The starting point is Einstein–Cartan gravity, an extension of general relativity in which the connection that defines parallel transport is treated as an independent field, à la Palatini, and can carry torsion. In ordinary general relativity, a certain pseudoscalar quantity built from the curvature—the Holst invariant—always vanishes, because the connection reduces to its torsion-free Levi-Civita part. In the class of models studied by Carlo Di Benedetto, Alessandro Di Marco, Emanuele Orazi and Gianfranco Pradisi, however, the torsionful contortion tensor is dynamical, and a nonlinear term in the Holst curvature gives rise to a genuine pseudoscalar degree of freedom. This field, dubbed the pseudoscalaron, is not inserted by hand: it emerges directly from the geometry of spacetime and plays the role of the inflaton.

After a field redefinition, the theory takes the form of a standard single-field slow-roll model with a canonical kinetic term and a potential shaped by two parameters: the exponent p of the nonlinear Holst term and the Barbero–Immirzi parameter γ, a constant that multiplies the Holst invariant. The sign of γ fixes the direction in which the inflaton rolls, while its magnitude controls the height of the inflationary plateau—smaller |γ| means a higher inflation scale and a shorter plateau. For the case p = 2 that the authors focus on, the potential features a flat slow-roll region, a vacuum at zero field value, and an exponential tail at large field amplitudes.

Comparing the model’s predictions for the scalar spectral index n_s and the tensor-to-scalar ratio r against the latest data from Planck, the Atacama Cosmology Telescope, the South Pole Telescope, BICEP/Keck and DESI baryon acoustic oscillations, the team finds broad compatibility. For Barbero–Immirzi parameters in the range roughly γ = −1/80 to −1/150 and 50 to 60 e-folds of inflation, the predicted (n_s, r) pairs sit comfortably within the 68 to 95 percent confidence regions of the observational datasets. For the benchmark γ ≈ −1/100, the model yields n_s ≈ 0.970 and r ≈ 0.004, with the tensor-to-scalar ratio safely below current upper limits. The authors also note a caveat: a mild 2–3 sigma tension exists between CMB and DESI BAO constraints within standard Lambda cold dark matter, so joint constraints should be interpreted with care.

The truly distinctive physics emerges after inflation ends. Because matter fermions are minimally coupled to the full torsionful spin connection, integrating out the contortion produces a universal derivative coupling between the pseudoscalaron and every fermion in the theory, of the form of the pseudoscalaron gradient times the axial fermion bilinear, suppressed by the reduced Planck mass. Crucially, the resulting decay rate of the inflaton into a fermion pair is proportional to the square of the fermion’s mass. Standard Model fermions—effectively massless before electroweak symmetry breaking, and topped by the top quark at roughly 171 GeV afterward—therefore absorb almost none of the inflaton’s energy. Heavy right-handed Majorana neutrinos, by contrast, are ideal decay products.

This mass-squared scaling has a dramatic consequence. In the benchmark scenario, the inflaton mass is of order 10^14 GeV, so only the lightest of the three right-handed neutrinos, N1, with a mass below roughly 5 × 10^13 GeV, is kinematically accessible. The heavier states N2 and N3 play no cosmological role. The inflaton decays almost exclusively into pairs of N1, which are produced nonrelativistically and out of equilibrium. These heavy neutrinos then decay rapidly into Standard Model leptons and Higgs bosons, generating both the hot radiation plasma that ends reheating and a net lepton asymmetry, controlled by the CP-violating parameter ε1, which later electroweak sphaleron processes convert into the baryon asymmetry of the Universe.

The hierarchy of decay rates is striking. With M_N1 ∼ 10^13 GeV and an effective light neutrino mass of about 10^−3 eV, the N1 decay width is around 7 × 10^7 GeV, while the inflaton’s decay width into N1 pairs is only about 7 × 10^−3 GeV—a ratio of roughly 10^−10. The heavy neutrinos therefore decay essentially instantaneously on the timescale set by the inflaton, meaning the inflaton’s lifetime alone dictates the duration of reheating and the reheating temperature, which comes out below about 3 × 10^8 GeV in the favored parameter region. The authors solve the coupled Einstein–Boltzmann equations for the inflaton, heavy-neutrino and radiation energy densities and the lepton asymmetry both numerically and analytically, finding that the approximate solutions reliably capture the late-time evolution toward radiation domination.

The final numbers are encouraging. For γ ≈ −1/100, a lightest right-handed neutrino mass above about 10^13 GeV, and a CP asymmetry parameter of order 3 × 10^−5 in magnitude—well within the Davidson–Ibarra upper bound of roughly 3.4 × 10^−2 set by neutrino oscillation data—the mechanism produces a baryon-to-entropy ratio n_B/s ≈ 8.7 × 10^−11, matching the observed value. Because the mechanism is nonthermal, there is no direct link between the reheating temperature and the heavy-neutrino mass, unlike in vanilla thermal leptogenesis where the lightest right-handed neutrino must weigh at least 10^9 to 10^10 GeV and force a very high reheating temperature. That decoupling helps avoid the gravitino overproduction problem that plagues supersymmetric extensions, and it opens a path toward embedding the scenario in supergravity and its ultraviolet completions such as string theory or M-theory.

The study remains theoretical, and the authors are candid about the limits of predictability. Seesaw models contain 21 free parameters beyond the Standard Model ones, and current neutrino data cannot fix the Yukawa couplings, the Majorana nature of active neutrinos, or the mass hierarchy of the heavy states. What the paper establishes is a consistency proof: over a wide window of the Barbero–Immirzi parameter, the same geometric inflaton that satisfies CMB constraints necessarily reheats the Universe through heavy-neutrino production, and that channel automatically yields the observed matter asymmetry. The team points toward future work that would add dark matter and dark energy to the picture, and toward the next generation of experiments that may finally constrain the seesaw parameter space. For now, the result stands as an unusually tight weave of spacetime geometry, inflation and the origin of matter—three puzzles usually treated separately, here resolved by a single torsion-driven field.

Subject of Research: Einstein–Cartan pseudoscalaron inflation, reheating and nonthermal leptogenesis in a type I seesaw extension of the Standard Model

Article Title: Einstein–Cartan pseudoscalaron inflation, reheating and nonthermal leptogenesis

Article References: Di Benedetto, C., Di Marco, A., Orazi, E., & Pradisi, G. (2026). Einstein–Cartan pseudoscalaron inflation, reheating and nonthermal leptogenesis. The European Physical Journal C, 86(10), Article 1206. https://doi.org/10.1140/epjc/s10052-026-16310-x

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16310-x

Keywords: cosmic inflation, Einstein–Cartan gravity, torsion, Barbero–Immirzi parameter, leptogenesis, right-handed neutrinos, seesaw mechanism, reheating, baryon asymmetry, cosmic microwave background, neutrino physics, theoretical physics

The type-I seesaw framework can explain light-neutrino masses and generate a lepton asymmetry through out-of-equilibrium decays of heavy right-handed neutrinos, which sphaleron processes convert into a baryon asymmetry. Its conventional version, however, places the right-handed neutrinos at scales that are difficult to access experimentally. With order-one Yukawa couplings, neutrino masses around 10^13 GeV can arise naturally, while hierarchical masses above roughly 10^9 GeV are generally needed to produce enough asymmetry. Alternative low-scale approaches include resonant leptogenesis and leptogenesis via neutrino oscillations, but both typically require a highly degenerate right-handed-neutrino spectrum.

The study instead considers a scalar singlet S that couples to different right-handed neutrinos through terms of the form SN_IN_J. These interactions open the decay channel N_I → N_JS and add one-loop vertex and self-energy contributions to the CP asymmetries in neutrino decays. The analysis treats this as a theoretical possibility, not an experimentally established mechanism, and finds that the scalar-assisted process can produce a sufficient asymmetry at TeV scales without mass degeneracy.

Yan Shao and Zhen-hua Zhao identify flavons in flavor-symmetry neutrino models as natural candidates for S. These scalar fields commonly acquire nonzero vacuum expectation values that help generate right-handed-neutrino masses. The authors first illustrate the idea with the classic A₄ flavor-symmetry model. That A₄ model predicts tri-bimaximal neutrino mixing, including a vanishing mixing angle θ₁₃, a prediction ruled out by experimental measurements.

For their numerical analysis, the authors therefore use a different flavor-symmetry construction based on A₄ and three auxiliary Z₂ symmetries. It is designed to realize the trimaximal TM1 mixing pattern, which modifies the tri-bimaximal pattern in the two-three plane and is consistent with current experimental results. The model contains one relevant flavon, S, which is allowed by the flavor symmetries to couple only to the second and third right-handed neutrinos through α₀SN₂⁰N₃⁰. Its vacuum expectation value generates an off-diagonal right-handed-neutrino mass term and the rotation required to transform tri-bimaximal mixing into TM1 mixing.

The same flavon interaction also supplies the couplings used in the leptogenesis calculation, making the mixing structure and baryogenesis mechanism consequences of one flavor-symmetry term rather than independent additions. The authors assume that the decoupled N₁ is the heaviest right-handed neutrino and neglect its effects on leptogenesis, while taking M₃ > M₂. Their flavor-dependent Boltzmann equations include standard neutrino decays and inverse decays, the transition N₃ → N₂S, and dominant scalar-mediated ΔL = 2 scattering processes. The resulting baryon-to-entropy ratio is compared with the observed value, (8.69 ± 0.04) × 10⁻¹¹.

In a representative numerical example, M₂ is 2 TeV, M₃ is 4 TeV, and both the flavon mass and the Higgs–flavon trilinear coupling β are 1 GeV. With |α₀| = 0.1, conventional flavored CP asymmetries from N₃ decays are estimated at about 10⁻¹⁶–10⁻¹⁴, whereas the flavon-mediated vertex and self-energy contributions raise the total to approximately 10⁻⁷–10⁻⁵. The new decay channel must be kinematically open, requiring m_S < M₃ − M₂. When it closes, the additional contributions and the D₃₂ transition disappear, and the conventional asymmetries are too small to account for the observed value in the TeV-scale regime examined.

Parameter scans reproduce the observed baryon asymmetry in significant regions for both normal and inverted light-neutrino mass orderings. In the normal-ordering case, the authors find successful leptogenesis with M₂ as low as about 200 GeV under their parameter setup, with viable β values extending to roughly 10 GeV. As M₂ increases, larger β values become viable; at M₂ = 5 TeV, successful regions occur at β values of order 10 TeV. The inverted-ordering case exhibits similar qualitative behavior but has a more restricted viable parameter space. Changing the flavon mass has only a slight effect on the final asymmetry in the studied scans.

The viable regions also satisfy constraints from the Higgs and flavon scalar sector. Higgs signal-strength data limit the scalar mixing angle to |sin θ| ≲ 0.3, and the Higgs invisible branching ratio is constrained to 0.23 or less. The scalar potential must also remain stable at its vacuum and perturbative. These requirements remove some parameter space but leave viable regions in both mass orderings. The study is theoretical and model-specific: its numerical conclusions apply to the selected TM1 flavor-symmetry construction and parameter ranges, rather than establishing a unique explanation for the cosmic asymmetry.

Subject of Research: Theoretical modeling of flavon-assisted low-scale leptogenesis in flavor-symmetry neutrino models

Article Title: Flavon assisted low scale leptogenesis

Article References: Shao, Y., & Zhao, Z.-H. (2026). Flavon assisted low scale leptogenesis. The European Physical Journal C, 86(10), Article 1179. https://doi.org/10.1140/epjc/s10052-026-16421-5

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16421-5

Keywords: leptogenesis, flavons, right-handed neutrinos, baryon asymmetry, TM1 mixing, type-I seesaw, CP violation, Higgs portal, neutrino flavor symmetry, Flavon, assisted, scale

The starting point is a set of facts the standard model simply cannot accommodate. Neutrino oscillation experiments have established beyond doubt that neutrinos have nonzero mass, something the standard model forbids. Observations of the abundances of light elements forged in the Big Bang, together with measurements of the cosmic microwave background, show that the early universe contained slightly more baryons than antibaryons, another phenomenon the standard model cannot produce. And a wealth of astrophysical and cosmological evidence points to dark matter, an invisible substance that outweighs ordinary matter roughly five to one, for which the standard model offers no candidate at all. Extending the model with right-handed neutrinos that carry Majorana masses has long been known to address the first two problems: the seesaw mechanism explains why observed neutrinos are so light, and leptogenesis, the out-of-equilibrium decay of heavy right-handed neutrinos, can seed the baryon asymmetry, provided those masses exceed roughly a billion giga-electronvolts.

What makes the new work striking is the claim that all three problems can be solved at the relatively low energy scale of a few tera-electronvolts, within the original scotogenic model and without adding any new interactions. The scotogenic model, introduced by Ernest Ma in 2006, extends the standard model with three right-handed neutrinos and an extra inert doublet scalar, both assigned odd parity under an imposed Z2 symmetry while all ordinary particles carry even parity. Because the inert doublet acquires no vacuum expectation value, neutrino masses vanish at tree level. Instead, they arise radiatively through a one-loop diagram in which the right-handed neutrinos couple to leptons and the inert scalar, with the small parameter lambda-5 in the scalar potential controlling the resulting tiny masses. The same Z2 symmetry renders the lightest odd particle absolutely stable, a built-in dark matter candidate.

Previous attempts to make the lightest right-handed neutrino the dark matter in this framework ran into two serious obstacles. First, if the dark matter particle annihilates efficiently enough to leave the correct relic abundance in the standard freezeout scenario, its neutrino Yukawa couplings must be of order one, and such large couplings induce lepton-flavor-violating processes such as the decay of a muon into an electron and a photon at levels already excluded by experiment. Second, generating sufficient lepton number asymmetry from right-handed neutrinos with masses of only a few tera-electronvolts is notoriously difficult, because the CP asymmetry in their decays is typically too small at that scale. Many authors have therefore extended the model with extra interactions, such as a new gauge symmetry, to circumvent these problems.

Suematsu’s solution exploits a detailed feature of the neutrino mass matrix that emerges when the diagonalization condition makes the mass eigenvalues expressible directly in terms of the Yukawa couplings. In the concrete example analyzed, the Yukawa texture yields the tribimaximal mixing pattern, with one neutrino mass eigenvalue exactly zero, and the charged-lepton sector supplies the small corrections needed to match oscillation data. Crucially, the CP asymmetry required for leptogenesis is proportional to the imaginary part of a combination of Yukawa couplings, which vanishes if those couplings are real. The analysis shows that complex Yukawa couplings, or the special case with a zero mass eigenvalue combined with Majorana phases in the right-handed neutrino masses, allow a nonzero asymmetry. A numerical benchmark with the two heavier right-handed neutrinos and the neutral component of the inert doublet all near three tera-electronvolts reproduces the measured mass-squared differences of neutrino oscillations while keeping lepton-flavor-violating decays safely below current bounds.

The dark matter abundance is handled through a mechanism quite different from the usual freezeout. Because the lightest right-handed neutrino’s Yukawa coupling is extremely small, it never reaches thermal equilibrium; instead it is produced by the gradual, so-called freeze-in process, mainly through the decay of the next-lightest inert scalar component, which itself is kept in equilibrium by standard model interactions and coannihilation. Solving the coupled Boltzmann equations for the number densities shows that the final dark matter abundance can be tuned to the observed value, corresponding to a density parameter of about 0.12, by choosing the small Yukawa coupling appropriately for dark matter masses ranging from a few giga-electronvolts up to the tera-electronvolt scale, and even down to the kilo-electronvolt range. When the dark matter mass approaches that of its decaying mother particle, the scalar quartic couplings lambda-3 and lambda-4, which control the coannihilation rate, become essential dials, and the analysis finds that a dark matter mass of at least about 8.5 giga-electronvolts is needed in the simplest case.

The leptogenesis side relies on an elegant trick: a strict near-degeneracy between the second-heaviest right-handed neutrino and the neutral inert scalar, with their masses differing by a fraction of order one hundred-thousandth or less. This degeneracy suppresses the decay width of the heavier neutrino through phase-space factors, delaying its decay until it falls far out of thermal equilibrium, exactly the condition leptogenesis requires. Meanwhile, a tiny mass splitting with the heaviest right-handed neutrino, of order one part in a billion, resonantly enhances the CP asymmetry through the self-energy diagram, boosting it to the level of ten to the minus seven needed to generate the observed lepton asymmetry of order ten to the minus ten. Quantum corrections to the right-handed neutrino masses, calculated at two loops, turn out to be far too small to spoil this delicate degeneracy, so no extra symmetry is needed to protect it.

The full numerical treatment, tracking the number densities of the decaying neutrino, the lepton asymmetry, the inert scalar and the dark matter candidate simultaneously, confirms that the scenario holds together. The late-time decay of the second-heaviest neutrino injects additional inert scalars into the plasma, which eventually decay into dark matter and modify the final abundance, so the couplings must be retuned compared with the simplified analysis. The study shows this retuning works across the mass range: for dark matter at 150 giga-electronvolts or 1.5 giga-electronvolts, a suitably small Yukawa coupling delivers the right abundance, while for dark matter near the tera-electronvolt scale the quartic couplings must be adjusted so that the combined abundance of the scalar and the dark matter particle converges to the required value. Notably, because the dark matter is the right-handed neutrino itself, direct detection experiments impose no constraint on the scalar quartics, a sharp contrast with the case where the inert scalar is the dark matter.

The scenario also carries testable consequences. The charged and neutral components of the inert doublet, with masses near three tera-electronvolts, could be produced at future colliders, where processes yielding multiple leptons plus missing transverse energy, displaced vertices from long-lived charged scalars, or deviations in the Higgs decays to two photons and to a photon plus a Z boson could distinguish this model from the ordinary inert doublet model. Predictions for the effective masses governing neutrinoless double beta decay and beta decay come out far below present experimental sensitivity, and the induced lepton-flavor-violating branching ratios and the electron electric dipole moment are similarly tiny, making them difficult but not impossible targets for next-generation searches. If the picture is right, the three great mysteries left unsolved by the standard model would trace back to a single family of particles, with the universe’s missing mass and its matter-antimatter imbalance written into the same small set of couplings, and the decisive evidence waiting in the debris of high-energy collisions rather than in a deep underground detector.

Subject of Research: Right-handed neutrino dark matter and leptogenesis in the scotogenic model

Article Title: Right-handed neutrino dark matter consistent with the generation of baryon number asymmetry

Article References: Suematsu, D. (2026). Right-handed neutrino dark matter consistent with the generation of baryon number asymmetry. The European Physical Journal C, 86(10), Article 1143. https://doi.org/10.1140/epjc/s10052-026-16425-1

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16425-1

Keywords: dark matter, right-handed neutrinos, scotogenic model, leptogenesis, baryon asymmetry, neutrino masses, seesaw mechanism, freeze-in, inert doublet, Z2 symmetry, CP asymmetry, particle physics

The mechanism hinges on a subtle piece of quantum field theory. The researchers considered a model in which a Dirac fermion, the class of matter particles that includes electrons and quarks, couples directly to the oscillating inflaton through a pseudoscalar Yukawa interaction. In plain terms, the coupling involves the gamma-five matrix, an object in the Dirac equation that distinguishes between the two possible spin orientations of a particle relative to its direction of motion. Because the inflaton field swings back and forth like a cosmic pendulum, the effective mass that the fermion experiences, which the authors call the pseudo-mass, repeatedly changes sign. Every time it crosses zero, the quantum vacuum becomes unstable and pairs of fermions are wrenched into existence, and crucially, the two helicity states are not created in equal numbers.

To make this statement precise, the team turned to the WKB approximation, a semiclassical technique borrowed from quantum mechanics in which wave functions are written as exponentials with slowly varying amplitude and phase. By matching the solutions on either side of each zero crossing of the pseudo-mass, they derived analytical expressions for the Bogoliubov coefficients, the mathematical objects that encode how many particles are produced in each quantum mode. The calculation, which involves parabolic cylinder functions, remains valid for an arbitrary number of successive production events, a significant advance over earlier treatments that could only handle a single pass of the oscillating field.

The key result is that the pseudoscalar coupling injects an imaginary contribution into the first-order adiabatic phase, denoted by the authors as the complex phase of the fermion mode. This imaginary piece depends on the helicity state of the particle, and it is solely responsible for breaking the symmetry between left- and right-handed fermions. When the coupling is switched off, the phase vanishes and the familiar helicity-symmetric result of standard fermionic preheating is recovered, with occupation numbers falling off as a clean Gaussian in momentum space. With the coupling present, that Gaussian is warped, and the two helicities peel apart in a way that can be computed exactly.

The researchers also identified a sharp boundary condition on where the asymmetry can live. Helical asymmetry is generated only for comoving momenta much smaller than a characteristic wavelength set by the fermion mass and the expansion rate of the Universe. Once a mode’s wavelength enters the corresponding horizon scale, the asymmetry is dramatically suppressed. This means the imbalance is fundamentally a large-scale phenomenon, imprinted on the longest wavelengths available in the early cosmos, precisely the scales that could matter for subsequent cosmological evolution.

Perhaps the most striking finding concerns coherence. In an expanding Universe, the authors show that the combined effects of parametric resonance and Pauli blocking, the quantum-mechanical exclusion principle that caps fermion occupation at one particle per mode, produce coherent enhancement in certain frequency bands and coherent suppression in others. Unlike bosons, whose occupation numbers grow exponentially through Bose enhancement, fermions can only be nudged up or down within strict limits. The real part of the complex WKB phase governs this coherent superposition, and the numerical simulations reveal that it significantly boosts the number density of each helicity state after roughly eight oscillations of the inflaton, a periodicity traced back to a numerical factor in the imaginary part of the phase.

The team validated their analytics with numerical simulations in both a static universe and an expanding one. In the static case, the helical asymmetry appears as isolated narrow resonance bands in momentum space, reminiscent of the instability bands familiar from bosonic preheating. When cosmic expansion is included, these bands wash out, but the deviation from Gaussian helicity distributions persists and grows with each successive production event. The authors also found that heavier fermions concentrate their production on smaller physical scales, and that massless fermions, consistent with earlier results on gravitational particle production, escape the mechanism entirely.

What elevates this work beyond a technical exercise is its potential connection to one of the deepest mysteries in cosmology: why the Universe contains vastly more matter than antimatter. Helicity-asymmetric fermion production is a natural ingredient in leptogenesis scenarios, in which an early asymmetry in neutrino-like particles is eventually converted into the baryon asymmetry we observe today. Because the mechanism identified by the authors does not depend on the precise value of the inflaton mass, it applies equally to low-scale inflationary models such as small-field and hybrid inflation, widening the range of theories in which such an asymmetry could have been seeded.

The framework is also extendable in directions that touch other observational frontiers. The authors note that the same WKB machinery can accommodate momentum-dependent pseudoscalar couplings, quantum chromodynamics effects, and electroweak interactions, and that helical fermion production may be linked to the generation of primordial magnetic fields, chiral gravitational waves, and even dark matter production in the early Universe. Each of these connections offers a potential observational handle on a process that unfolded when the cosmos was a fraction of a second old.

For now, the result remains theoretical, resting on analytical mathematics and numerical simulation rather than direct measurement. But it sharpens a growing realization among cosmologists that the transition from inflation to the hot Big Bang was not a passive fade but an active, symmetry-breaking crucible. If the inflaton really did couple to fermions through a pseudoscalar channel, the newborn Universe may have emerged from preheating with a slight but decisive twist, a handedness written into its matter content that echoes, in principle, all the way to the galaxies we see today.

Subject of Research: Helical asymmetry in fermionic preheating induced by a pseudoscalar Yukawa coupling between the inflaton and Dirac fermions after inflation

Article Title: Pseudoscalar Yukawa coupling induced helical asymmetry in fermionic preheating

Article References: Fu, K., Liu, L.-S., Wang, Y.-F., Gu, X.-Y., & Li, X.-B. (2026). Pseudoscalar Yukawa coupling induced helical asymmetry in fermionic preheating. The European Physical Journal C, 86(9), Article 1083. https://doi.org/10.1140/epjc/s10052-026-16298-4

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16298-4

Keywords: preheating, cosmic inflation, fermion production, helicity asymmetry, pseudoscalar Yukawa coupling, inflaton, WKB approximation, Bogoliubov coefficients, leptogenesis, baryogenesis, early universe, quantum field theory