Sarunas Verner

Research

I work on four main areas of research, described below with a few results from each. Most of my projects combine analytical calculations in quantum field theory with numerical methods.

Cosmology

Inflation, reheating & dark matter

Reheating is the stage at which the inflaton transfers its energy to the particles of the hot Big Bang. I study how particles are produced during inflation and reheating, including cases in which gravity is the only interaction between the inflaton, the Standard Model, and dark matter.

Glowing cyan shells and bubbles of energy on a deep indigo field, from a lattice simulation of preheating
Preheating on a lattice. A two-dimensional lattice simulation computed for this site. An oscillating inflaton drives parametric resonance in a second field, χ. The image shows the energy density of χ on a logarithmic scale, just after the resonance turns nonlinear and the inflaton begins to fragment.

  • Gravitational portals

    We compute the production of dark matter and radiation through graviton exchange, from both the inflaton condensate and the thermal bath. In particular, we determine when gravity alone sets the dark matter abundance.

    Read the paper, arXiv:2112.15214

  • Nonminimal superheavy dark matter

    We study how couplings to spacetime curvature change the production of superheavy scalar dark matter after inflation, and we compute the resulting relic abundance and isocurvature constraints.

    Read the paper, arXiv:2408.11889

  • Axion kinetic misalignment

    Standard misalignment requires an axion decay constant of about 10¹¹ GeV or more to explain the observed dark matter. We show that when inflation leaves the Peccei–Quinn field at a large value, the field can start rotating, a mechanism known as kinetic misalignment, which produces the observed abundance for much smaller decay constants.

    Read the paper, arXiv:2004.00629

Attractor inflation, confronted with data

In α-attractor models, the spectral index ns and tensor-to-scalar ratio r depend on the attractor parameter α and on how the universe reheated after inflation. Choose a model and move α to see where its predictions fall against current CMB constraints.

Predictions of α-attractor inflation in the n_s, r planeThe spectral index n_s runs horizontally from 0.950 to 0.984 and the tensor-to-scalar ratio r vertically from 0 to 0.055. Shaded regions show Planck and P-ACT-LB 68% and 95% constraints and the CMB-SPA band. The model band shows predictions for reheating temperatures from the electroweak scale to 10^10 GeV.TBBNTEWN = 501010 GeVΓφ = Hendnsr0.9500.9550.9600.9650.9700.9750.9800.000.010.020.030.040.05

At α = 1, the E-model predicts ns between 0.9579 and 0.9628 and r between 0.0035 and 0.0044.

Planck
Inside the 68% region
P-ACT-LB
Outside the 95% region
CMB-SPA
Within 2σ

The shaded band covers reheating temperatures from the electroweak scale to 1010 GeV. The outer curves mark reheating at the BBN limit and instantaneous reheating, and the dashed curve marks N = 50. The solid segment shows the band at the chosen α, and its dotted extension spans the full reheating range. Planck and P-ACT-LB regions are 68% and 95%. The CMB-SPA band shows 1σ and 2σ in ns with r < 0.036. From Ellis, Garcia, Olive & Verner, Phys. Rev. D 113, 063571 (2026).

Theory

Particle physics

I work on physics beyond the Standard Model, including models of dark matter, flavor physics, supersymmetry, supergravity, and electroweak sphalerons. These problems require both analytical methods in field theory and numerical solutions of coupled nonlinear equations.

Energy against Chern–Simons number: a row of barriers between electroweak vacua, with the sphaleron on top of a barrier at 9.1 TeV, a thermal transition passing over it and tunneling passing underneath
The electroweak energy barrier. Energy of gauge and Higgs field configurations along the minimum-energy path between electroweak vacua, which sit at integer Chern–Simons number. The sphaleron sits on top of the barrier, with Esph ≃ 9.1 TeV for mH = 125.1 GeV (Matchev and Verner, 2025). A thermal transition over the barrier changes baryon and lepton number by three units each, while tunneling underneath is suppressed by e−4π/αW. The barrier shape is the standard sin² approximation.

  • Electroweak sphalerons

    We revisit the static electroweak sphaleron, its energy barrier, and its unstable mode, and then study its nonlinear decay. A public C solver and Mathematica notebook accompany the decay study.

    Read the papers, arXiv:2505.05607 and arXiv:2505.05608

  • Scattering in curved field space

    We calculate supergravity scattering amplitudes in Riemann and Kähler normal coordinates. Comparing the two approaches shows how the background and the field-space geometry enter the calculation.

    Read the paper, arXiv:2302.05456

  • No-scale supergravity and model building

    We construct no-scale supergravity models that unify inflation, modulus fixing, supersymmetry breaking, and dark energy. Related work studies the production of gravitinos after inflation.

    Read the paper, arXiv:1903.05267

Observables

Gravitational waves & new probes

Many particles beyond the Standard Model interact so weakly that they are difficult to detect in laboratory experiments, but they can still leave gravitational signatures. I develop cosmological and astrophysical probes of such physics, with a focus on spectator scalar fields, cosmic strings, and ultralight dark matter.

The gravitational wave landscape

This figure shows the sensitivity of current and future experiments to a stochastic gravitational wave background over 24 orders of magnitude in frequency.

Gravitational-wave sensitivity across 24 decades in frequencyEnergy density of a stochastic gravitational-wave background, Omega_GW h^2 from 10^-21 to 10^-4, against frequency from 10^-20 to 10^4 Hz. Shaded regions above each curve are the reach of CMB missions (Planck, LiteBIRD, PIXIE, Voyage 2050), pulsar timing and astrometry (EPTA, SKA, Gaia, Theia), space interferometers (LISA, μAres, DECIGO, BBO, Ultimate DECIGO), atom interferometers (AION, AEDGE) and ground-based interferometers (Advanced LIGO, Einstein Telescope, Cosmic Explorer). Also shown: the NANOGrav 15-year signal, the LIGO–Virgo–KAGRA O3 limit and the region excluded by the Planck 2018 bound on Delta N_eff.f [Hz]ΩGW h210−2010−1810−1610−1410−1210−1010−810−610−410−210010210410−2110−1810−1510−1210−910−6ΔNeff, Planck 2018PlanckLiteBIRDPIXIEVoyage 2050NANOGravEPTAGaiaSKATheiaμAresLISADECIGOBBOUltimate DECIGOAIONAEDGEaLIGOO3ETCE

Scroll the figure sideways to see all 24 decades.

CMB

Pulsar timing and astrometry

Space interferometers

Atom interferometers

Ground interferometers

Total energy, ΔNeff

Solid lines are current data, dashed lines are planned or proposed.

  • Spectator fields and gravitational waves

    We study how fluctuations of spectator scalar fields evolve after inflation and source a stochastic gravitational wave background. The resulting signal depends on particle production, reheating, and the growth of perturbations.

    Read the paper, arXiv:2512.04240

  • Astrometric searches for ultralight dark matter

    Ultralight dark matter perturbs the spacetime metric and shifts the apparent positions of distant sources such as quasars. We show that these secular and annually modulating signals can be searched for with astrometric surveys and radio interferometry.

    Read the paper, arXiv:2406.03526

  • Cosmic strings and their loops

    We compute the gravitational wave background produced by a network of cosmic strings, including the contributions of both long strings and loops.

    Read the paper, arXiv:2609.22430

Methods

Machine learning for theoretical physics

I develop machine learning methods for problems that are usually solved analytically, such as identifying symmetries, determining their algebraic structure, and searching for models with desired properties. Importantly, the results are interpretable: the learned symmetry generators and Lie algebra relations can be used in further theoretical work.

A twelve-fold symmetric web of violet lines connecting 72 points in concentric rings
The root system of E6. The 72 roots of the exceptional Lie algebra E6, projected onto its Coxeter plane, with an edge between every pair of roots whose inner product is one. E6 is among the groups recovered from data in our work on machine-learned symmetries.

  • Discovering continuous symmetries

    We develop neural networks that learn the transformations preserving labeled data, with constraints that enforce the structure of symmetry generators and closed algebras.

    Read the paper, arXiv:2301.05638

  • Exceptional Lie groups

    We also speed up these algorithms and identify the group structure of the learned symmetries, including the exceptional Lie groups G2, F4, and E6.

    Read the paper, arXiv:2307.04891

  • Exploring theory landscapes

    We construct loss functions that reward both agreement with data and structural properties such as sparsity, uniformity, or symmetry, using the quark Yukawa sector as an example.

    Read the paper, arXiv:2401.11513

Current directions

I work on several projects that are still in preparation. These include a review of reheating, studies of gravitational particle production in multifield inflation and supergravity, Hawking axions, the cosmic axion background, thermal damping of spectator fields, and AI agents for particle physics.

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