Star.
   • Key difference: Because they formed this way, they could be as light as 0.1 times the mass of our Sun, whereas normal neutron stars are usually at least 1.4 times the Sun's mass.

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Why Don't We See Them? (The "Ghost" Problem)

If these things exist, why haven't we found them?

• They are Cold: Normal neutron stars are born in fiery explosions, so they are hot and glow with X-rays. These baby stars formed in the quiet, dark early universe. They have been cooling down for 13 billion years. They are essentially cosmic ice cubes—invisible to our telescopes.
• They are Lonely: They don't spin fast like pulsars (which act like lighthouses) because they never had a companion star to spin them up. They are just silent, dark balls of neutrons drifting through space.
• They are Ghosts: They might be hiding in the "Dark Matter" of our galaxy. They are so hard to detect that they could make up a small percentage of the invisible mass holding galaxies together.

The "Survival" Test

The paper also asks: Could a neutron star survive being born in a hot, chaotic oven?

• The Analogy: Imagine a snowball being thrown into a blast furnace. Usually, it melts instantly.
• The Answer: Neutron stars are incredibly tough. Their gravity is so strong that even if the universe around them was hot (but not too hot), the particles on the surface couldn't escape. The paper calculates that as long as the universe didn't get hotter than about 200 million degrees, these baby stars would survive the "reheating" phase and live to tell the tale today.

Why Does This Matter?

This paper is a "what if" scenario. It doesn't prove these stars exist, but it proves that it is physically possible for them to exist under the right conditions.

• It changes the rules: It suggests the universe could have made "mini" neutron stars that we didn't know were possible.
• It solves a mystery: If we find a lot of invisible, low-mass neutron stars, it could explain where some of the universe's "missing mass" (Dark Matter) is hiding.
• It needs a check: The authors admit they need to run super-computer simulations to see if these stars actually survive the crash or if they inevitably turn into black holes.

In short: The universe might have a secret population of tiny, cold, ancient neutron stars hiding in the dark, waiting for us to figure out how to find them.

Technical Summary

1. Problem Statement

Standard cosmology posits that neutron stars (NS) form exclusively from the gravitational collapse of massive stars ($>1.4 M_\odot$) at the end of their stellar evolution. Consequently, the formation of neutron stars is restricted to late cosmic times (redshift $z \sim 20$ or later).

The authors address a theoretical gap: Can neutron stars form in the early universe (primordially)?

• The Constraint: In standard Big Bang Nucleosynthesis (BBN) cosmology, the baryon-to-photon ratio is $Y_B \sim 10^{-10}$. Under these conditions, the baryonic mass contained within a cosmological horizon is insufficient to form a neutron star ($M_{NS} \gtrsim 0.1 M_\odot$) until well after BBN.
• The Challenge: To form a primordial neutron star (PNS) before BBN, the universe must temporarily possess a much higher baryon density, and density perturbations must be large enough to trigger collapse, yet not so large that they inevitably form Primordial Black Holes (PBHs).

2. Methodology and Cosmological Model

The authors propose a novel cosmological scenario involving three specific ingredients to enable PNS formation before BBN:

A. Enhanced Baryon Asymmetry ($Y_B \gg 10^{-10}$)

• Mechanism: The paper utilizes Affleck-Dine baryogenesis, where a complex scalar field with baryon number acquires a large vacuum expectation value after inflation.
• Effect: This generates an initial baryon yield $Y_B(a_{BG}) \gg 10^{-10}$.
• Consequence: As the universe cools below the QCD confinement scale ($\Lambda_{QCD} \sim 200$ MeV), quarks and gluons confine into non-relativistic protons and neutrons. Due to the high $Y_B$, the universe transitions immediately into a baryon-dominated era (rather than radiation-dominated) shortly after confinement.

B. Enhanced Small-Scale Density Perturbations

• Requirement: The model assumes primordial fluctuations are significantly enhanced on small scales (horizon masses $M_H \sim 0.1 - 2 M_\odot$), while preserving the standard power spectrum on large scales (to satisfy CMB constraints).
• Dynamics: During the baryon-dominated era, these overdensities re-enter the horizon. Because the background is matter-dominated, perturbations grow linearly with the scale factor ($\delta \propto a$).

C. Entropy Injection (Reheating)

• Problem: The high initial $Y_B$ would ruin standard BBN predictions if it persisted.
• Solution: The model introduces an Early Dark Energy (EDE) component (modeled as a scalar field trapped in a false vacuum).
• Process:
  1. The EDE eventually dominates the universe, causing exponential expansion (inflation-like) which dilutes the baryon density relative to the entropy.
  2. The EDE field tunnels to a true minimum, decaying into Standard Model particles.
  3. This reheats the universe to a temperature $T_{RH}$ (where $MeV < T_{RH} < \Lambda_{QCD}$), injecting entropy and diluting the baryon-to-photon ratio back to the observed value $Y_B \sim 10^{-10}$ just before BBN begins.

3. Key Contributions and Formation Criteria

The paper derives the specific physical conditions required for a collapsing overdensity to form a neutron star rather than a black hole.

• The "Goldilocks" Overdensity Window:
  • Collapse Initiation: A perturbation must exceed the Jeans criterion at horizon crossing: $\delta_H > c_s^2(t^*)$, where $c_s$ is the sound speed of the baryonic fluid.
  • Arrested Collapse (PNS vs. PBH):
    • If $\delta_H > c_{s, nuc}^2$ (where $c_{s, nuc} \approx 0.2 - 0.6$ is the sound speed in nuclear matter), the collapse is unstoppable, leading to a Primordial Black Hole (PBH).
    • If $c_s^2(t^*) \lesssim \delta_H \lesssim c_{s, nuc}^2$, the overdensity collapses initially but is arrested by nuclear pressure once the density reaches nuclear saturation ($\rho_{nuc} \approx 2 \times 10^{14}$ g/cm$^3$). This results in a Primordial Neutron Star (PNS).
• Mass Range: Unlike stellar NS, PNS can theoretically be as light as $\sim 0.1 M_\odot$, limited only by the nuclear equation of state, as they do not require a progenitor star.
• Survival: The authors demonstrate that PNS formed during the baryon-dominated era can survive the subsequent reheating phase. The binding energy of a neutron star ($\sim 10^{53}$ erg) vastly exceeds the energy deposited by the reheating plasma ($\sim 10^{50}$ erg), provided $T_{RH} \lesssim 200$ MeV.

4. Results and Parameters

• Benchmark Scenarios: The authors provide three benchmark models (Table I) satisfying the formation criteria.
  • Example: A scenario with initial $Y_B \approx 0.5$, reheating temperature $T_{RH} \approx 10-50$ MeV, and EDE domination lasting $\sim 4.5-6.5$ e-folds.
  • Outcome: These parameters allow for the formation of stable PNS with masses between $0.9 M_\odot$ and $1.9 M_\odot$ (and potentially lower) before BBN.
• Abundance: The abundance of PNS depends on the probability distribution of primordial perturbations within the narrow window defined by Eq. (14). While a dedicated numerical simulation is required for precise abundance estimates, the authors argue that PNS could constitute a sub-component of Dark Matter ($\rho_{PNS}/\rho_{DM} \lesssim 10^{-1}$).

5. Significance and Observational Consequences

• Novelty: This is the first proposal suggesting that neutron stars can form primordially, distinct from the standard stellar collapse channel.
• Distinctive Properties:
  • Temperature: PNS would be extremely cold (kinetically coupled to the CMB for most of history) compared to astrophysical NS.
  • Magnetic Fields: They are unlikely to host strong magnetic fields or become pulsars, as they lack the dynamo mechanisms of stellar progenitors.
  • Mass Spectrum: They could populate the "sub-solar" mass range ($< 1 M_\odot$), which is difficult to explain via standard stellar evolution.
• Dark Matter Candidate: PNS could serve as a form of compact dark matter. However, constraints from microlensing (typically applied to PBHs) may be weaker for PNS if their formation mechanism differs significantly from PBH formation.
• Gravitational Waves: The phase transition of the EDE field responsible for reheating could generate a stochastic gravitational wave background detectable by Pulsar Timing Arrays (PTAs) in the nanohertz frequency range.

Conclusion

The paper establishes a theoretically plausible pathway for the formation of primordial neutron stars. It identifies a specific window in the early universe where high baryon density and enhanced perturbations allow for gravitational collapse that is halted by nuclear pressure rather than forming a black hole. The scenario requires subsequent entropy injection to restore standard cosmology, a process that leaves the PNS intact. The authors emphasize that while the analytic conditions are met, dedicated numerical simulations are necessary to confirm the nonlinear collapse dynamics and precise abundance predictions.