Primordial Neutron Stars

• Primordial neutron stars are hypothetical compact objects formed from early-universe overdensities rather than from stellar core collapse.
• They emerge under a baryon-dominated phase with enhanced density perturbations and require a secondary entropy injection to align with observed baryon asymmetry.
• Their structure obeys relativistic stellar constraints and TOV equations, with potential signatures in gravitational-wave signals and unique low-mass measurements.

Primordial neutron stars are hypothetical neutron stars formed in the early universe rather than through late-time stellar core collapse. In current literature, the term spans several distinct contexts: genuinely cosmological baryonic neutron stars formed before big bang nucleosynthesis, the proto-neutron-star phase that constitutes the earliest state of any newly born neutron star, and, more loosely, neutron stars whose evolution is shaped by primordial black holes. The most explicit cosmological scenario invokes a temporary baryon-dominated epoch, enhanced small-scale density perturbations, and a later entropy-injection stage to restore the observed baryon asymmetry, while any long-lived object produced in such a scenario must still satisfy the same general-relativistic stellar-structure and dense-matter constraints as ordinary neutron stars (Krnjaic et al., 9 Apr 2026, Piekarewicz, 2022).

1. Terminology and conceptual scope

The most direct use of the term refers to neutron stars that form primordially in the early universe. In this sense, the defining distinction is not composition but formation channel: collapse of early-universe overdensities before stellar populations exist, rather than collapse of an evolved stellar core (Krnjaic et al., 9 Apr 2026). A separate and older usage concerns the proto-neutron star, the first phase of life of a neutron star immediately after core collapse, when the remnant is hot, lepton-rich, and initially opaque to neutrinos (Camelio, 2018). These two ideas are related only insofar as both concern the earliest phases of neutron-star existence.

The literature also identifies a third, conceptually different class of systems: neutron stars that capture or harbor primordial black holes. In that setting, the phrase “primordial neutron star” is explicitly described as not standard, but primordial black holes embedded in neutron stars can generate exotic compact remnants, unusual gravitational-wave signatures, and compact-object phenomenology that can mimic or constrain primordial scenarios (Baumgarte et al., 2024). By contrast, the nuclear-physics review of neutron stars does not discuss primordial formation at all; its relevance is that the same TOV and equation-of-state framework constrains any neutron star, regardless of origin (Piekarewicz, 2022).

A common source of ambiguity is therefore terminological. “Primordial neutron star” may denote a truly cosmological neutron star, a proto-neutron star in its first seconds, or a neutron star modified by a primordial compact object. The underlying physics, observational signatures, and cosmological implications differ substantially across these usages.

2. Pre-BBN cosmological formation

A concrete cosmological scenario for primordial neutron-star formation assumes that baryogenesis initially produces an excessively large baryon asymmetry,

$Y_B \equiv \frac{n_B}{s} \gg 10^{-10},$

whereas the observed value is

$Y_B^{\rm obs} = (8.7 \pm 0.04)\times 10^{-11}.$

Under standard radiation domination with the observed yield, the baryonic mass inside the horizon is

$$M_B = \frac{4\pi m_p s Y_B}{3 H^3} \approx 0.3\,M_\odot\, \left(\frac{Y_B}{10^{-10}}\right) \left(\frac{500\,\text{keV}}{T}\right)^3,$$

so purely cosmological neutron-star formation before BBN is impossible in the standard thermal history (Krnjaic et al., 9 Apr 2026).

The proposed mechanism changes this by taking $Y_B(a_{\rm BG}) \gtrsim 10^{-2}-1$ after baryogenesis. When

$\sqrt{T^2 + (\mu/7)^2}\lesssim \Lambda_{\rm QCD},$

quarks confine into non-relativistic baryons and, because the asymmetry is large, baryon rest mass can dominate the energy density before BBN. In that baryon-dominated phase, the horizon mass in baryons is

$$M_H = \left(\frac{3}{32 \pi G^3 \rho_B}\right)^{1/2} \approx 1\,M_\odot \left(\frac{10^2\,\rho_{\rm nuc}}{\rho_B}\right)^{1/2},$$

with $$\rho_{\rm nuc} \approx 2\times 10^{14}\,\text{g cm}^{-3}$$, and the relevant horizon masses lie in the range

$M_H \in (0.1 - 2)\,M_\odot.$

This is precisely the range in which neutron-star formation becomes kinematically plausible (Krnjaic et al., 9 Apr 2026).

During baryon domination, subhorizon perturbations grow linearly,

$\delta(t)\propto a(t).$

For a spherically symmetric overdense patch entering the horizon with amplitude $\delta_H$, the adapted Jeans condition at turnaround is

$Y_B^{\rm obs} = (8.7 \pm 0.04)\times 10^{-11}.$0

The distinctive feature of the primordial neutron-star scenario is that the sound speed is initially small but stiffens sharply near nuclear density. The proposed window for neutron-star rather than black-hole formation is

$Y_B^{\rm obs} = (8.7 \pm 0.04)\times 10^{-11}.$1

with

$Y_B^{\rm obs} = (8.7 \pm 0.04)\times 10^{-11}.$2

If $Y_B^{\rm obs} = (8.7 \pm 0.04)\times 10^{-11}.$3 is too small, collapse never begins; if it is too large, even nuclear pressure cannot halt collapse and the outcome is a primordial black hole (Krnjaic et al., 9 Apr 2026).

The scenario requires a second cosmological ingredient: entropy injection after primordial neutron-star formation but before standard BBN. This is implemented through an early-dark-energy-like component that later reheats the universe to

$Y_B^{\rm obs} = (8.7 \pm 0.04)\times 10^{-11}.$4

so that baryons inside primordial neutron stars are not deconfined and standard BBN remains viable. The final baryon asymmetry after reheating is

$Y_B^{\rm obs} = (8.7 \pm 0.04)\times 10^{-11}.$5

where $Y_B^{\rm obs} = (8.7 \pm 0.04)\times 10^{-11}.$6. For $Y_B^{\rm obs} = (8.7 \pm 0.04)\times 10^{-11}.$7 MeV, reducing $Y_B^{\rm obs} = (8.7 \pm 0.04)\times 10^{-11}.$8 from order unity to the observed value requires $Y_B^{\rm obs} = (8.7 \pm 0.04)\times 10^{-11}.$9 (Krnjaic et al., 9 Apr 2026).

Within this framework, primordial neutron stars can, in principle, be as light as $$M_B = \frac{4\pi m_p s Y_B}{3 H^3} \approx 0.3\,M_\odot\, \left(\frac{Y_B}{10^{-10}}\right) \left(\frac{500\,\text{keV}}{T}\right)^3,$$0, limited only by the nuclear equation of state (Krnjaic et al., 9 Apr 2026). The collapse dynamics, however, are explicitly described as heuristic: the true threshold between primordial black-hole and primordial neutron-star formation depends on the full nonlinear hydrodynamics, the evolving equation of state, shocks, heating, turbulence, and neutrino transport. This leaves the primordial neutron-star abundance and mass function undetermined at present.

3. Relativistic stellar structure and dense-matter constraints

Regardless of formation channel, the macroscopic structure of a neutron star is governed by the TOV equations with an equation of state $$M_B = \frac{4\pi m_p s Y_B}{3 H^3} \approx 0.3\,M_\odot\, \left(\frac{Y_B}{10^{-10}}\right) \left(\frac{500\,\text{keV}}{T}\right)^3,$$1 (Piekarewicz, 2022). The compactness,

$$M_B = \frac{4\pi m_p s Y_B}{3 H^3} \approx 0.3\,M_\odot\, \left(\frac{Y_B}{10^{-10}}\right) \left(\frac{500\,\text{keV}}{T}\right)^3,$$2

controls both the relativistic structure and the escape speed, while the tidal deformability,

$$M_B = \frac{4\pi m_p s Y_B}{3 H^3} \approx 0.3\,M_\odot\, \left(\frac{Y_B}{10^{-10}}\right) \left(\frac{500\,\text{keV}}{T}\right)^3,$$3

links the internal equation of state to binary-merger observables (Piekarewicz, 2022).

This framework imposes immediate constraints on any primordial neutron star. Observations of ordinary neutron stars require multiple objects with $$M_B = \frac{4\pi m_p s Y_B}{3 H^3} \approx 0.3\,M_\odot\, \left(\frac{Y_B}{10^{-10}}\right) \left(\frac{500\,\text{keV}}{T}\right)^3,$$4, NICER radii of order $$M_B = \frac{4\pi m_p s Y_B}{3 H^3} \approx 0.3\,M_\odot\, \left(\frac{Y_B}{10^{-10}}\right) \left(\frac{500\,\text{keV}}{T}\right)^3,$$5 km for stars in the $$M_B = \frac{4\pi m_p s Y_B}{3 H^3} \approx 0.3\,M_\odot\, \left(\frac{Y_B}{10^{-10}}\right) \left(\frac{500\,\text{keV}}{T}\right)^3,$$6 range, and GW170817-compatible tidal deformabilities with $$M_B = \frac{4\pi m_p s Y_B}{3 H^3} \approx 0.3\,M_\odot\, \left(\frac{Y_B}{10^{-10}}\right) \left(\frac{500\,\text{keV}}{T}\right)^3,$$7 (Piekarewicz, 2022). A plausible implication is that any long-lived primordial neutron star with mass in the ordinary neutron-star range must lie on essentially the same mass-radius curve as ordinary neutron stars once it has cooled and reached beta equilibrium.

The most distinctive structural difference arises at the low-mass end. The primordial-formation scenario allows neutron stars down to

$$M_B = \frac{4\pi m_p s Y_B}{3 H^3} \approx 0.3\,M_\odot\, \left(\frac{Y_B}{10^{-10}}\right) \left(\frac{500\,\text{keV}}{T}\right)^3,$$8

whereas the lightest known neutron star formed through ordinary stellar evolution is $$M_B = \frac{4\pi m_p s Y_B}{3 H^3} \approx 0.3\,M_\odot\, \left(\frac{Y_B}{10^{-10}}\right) \left(\frac{500\,\text{keV}}{T}\right)^3,$$9 in J0453+1559 (Krnjaic et al., 9 Apr 2026). The difference is attributed to formation channel rather than equilibrium microphysics: core-collapse remnants inherit a mass floor from the progenitor core, whereas a cosmological collapse halted by nuclear pressure need only exceed the equation-of-state stability limit (Krnjaic et al., 9 Apr 2026).

The internal layering is expected to remain the standard neutron-star stratification once the object has cooled. The outer crust occupies densities $Y_B(a_{\rm BG}) \gtrsim 10^{-2}-1$0–$Y_B(a_{\rm BG}) \gtrsim 10^{-2}-1$1, the inner crust extends from neutron drip to $Y_B(a_{\rm BG}) \gtrsim 10^{-2}-1$2–$Y_B(a_{\rm BG}) \gtrsim 10^{-2}-1$3, the outer core contains $Y_B(a_{\rm BG}) \gtrsim 10^{-2}-1$4 matter with a typical proton fraction $Y_B(a_{\rm BG}) \gtrsim 10^{-2}-1$5, and the inner core above $Y_B(a_{\rm BG}) \gtrsim 10^{-2}-1$6 may contain hyperons, meson condensates, or deconfined quark matter, subject to the observed requirement that the equation of state still support $Y_B(a_{\rm BG}) \gtrsim 10^{-2}-1$7 stars (Piekarewicz, 2022).

The same dense-matter uncertainties that affect ordinary neutron stars therefore also affect primordial ones. In particular, the minimum mass $Y_B(a_{\rm BG}) \gtrsim 10^{-2}-1$8, the maximum mass $Y_B(a_{\rm BG}) \gtrsim 10^{-2}-1$9, and the nuclear-density stiffness window $\sqrt{T^2 + (\mu/7)^2}\lesssim \Lambda_{\rm QCD},$0 all depend directly on the poorly constrained high-density equation of state (Krnjaic et al., 9 Apr 2026, Piekarewicz, 2022).

4. Thermal birth state and relaxation to a cold neutron star

The best-developed early-time neutron-star framework is the proto-neutron-star literature. A proto-neutron star is the first phase of life of a neutron star after core collapse. After about $\sqrt{T^2 + (\mu/7)^2}\lesssim \Lambda_{\rm QCD},$1 ms from core collapse, its evolution may be approximated as a sequence of quasi-stationary configurations governed by neutrino diffusion and relativistic stellar-structure equations (Camelio, 2018).

The characteristic thermodynamic state is hot and lepton rich:

• $\sqrt{T^2 + (\mu/7)^2}\lesssim \Lambda_{\rm QCD},$2 MeV in the interior,
• $\sqrt{T^2 + (\mu/7)^2}\lesssim \Lambda_{\rm QCD},$3,
• neutrino mean free paths much shorter than the stellar radius.

Over the next tens of seconds, the object experiences Joule heating, deleptonization, and contraction. The radius shrinks from $\sqrt{T^2 + (\mu/7)^2}\lesssim \Lambda_{\rm QCD},$4 km to $\sqrt{T^2 + (\mu/7)^2}\lesssim \Lambda_{\rm QCD},$5 km, and when the temperature falls below $\sqrt{T^2 + (\mu/7)^2}\lesssim \Lambda_{\rm QCD},$6 MeV and the neutrino mean free path exceeds the radius, the star becomes transparent to neutrinos and turns into a cold, catalyzed neutron star (Camelio, 2018).

The same work gives a consistent finite-temperature transport framework based on TOV structure, neutrino-number and energy-transport equations, and microphysically consistent neutrino opacities (Camelio, 2018). It also shows that the detailed cooling and deleptonization timescales depend sensitively on the equation of state and on many-body corrections to neutrino cross sections. For example, different nucleonic equations of state produce different peak temperatures, different deleptonization times, and different neutrino light curves (Camelio, 2018).

This does not directly prove that a cosmologically formed primordial neutron star would follow the same thermal trajectory, because the cosmological collapse problem has not yet been simulated in comparable detail. It does, however, suggest that any primordial neutron star born hot and neutrino trapped would tend toward the same cold, beta-equilibrated endpoint as an ordinary neutron star once neutrino diffusion and contraction have run their course. In that sense, primordial origin primarily changes the initial conditions and cosmological context, not the attractor state of cold dense matter.

5. Primordial black holes, hybrid objects, and gravitational-wave phenomenology

A substantial adjacent literature studies neutron stars that capture primordial black holes. This is not the same problem as primordial neutron-star formation, but it is central to the modern phenomenology of primordial compact objects. Small primordial black holes of mass $\sqrt{T^2 + (\mu/7)^2}\lesssim \Lambda_{\rm QCD},$7 can be captured by neutron stars, lose energy through dynamical friction, accretion drag, and gravitational radiation, become confined inside the star, and then grow by accretion of stellar material (Baumgarte et al., 2024).

In the relativistic point-mass treatment, the neutron star is modeled as a non-rotating relativistic star with

$\sqrt{T^2 + (\mu/7)^2}\lesssim \Lambda_{\rm QCD},$8

and the PBH is treated as a relativistic point mass moving in the fixed neutron-star spacetime, valid while $\sqrt{T^2 + (\mu/7)^2}\lesssim \Lambda_{\rm QCD},$9 (Baumgarte et al., 2024). For a first passage through the star, the energy-loss estimate

$$M_H = \left(\frac{3}{32 \pi G^3 \rho_B}\right)^{1/2} \approx 1\,M_\odot \left(\frac{10^2\,\rho_{\rm nuc}}{\rho_B}\right)^{1/2},$$0

implies a capture condition

$$M_H = \left(\frac{3}{32 \pi G^3 \rho_B}\right)^{1/2} \approx 1\,M_\odot \left(\frac{10^2\,\rho_{\rm nuc}}{\rho_B}\right)^{1/2},$$1

After capture, the PBH often requires many passages before full confinement, with a characteristic number

$$M_H = \left(\frac{3}{32 \pi G^3 \rho_B}\right)^{1/2} \approx 1\,M_\odot \left(\frac{10^2\,\rho_{\rm nuc}}{\rho_B}\right)^{1/2},$$2

and the confined orbit generally remains highly eccentric rather than circularizing efficiently (Baumgarte et al., 2024).

Once confined, the PBH emits long-lived, quasi-periodic continuous gravitational waves in the kHz band. A distinct feature is that, in realistic neutron-star models, the gravitational-wave frequency rises near the surface, then decreases to a constant value deeper within the star, a behavior proposed as a smoking gun of a compact object inspiraling inside a self-gravitating fluid rather than in vacuum (Gao et al., 2023). The same work finds that the Einstein Telescope can differentiate between various equations of state for neutron stars using these signals (Gao et al., 2023).

If the PBH reaches the center and accretes quasi-spherically, the survival time of the host neutron star becomes very short on astrophysical scales. For an endoparasitic central black hole, the maximum survival time is

$$M_H = \left(\frac{3}{32 \pi G^3 \rho_B}\right)^{1/2} \approx 1\,M_\odot \left(\frac{10^2\,\rho_{\rm nuc}}{\rho_B}\right)^{1/2},$$3

with only weak dependence on the stiffness of stiff polytropic equations of state for $$M_H = \left(\frac{3}{32 \pi G^3 \rho_B}\right)^{1/2} \approx 1\,M_\odot \left(\frac{10^2\,\rho_{\rm nuc}}{\rho_B}\right)^{1/2},$$4 (Baumgarte et al., 2021). A captured PBH can therefore convert an ordinary neutron star into a stellar-mass black hole, potentially mimicking an exotic primordial remnant (Baumgarte et al., 2024).

Environmental limits matter. A refined study of PBH capture near the Galactic center finds that the velocity dispersion is too high for dynamical capture of PBHs to explain the lack of observed pulsars there, and that constraints from old neutron stars near Sgr A* cannot presently be extended into the asteroid-mass window because low-mass PBHs lose too little energy and end up on loosely bound orbits likely to be disrupted by other stars (Caiozzo et al., 2024). This clarifies a common misconception: primordial-black-hole effects on neutron stars are potentially important, but they do not automatically imply a large contemporary population of PBH-modified neutron stars in every dense environment.

6. Alternative proposals, surface composition, and open problems

An alternative and much more speculative proposal treats primordial neutron stars as dark-matter candidates formed from a neutrino-neutron superfluid seed. In that scenario, $$M_H = \left(\frac{3}{32 \pi G^3 \rho_B}\right)^{1/2} \approx 1\,M_\odot \left(\frac{10^2\,\rho_{\rm nuc}}{\rho_B}\right)^{1/2},$$5-boson exchange induces an attractive interaction between left-handed neutrinos and neutrons, producing a $$M_H = \left(\frac{3}{32 \pi G^3 \rho_B}\right)^{1/2} \approx 1\,M_\odot \left(\frac{10^2\,\rho_{\rm nuc}}{\rho_B}\right)^{1/2},$$6 pair condensate and superfluidity below a critical temperature

$$M_H = \left(\frac{3}{32 \pi G^3 \rho_B}\right)^{1/2} \approx 1\,M_\odot \left(\frac{10^2\,\rho_{\rm nuc}}{\rho_B}\right)^{1/2},$$7

with accretion of surrounding fermions becoming efficient near

$$M_H = \left(\frac{3}{32 \pi G^3 \rho_B}\right)^{1/2} \approx 1\,M_\odot \left(\frac{10^2\,\rho_{\rm nuc}}{\rho_B}\right)^{1/2},$$8

The resulting horizon-scale condensates have characteristic sizes $$M_H = \left(\frac{3}{32 \pi G^3 \rho_B}\right)^{1/2} \approx 1\,M_\odot \left(\frac{10^2\,\rho_{\rm nuc}}{\rho_B}\right)^{1/2},$$9 to $$\rho_{\rm nuc} \approx 2\times 10^{14}\,\text{g cm}^{-3}$$0 cm and masses between Earth and sub-solar scales, after which accretion of $$\rho_{\rm nuc} \approx 2\times 10^{14}\,\text{g cm}^{-3}$$1 matter in beta equilibrium is proposed to form primordial neutron stars (Yoshimura, 2022). The same work argues that the diffuse condensate behaves like dark energy while the compact objects behave like cold dark matter (Yoshimura, 2022).

That proposal is explicitly incomplete. It does not present a detailed microscopic equation of state for the final compact object, does not solve the TOV equations, and leaves relic abundance, stability, and mass-spectrum calculations for future work (Yoshimura, 2022). In contrast, the baryon-dominated-collapse scenario is structurally closer to standard compact-object physics because it invokes gravitational collapse halted by nuclear pressure and then embeds the result in the ordinary neutron-star equation-of-state framework (Krnjaic et al., 9 Apr 2026).

Surface composition provides an additional observational discriminator. In the absence of subsequent accretion, diffusive nuclear burning removes primordial hydrogen and helium from neutron-star surfaces during early cooling. For helium on carbon, once the base temperature satisfies

$$\rho_{\rm nuc} \approx 2\times 10^{14}\,\text{g cm}^{-3}$$2

helium is readily captured onto carbon, and the conclusion is that primordial H and He are depleted from the surface like the case for primordial H (Chang et al., 2010). A plausible implication is that an old primordial neutron star with no later accretion should expose a mid-$$\rho_{\rm nuc} \approx 2\times 10^{14}\,\text{g cm}^{-3}$$3 atmosphere rather than a persistent H/He photosphere (Chang et al., 2010).

The principal open problems remain those identified in the formation literature. They include full nonlinear GR hydrodynamical simulations of the collapse and the PBH/PNS threshold, the required small-scale primordial power spectrum, the microphysics of entropy injection and reheating, the relic abundance and spatial distribution of primordial neutron stars, and the equation-of-state dependence of the minimum stable mass and nuclear-density stiffness (Krnjaic et al., 9 Apr 2026). Observationally, the clearest targets are sub-solar-mass neutron stars, which ordinary stellar evolution does not produce, and auxiliary signatures such as an nHz gravitational-wave background from the MeV-scale phase transition associated with reheating in the baryon-dominated scenario (Krnjaic et al., 9 Apr 2026).

Taken together, the literature supports a narrow but technically coherent statement. A primordial neutron star, in the strict cosmological sense, is a neutron star formed before BBN from early-universe collapse rather than stellar evolution; if such objects exist, their equilibrium structure is still controlled by the same dense-matter and relativistic-stellar-structure physics as ordinary neutron stars, but their allowed mass range may extend down to $$\rho_{\rm nuc} \approx 2\times 10^{14}\,\text{g cm}^{-3}$$4 and their cosmological formation history introduces new collapse thresholds, entropy-dilution requirements, and observational signatures (Krnjaic et al., 9 Apr 2026, Piekarewicz, 2022).