ABSTRACT
The observed dominance of matter over antimatter in the universe remains one of the most profound open questions in cosmology. Traditional explanations such as baryogenesis and leptogenesis invoke new physics beyond the Standard Model, relying on CP violation and out-of-equilibrium conditions, but often treat entropy as a passive constraint. In this work, we propose a novel mechanism in which entropic and statistical constraints during the reheating phase of the early universe actively drive the emergence of a matter–antimatter asymmetry. As the universe approaches thermal equilibrium and maximal entropy, the production and annihilation dynamics of particles become biased by constraints imposed due to entropy after the reheating phase of inflation. This scenario operates entirely within the bounds of established thermodynamics and quantum field theory, requiring no new physics. Our approach offers a fresh perspective on the origin of the cosmic matter–antimatter asymmetry and suggests new avenues for connecting statistical mechanics with fundamental cosmological observations.
Inflation 1 is a period of extremely rapid, accelerated expansion of space-time, during which the universe expands much faster than the speed of light (note: this is the expansion of space itself, not objects moving through space).
- This inflationary phase smooths out the universe and stretches quantum fluctuations to cosmic scales.
- Inflation ends with a process called reheating (including preheating), during which the energy driving inflation is converted into a hot, dense plasma of particles.
- This process of particle production and thermalization marks the beginning of the hot Big Bang phase, from which the universe continues to expand and cool, eventually forming the structures we observe today.
Inflation rapidly expands the universe, ends with the creation and thermalization of particles, and sets the stage for the hot Big Bang.
Quantum vacuum fluctuations stretched by inflation become the seeds for galaxies. The inflaton decays through preheating (non-perturbative, rapid) and reheating (perturbative, slower), producing all Standard Model particles. After reheating, no new particles are produced from the inflaton, and the universe evolves through interactions among existing particles, with structure forming from the original density fluctuations.
Quantum Fluctuations and Inflation
- Tiny quantum fluctuations of the vacuum exist everywhere.
- During inflation, the universe expands exponentially, stretching these fluctuations to macroscopic (cosmic) scales.
- As they are stretched beyond the horizon (faster than light due to space expansion), these fluctuations become "classical" and get imprinted as density variations.
End of Inflation: Particle Production
- Preheating :The inflaton field (which drove inflation) oscillates and decays non-perturbatively, rapidly producing large numbers of particles (including Standard Model particles) through collective effects like parametric resonance.
- Reheating: Any remaining inflaton energy decays perturbatively (slower, standard quantum decay), producing more particles and allowing the universe to thermalize into a hot, dense plasma.
After Reheating
- Once reheating ends, the inflaton has decayed, and no new particles are produced from it.
- The universe is filled with a hot soup of Standard Model particles.
- Particle interactions (scattering, annihilation, decay) continue, but these just transform existing particles—they don’t create new ones from the inflaton.
Formation of Structure
- The density variations ("frozen in" during inflation) serve as seeds for all cosmic structures.
- Over time, gravity amplifies these small variations, leading to the formation of galaxies and larger structures as mass clusters in the denser regions.
Inflation → Reheating → Hot Big Bang (radiation-dominated universe, nucleosynthesis, cosmic microwave background, etc.)
During reheating the universe reaches a state of thermal equilibrium
For a system in thermodynamic equilibrium, the entropy is maximized and remains constant for the given constraints 2.
- At equilibrium, all thermodynamic quantities—including entropy—are constant in time.
- The system’s entropy cannot increase further because it has already reached the maximum possible value allowed by the constraints.
- If the entropy could still increase, the system would not be at equilibrium by definition.
The state of the universe during reheating was of maximal entropy.
During the reheating phase of the Big Bang, the second law of thermodynamics and thermalization imposed a maximum entropy constraint, driving asymmetric particle production (single particles or antiparticles) over symmetric particle-antiparticle pair production. We postulate that the second law and thermalization drove this asymmetric particle production during reheating, maintaining maximum entropy and ensuring a matter/antimatter excess.
(The fluctuation theorem indicates that local entropy decreases, are possible but exponentially unlikely, favoring processes that maintain or increase entropy.)
Asymmetric production avoids excessive entropy spikes from pair annihilation into photons and can also absorb photons to balance entropy fluctuations. This ensures a matter or antimatter excess persists, preventing a photon-dominated universe. The inflaton’s energy sustains particle production during thermalization, with asymmetric processes aligning with the second law to maintain maximum entropy.
Post-thermalization, the universe’s entropy continues to increase via expansion and interactions, consistent with thermodynamic principles. This framework explains the observed matter-antimatter asymmetry and guarantees that complete annihilation into photons is avoided, ensuring the presence of matter or antimatter in the universe.
The pair production during the reheating stage was suppressed because their annihilation produces photons which have higher entropy due to a larger number of microstates available than fermions.
Why do photons tend to have more microstates?
Bose-Einstein Statistics:
- Photons are bosons: there's no limit on how many photons can occupy the same quantum state.
- This leads to many more accessible microstates at a given energy — you can "pile up" photons into the same state, creating a large number of configurations.
Fermi-Dirac Statistics:
- Baryons are fermions: subject to the Pauli exclusion principle, so no two identical baryons can occupy the same quantum state.
- This severely restricts the number of microstates available to a system of baryons.
Degrees of Freedom:
- Photons have 2 polarization states (even though they’re spin-1, they’re transverse), but still far more microstates because they can occupy any energy level.
- Baryons have more internal structure, but due to their mass and quantum restrictions, this doesn’t translate to more thermal microstates at a given energy.
In the early universe:
- Photons outnumbered baryons by 1 billion to 1.
- Most of the universe’s entropy is carried by relativistic particles like photons (and neutrinos), not baryons.
The Big Bang should have produced equal amounts of matter and antimatter. This is clearly not the case and in our universe we observe dominance of matter over anti matter 3. To date this remains one of the great unsolved problems in physics . Typically Baryogenisis and Leptogenisis are used to explain why matter dominates over anti matter
- Baryogenesis refers to the generation of an asymmetry between baryons (particles like protons and neutrons) and antibaryons in the early universe, resulting in the excess of matter over antimatter we observe today 4.
- Leptogenesis specifically refers to the generation of an asymmetry between leptons (such as electrons and neutrinos) and antileptons. In many models, this lepton asymmetry is later partially converted into a baryon asymmetry through processes that violate both baryon and lepton number conservation, such as sphaleron transitions in the Standard Model 4.
Baryogenesis is about the direct creation of more baryons than antibaryons, while leptogenesis creates a lepton asymmetry first, which is then converted into a baryon asymmetry through known particle physics processes 4.
Both baryogenesis and leptogenesis require extensions to the Standard Model (SM) of particle physics. The SM alone does not provide sufficient sources of CP violation or mechanisms to generate the observed matter-antimatter asymmetry in the universe.
- Leptogenesis typically involves extending the SM by introducing heavy right-handed Majorana neutrinos (as in the seesaw mechanism) or other new particles, which decay out of equilibrium and violate lepton number and CP symmetry, generating a lepton asymmetry that is partially converted to a baryon asymmetry via sphaleron processes.
- Baryogenesis also generally requires new physics beyond the SM, such as additional Higgs fields, supersymmetry, or other mechanisms that can provide the necessary out-of-equilibrium conditions and sufficient CP violation to create a baryon asymmetry.
Neither baryogenesis nor leptogenesis can be fully realized within the Standard Model; both require new particles or interactions beyond those currently known.
Both Baryogenisis and Leptogenisis don't take the entropy of the universe into account.
During the reheating phase as the universe reaches a thermal equilibrium asymmetrical production could be initiated by the presence of an isolated bayron or lepton(particle pairs move in an opp direction to conserve their momentum as they are created)
This happens because of the following reasons
- As discussed above bosons have more microstates than fermions
- Particle anti particle pairs tend to annihilate leading to photon production. As the universe reaches maximal entropy this outcome becomes less likely.
- A single particle skews the production to more particles of the same kind. This suppresses the probability of production of corresponding anti particles. For example an un annihilated electron may lead to production of more electrons.
- To preserve charge equivalent amounts of quarks are produced ,if for example the initial seed is an electron or electrons are produced if the initial seed is a quark. Reverse could also be true if the initial seed is a positron or an anti quark.
- These fermions maintain the maximal entropy by absorbing excess photons.
Mechanism Details
Reheating introduces new thermodynamic constraints that were not active during preheating. Now the system has additional entropic constraints that it needs to account for. Any snapshot of the universe we take at this time would be in local thermodynamic equilibrium and in a state of maximal entropy. The universe continues to expand and increase its entropy but it remains maximised at any instant. This tension leads to asymmetric particle production.
- Particle-antiparticle pairs are produced as usual during preheating, but their rapid separation (due to momentum conservation) prevents immediate annihilation.
- Entropic effects that emerge during reheating suppress further pair production, as it would lead to annihilation and photon production, increasing entropy beyond the maximal value allowed in thermal equilibrium. Single particle production is favoured and their conjugate production becomes less likely.
- Newly produced particles are energized and occupy high-entropy states, with excess photons absorbed to stabilize entropy if it approaches or exceeds the maximum allowable value.
- Pair production is disfavored because it leads to instability (via annihilation and photon production), while single-particle production maintains entropy and charge is balanced through production of oppositely charged particles that are not antiparticles.
Distinction from Baryogenesis/Leptogenesis
- Unlike baryogenesis and leptogenesis, which require new physics (e.g., heavy Majorana neutrinos, extra Higgs fields, or supersymmetry), this model operates entirely within the SM, using thermodynamic and statistical principles.
- This model tries to explain the matter–antimatter asymmetry “cleanly” by relying on entropy constraints, avoiding new particles needed in traditional models.
Baryon-to-Photon Ratio:
- The observed baryon-to-photon ratio (η ≈ 6 × 10⁻¹⁰) results from most particle-antiparticle pairs annihilating into photons, with excess single particles produced to prevent further annihilation and maintain maximal entropy.
Thermal Equilibrium and Entropy:
- The universe reaches thermal equilibrium during reheating, implying maximal entropy at that stage. The fluctuation theorem ensures that entropy-decreasing processes (e.g., symmetric pair production) are statistically unlikely.
- Photon absorption by newly produced particles prevents entropy from exceeding the maximum allowable value, stabilizing the system.
To get a sense of scale we begin by considering the size of the observable universe today -- 93 Billion light years across. At the end of inflation its scale factor was 10^-30 times smaller than what it is presently 5,6. If we plug in the numbers this gives us a size of about .88mm at the end of the reheating period.
There are an estimated 10^97 particles in the observable universe 7. (Some estimates claim the number of particles to be 10^88). All of these particles had to be constrained in a volume that was just .88mm in radius. Even if we take eventual expansion into account this small volume leads to massive entropic constraints on the observable universe at the end of inflation changing the particle production behaviour. So the brief period when the universe was thermalised and the reheating was in effect these entropic constraints drove the particle production process.
A comparison of bosonic and fermionic degrees of freedom in a relativistic plasma 8,9 such as during the end of the reheating period reveals that fermions have an entropy of about 2.701kb while bosons have entropy of about 3.602kb.
During reheating, entropic constraints in thermal equilibrium favor single particle production (e.g., an electron) over particle-antiparticle pairs (e.g., electron-positron). Pair production is suppressed because annihilation causes quantized excitations in the electromagnetic (EM) field, producing photons and increasing entropy beyond the maximum value allowed. When the electron is emitted, for example, the system suppresses positron field excitation to prevent its emission thereby reducing the chance of annihilation that could cause excitations of the EM field leading to photon emission and hence stabilizing entropy.
During the reheating phase, photons were continuously absorbed and re-emitted as well as scattered—all these interactions were so frequent that photons couldn’t travel freely, making the universe effectively opaque.
This brings us to another important aspect. Charge neutralisation. Why balance charges? Why not simply produce particles of one type? All electrons or all up quarks?
Although all fermions have the same entropy in a relativistic plasma domination by a single charge would have led to massive electrostatic repulsion producing photons via bremstrahllung, electron electron collision resulting in an increase of entropy. For this reason charges were balanced with emission of particles of different charges that could not annihilate. For example electrons with quarks.
Single particles absorb excess photons and maintain entropy, leading to the matter–antimatter asymmetry within the Standard Model.
This is also one of the reasons why charged particle production was favoured during this very brief phase. Because unlike neutrinos they have the capacity to absorb photons and maintain entropy. Neutrinos don't interact with the EM field at all.
The universe was in local thermal equilibrium within the small volume (~0.88 mm), where entropy was maximized for the given energy and constraints, as per the second law and fluctuation theorem.Note that the reheating timescale is so short (10^-35 to 10^-32s)that expansion-driven entropy increase(10^-32 to 10^-10 seconds) is negligible during particle production, allowing the system to prioritize single particle production to avoid photon-driven entropy spikes.
In the brief period of reheating we got all of the excess matter particles that dominate the present universe. This model suggests that the dominance of matter over anti matter is not due to a finely tuned process but a randomness in a thermal bath that led to an isolated elementary particle shifting the pair production process to balance entropic and charge constraints.
CONCLUSION
The persistent mystery of the universe’s matter–antimatter asymmetry has long motivated the search for new physics beyond the Standard Model. In this article, we have introduced a novel perspective: that entropic and statistical constraints during the reheating phase of the early universe may have played a direct, active role in generating the observed matter excess. By considering the maximization of entropy and the dynamics of particle production at thermal equilibrium, we propose that randomness—rather than new physics—could have seeded an initial imbalance, which was then amplified by entropic constraints to favor matter over antimatter. This approach is firmly grounded in established principles of thermodynamics and quantum field theory, and offers a compelling alternative to conventional baryogenesis and leptogenesis scenarios. While further quantitative modeling and comparison with observational data are needed, this entropic mechanism provides a promising new direction for understanding one of cosmology’s deepest puzzles, and highlights the profound interplay between statistical mechanics and the evolution of the early universe.
REFERENCES
1 Introductory review of cosmic inflation
https://arxiv.org/abs/hep-ph/0304257
2 https://en.m.wikipedia.org/wiki/Entropy_(classical_thermodynamics)
3 Matter and Antimatter in the Universe
https://arxiv.org/abs/1204.4186
4 Baryogenesis and Leptogenesis
https://www.slac.stanford.edu/econf/C040802/papers/L018.PDF
5 Inflation and the cosmic microwave background
https://arxiv.org/PS_cache/astro-ph/pdf/0305/0305179v1.pdf
6 Size of the universe after inflation
https://physics.stackexchange.com/questions/32917/size-of-universe-after-inflation
7 Elementary particles
https://en.m.wikipedia.org/wiki/Elementary_particle
8 On Effective Degrees of Freedom in the
Early Universe
https://arxiv.org/pdf/1609.04979
9 https://en.m.wikipedia.org/wiki/Ap%C3%A9ry's_constant
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