Large language models (LLMs) have shown strong capabilities in complex reasoning, and test-time scaling techniques can enhance their performance with comparably low cost. Many of these methods have been developed and evaluated on mathematical reasoning benchmarks such as AIME. This paper investigates whether the lessons learned from these benchmarks generalize to the domain of advanced theoretical physics. We evaluate a range of common test-time scaling methods on the TPBench physics dataset and compare their effectiveness with results on AIME. To better leverage the structure of physics problems, we develop a novel, symbolic weak-verifier framework to improve parallel scaling results. Our empirical results demonstrate that this method significantly outperforms existing test-time scaling approaches on TPBench. We also evaluate our method on AIME, confirming its effectiveness in solving advanced mathematical problems. Our findings highlight the power of step-wise symbolic verification for tackling complex scientific problems.

One well-known method of generating a large blue spectral index for axionic isocurvature perturbations is through a flat direction not having a quartic potential term for the radial partner of the axion field. In this work, we show how one can obtain a large blue spectral index even with a quartic potential term associated with the Peccei-Quinn symmetry breaking radial partner. We use the fact that a large radial direction with a quartic term can naturally induce a conformal limit which generates an isocurvature spectral index of 3. We point out that this conformal representation is intrinsically different from both the ordinary equilibrium axion scenario or massless fields in Minkowski spacetime. Another way to view this limit is as a scenario where the angular momentum of the initial conditions slows down the radial field or as a superfluid limit. Quantization of the nonstatic system in which the derivative of the radial field and the derivative of the angular field do not commute is treated with great care to compute the vacuum state. The parametric region consistent with axion dark matter and isocurvature cosmology is discussed.

We introduce a benchmark to evaluate the capability of AI to solve problems in theoretical physics (TP), focusing on high-energy theory and cosmology. The first iteration of our benchmark consists of 57 problems of varying difficulty, from undergraduate to research level. These problems are novel in the sense that they do not come from public problem collections. We evaluate our data set on various open and closed language models, including o3-mini, o1, DeepSeek-R1, GPT-4o and versions of Llama and Qwen. While we find impressive progress in model performance with the most recent models, our research-level difficulty problems are mostly unsolved. We address challenges of auto-verifiability and grading, and discuss common failure modes. While currently state-of-the art models are still of limited use for researchers, our results show that AI assisted TP research may become possible in the near future. We discuss the main obstacles towards this goal and possible strategies to overcome them. The public problems and solutions, results for various models, and updates to the data set and score distribution, are available on the website of the dataset tpbench.org.

Large blue tilted spectral index axionic isocurvature perturbations can be produced when the axion sector is far out of equilibrium during inflation through an initial Peccei-Quinn (PQ) symmetry breaking field displacement along a nearly flat direction in the effective potential. As a companion to a previous work, we present analytic formulae for the blue isocurvature spectrum for the case of the kinetic energy density of the PQ symmetry breaking field being larger than the quartic power of the final spontaneous PQ symmetry breaking scale. It corresponds to a regime in which the nonlinearities of the classical potential become important many times during the formation of the axion isocurvature quantum perturbations leading to interesting resonant behavior. One consequence of this nonlinearity-driven resonance is the chaotic nature of the map that links the underlying Lagrangian parameters to the isocurvature amplitudes. We point out an accidental duality symmetry between the perturbation equations and the background field equations that can be used to understand this. Finally, we present two types of analytic results. The first relies on a computation utilizing an effective potential wherein fast time scale fluctuations have been integrated out. The second is grounded in a functional ansatz, requiring only a limited set of fitting parameters. Both analytic results should be useful for carrying out forecasts and fits to the data.

Isocurvature perturbations with a blue power spectrum are one of the natural targets for the future large scale structure observations which are probing shorter length scales with greater accuracy. We present a Fisher forecast for the Euclid and MegaMapper (MM) experiments in their ability to detect blue isocurvature perturbations. We construct the theoretical predictions in the EFTofLSS and bias expansion formalisms at quartic order in overdensities which allows us to compute the power spectrum at one loop order and bispectrum at tree level and further include theoretical error at the next to leading order for the covariance determination. We find that Euclid is expected to provide at least a factor of few improvement on the isocurvature spectral amplitude compared to the existing Planck constraints for large spectral indices while MM is expected to provide about 1 to 1.5 order of magnitude im provement for a broad range of spectral indices. We find features that are specific to the blue isocurvature scenario including the leading parametric degeneracy being with the Laplacian bias and a UV sensitive bare sound speed parameter.

Previous numerical investigations of gravitational particle production during the coherent oscillation period of inflation displayed unexplained fluctuations in the spectral density of the produced particles. We argue that these features are due to the quantum interference of the coherent scattering reactions that produce the particles. We provide accurate analytic formulae to compute the particle production amplitude for a conformally-coupled scalar field, including the interference effect in the kinematic region where the production can be interpreted as inflaton scattering into scalar final states via graviton exchange.

Previous computations of strongly blue tilted axionic isocurvature spectra were computed in the parametric region in which the lightest time-dependent mass is smaller than the Hubble expansion rate during inflation, leading to an overdamped time evolution. Here we present the strongly blue tilted axionic isocurvature spectrum in an underdamped time evolution parametric regime. Somewhat surprisingly, there exist parametric regions with a strong resonant spectral behavior that leads to a rich isocurvature spectral shape. We focus on computing this resonant spectrum analytically in a large parametric region amenable to such computations. Because the spectrum is sensitive to nonperturbative classical field dynamics, a wide variety of analytic techniques are used including a time-space effective potential obtained by integrating out high frequency fluctuations.

Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of U(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an [Formula: see text] permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame-dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field.

Analytic and numerical techniques are presented for computing gravitational production of scalar particles in the limit that the inflaton mass is much larger than the Hubble expansion rate at the end of inflation. These techniques rely upon adiabatic invariants and time modeling of a typical inflaton field which has slow and fast time variation components. A faster computation time for numerical integration is achieved via subtraction of slowly varying components that are ultimately exponentially suppressed. The fast oscillatory remnant results in production of scalar particles with a mass larger than the inflationary Hubble expansion rate through a mechanism analogous to perturbative particle scattering. An improved effective Boltzmann collision equation description of this particle production mechanism is developed. This model allows computation of the spectrum using only adiabatic invariants, avoiding the need to explicitly solve the inflaton equations of motion.

Basis tensor gauge theory is a vierbein analog reformulation of ordinary gauge theories in which the difference of local field degrees of freedom has the interpretation of an object similar to a Wilson line. Here we present a non-Abelian basis tensor gauge theory formalism. Unlike in the Abelian case, the map between the ordinary gauge field and the basis tensor gauge field is nonlinear. To test the formalism, we compute the beta function and the two-point function at the one-loop level in non-Abelian basis tensor gauge theory and show that it reproduces the well-known results from the usual formulation of non-Abelian gauge theory.

Through a mechanism similar to perturbative particle scattering, particles of mass mχ larger than the Hubble expansion rate Hinf during inflation can be gravitationally produced at the end of inflation without the exponential suppression powers of exp(−mχ/Hinf ). Here we develop an analytic formalism for computing particle production for such massive particles. We apply our formalism to specific models that have been previously been studied only numerically, and we find that our analytical approximations reproduce those numerical estimates well.

The research at the energy frontier was to explore high energy and luminosity collisions at the LHC using the ATLAS and CMS detectors to lead physics analyses in characterization of the Higgs Boson, to search for its potential partners, to lead searches for Dark Matter and to make extensive studies of Electroweak phenomena. The objectives are also to operate and upgrade the ATLAS and CMS detectors and their computing to optimize their physics performance in the present data taking and to enable the full exploitation of planned High Luminosity LHC. The research for the theory frontier was to analyze and interpret the new data from the experimental frontiers: energy, cosmic and intensity (Phenomenology), to investigate new theories of high energy physics extending the standard model by including gravity within consistent frameworks such as string theory, and examine their phenomenological and cosmological implications (String Theory and Theoretical Cosmology.)

It is known that if the Peccei-Quinn symmetry-breaking field is displaced from its minimum during inflation, the axion isocurvature spectrum is generically strongly blue tilted with a break transition to a flat spectrum. We fit this spectrum (incorporated into the "vanilla" Lambda-CDM cosmological model) to the Planck and BOSS DR11 data to assess how much the existing data can accommodate the presence of axionic bluetilted isocurvature perturbations. We find that the preferred parameter region is consistent with all of the dark matter being composed of QCD axions in the context of inflationary cosmology with an expansion rate of order 10(8) GeV, the axion decay constant of order 10(13) GeV, and the initial misalignment angle of order unity. The data are consistent with there being no isocurvature perturbations at the level of just above one sigma. Intriguingly, isocurvature with a spectral break may at least partially explain the low-l vs high-l anomalies seen in the CMB data.

Basis tensor gauge theory (BTGT) is a reformulation of ordinary gauge theory that is an analog of the vierbein formulation of gravity and is related to the Wilson line formulation. To match ordinary gauge theories coupled to matter, the BTGT formalism requires a continuous symmetry that we call the BTGT symmetry in addition to the ordinary gauge symmetry. After classically interpreting the BTGT symmetry, we construct using the BTGT formalism the Ward identities associated with the BTGT symmetry and the ordinary gauge symmetry. For a way of testing the quantum stability and the consistency of the Ward identities with a known regularization method, we explicitly renormalize the scalar QED at one loop using dimensional regularization using the BTGT formalism.

It is known that if the Peccei-Quinn symmetry breaking field is displaced from its minimum during inflation, the axion isocurvature spectrum is generically strongly blue tilted with a break transition to a flat spectrum. We fit this spectrum (incorporated into the vanilla $Lambda$-CDM cosmological model) to the Planck and BOSS DR11 data and find a mild hint for the presence of axionic blue-tilted isocurvature perturbations. We find the best fit parameter region is consistent with all of the dark matter being composed of QCD axions in the context of inflationary cosmology with an expansion rate of order $10^{8}$ GeV, the axion decay constant of order $10^{13}$ GeV, and the initial misalignment angle of order unity. Intriguingly, isocurvature with a spectral break may at least partially explain the low-$ell$ vs. high-$ell$ anomalies seen in the CMB data.

Blue axion isocurvature perturbations are both theoretically well motivated and interesting from a detectability perspective. These power spectra generically have a break from the blue region to a flat region. Previous investigations of the power spectra were analytic, which left a gap in the predicted spectrum in the break region due to the nonapplicability of the used analytic techniques. We therefore compute the isocurvature spectrum numerically for an explicit supersymmetric axion model. We find a bump that enhances the isocurvature signal for this class of scenarios. A fitting function of three parameters is constructed that fits the spectrum well for the particular axion model we study. This fitting function should be useful for blue isocurvature signal hunting in data and making experimental sensitivity forecasts.

We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under the dual representation of the charged matter field. These local fields, which naively have the interpretation of nonlocal operators similar to Wilson lines, satisfy constraint equations. A set of basis tensor fields is used to solve these constraint equations, and their field theory is constructed. A new local symmetry in terms of the basis tensor fields is used to make this field theory local and maintain a Hamiltonian that is bounded from below. The field theory of the basis tensor fields is what we call the basis tensor gauge theory.

We show that if a spectator linear isocurvature dark matter field degree of freedom has a constant mass through its entire evolution history, the maximum measurable isocurvature spectral index that is consistent with the current tensor-to-scalar ratio bound is about 2.4, even if experiments can be sensitive to a $10^{-6}$ contamination of the predominantly adiabatic power spectrum with an isocurvature power spectrum at the shortest observable length scales. Hence, any foreseeable future measurement of a blue isocurvature spectral index larger than about 2.4 may provide nontrivial evidence for dynamical degrees of freedom with time-dependent masses during inflation. The bound is not sensitive to the details of the reheating scenario and can be made mildly smaller if the tensor-to-scalar ratio is better constrained in the future.

Blue CDM-photon isocurvature perturbations are attractive in terms of observability and may be typical from the perspective of generic mass relations in supergravity. We present and apply three theorems useful for blue isocurvature perturbations arising from linear spectator scalar fields. In the process, we give a more precise formula for the blue spectrum associated with the axion model of 0904.3800, which can in a parametric corner give a factor of O(10) correction. We explain how a conserved current associated with Peccei-Quinn symmetry plays a crucial role and explicitly plot several example spectra including the breaks in the spectra. We also resolve a little puzzle arising from a naive multiplication of isocurvature expression that sheds light on the gravitational imprint of the adiabatic perturbations on the fields responsible for blue isocurvature fluctuations.

Isocurvature perturbations in the inflationary literature typically involve quantum fluctuations of bosonic field degrees of freedom. In this work, we consider isocurvature perturbations from fermionic quantum fluctuations during inflation. When a stable massive fermion is coupled to a non-conformal sector different from the scalar metric perturbations, observably large amplitude scale invariant isocurvature perturbations can be generated. In addition to the computation of the isocurvature two-point function, an estimate of the local non-Gaussianities is also given and found to be promising for observations in a corner of the parameter space. The results provide a new class of cosmological probes for theories with stable massive fermions. On the technical side, we explicitly renormalize the composite operator in curved spacetime and show that gravitational Ward identities play an important role in suppressing certain contributions to the fermionic isocurvature perturbations.