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Based on a previously derived superstring model possessing a cosmological sector that mimics Starobinsky inflation, we analyze several questions addressed in the recent literature: the generation of an effective $R^2$-term, the stability of the sgoldstino , the modular symmetry of the inflaton potential and the large distance swampland conjecture. We first show that the presence of the string dilaton stabilizes the sgoldstino direction in the supersymmetric case and no modification of the K\"ahler potential is needed. This is a generic property of a large class of Starobinsky type models within the framework of no-scale supergravity. We then present an explicit example of a string derived inflaton potential where the large values of the inflaton field during inflation imply a decompactification of two extra dimensions, while the scale of inflation is generated by higher order $\alpha'$-corrections via expectation values that cancel the D-term of an anomalous $U(1)$ symmetry and break the modular symmetry of the scalar potential. As a result, the scale of inflation is much lower than the compactification scale which at the end of inflation is fixed at the free-fermionic self-dual point at an (approximate) supersymmetric minimum., Comment: 24 pages

Though there is much interest in fair AI systems, the problem of fairness noncompliance -- which concerns whether fair models are used in practice -- has received lesser attention. Zero-Knowledge Proofs of Fairness (ZKPoF) address fairness noncompliance by allowing a service provider to verify to external parties that their model serves diverse demographics equitably, with guaranteed confidentiality over proprietary model parameters and data. They have great potential for building public trust and effective AI regulation, but no previous techniques for ZKPoF are fit for real-world deployment. We present OATH, the first ZKPoF framework that is (i) deployably efficient with client-facing communication comparable to in-the-clear ML as a Service query answering, and an offline audit phase that verifies an asymptotically constant quantity of answered queries, (ii) deployably flexible with modularity for any score-based classifier given a zero-knowledge proof of correct inference, (iii) deployably secure with an end-to-end security model that guarantees confidentiality and fairness across training, inference, and audits. We show that OATH obtains strong robustness against malicious adversaries at concretely efficient parameter settings. Notably, OATH provides a 1343x improvement to runtime over previous work for neural network ZKPoF, and scales up to much larger models -- even DNNs with tens of millions of parameters.

The expected improvements in the precision of inflationary physics observables including the scalar spectral index $n_{s}$ and the tensor-to-scalar ratio $r$ will reveal more than just the viability of a particular model of inflation. In the presence of a curvaton field $\chi$, supposedly dead models of inflation can be resurrected as these observables are affected by curvaton perturbations. For currently successful models, improved constraints will enable us to constrain the properties of extra decaying scalar degrees of freedom produced during inflation. In this work, we demonstrate these diverse uses of a curvaton field with the most recent constraints on ($n_{s},r$) and two exemplary inflation models, the Starobinsky model, and a model of new inflation. Our analysis invokes three free parameters: the curvaton mass $m_{\chi}$, its decay rate $\Gamma_{\chi}$ the reheating temperature $T_{\rm RH}$ produced by inflaton decays. We systematically analyze possible post-inflationary era scenarios of a curvaton field. By projecting the most recent CMB data on ($n_{s},r$) into this parameter space, we can either set constraints on the curvaton parameters from successful models of inflation (so that the success is not spoiled) or determine the parameters which are able to save a model for which $n_{s}$ is predicted to be below the experimental data. We emphasize that the initial value of $\langle \chi^2 \rangle \propto H^4/m_\chi^2$ produced during inflation is determined from a stochastic approach and thus not a free parameter in our analysis. We also investigate the production of local non-Gaussianity $f_{NL}^{(\rm loc)}$ and apply current CMB constraints to the parameter space. Intriguingly, we find that a large value of $f_{NL}^{(\rm loc)}$ of $\mathcal{O}(1)$ can be produced for both of the two representative inflation models., Comment: 14 pages, 4 figures

We study the anomalous magnetic moment of the muon, $g_\mu - 2 \equiv 2 a_\mu$, in the context of supersymmetric models beyond the CMSSM, where the unification of either the gaugino masses $M_{1,2,3}$ or sfermion and Higgs masses is relaxed, taking into account the measured mass of the Higgs boson, $m_H$, the cosmological dark matter density and the direct detection rate. We find that the model with non-unified gaugino masses can make a contribution $\Delta a_\mu\sim 20 \times 10^{-10}$ to the anomalous magnetic moment of the muon, for example if $M_{1,2} \sim 600$ GeV and $M_3\sim 8$ TeV. The model with non-universal sfermion and Higgs masses can provide even larger $\Delta a_\mu \sim 24 \times 10^{-10}$ if the sfermion masses for the first and the second generations are $ \sim 400 $ GeV and that of the third is $ \sim 8 $ TeV. We discuss the prospects for collider searches for supersymmetric particles in specific benchmark scenarios illustrating these possibilities, focusing in particular on the prospects for detecting the lighter smuon and the lightest neutralino., Comment: 34 pages, 17 figures

We study the effects on particle production of a Planck-suppressed coupling between the inflaton and a scalar dark matter candidate, $\chi$. In the absence of this coupling, the dominant source for the relic density of $\chi$ is the long wavelength modes produced from the scalar field fluctuations during inflation. In this case, there are strong constraints on the mass of the scalar and the reheating temperature after inflation from the present-day relic density of $\chi$ (assuming $\chi$ is stable). When a coupling $\sigma \phi^2 \chi^2$ is introduced, with $\sigma = {\tilde \sigma} m_\phi^2/ M_P^2 \sim 10^{-10} {\tilde \sigma}$, where $m_\phi$ is the inflaton mass, the allowed parameter space begins to open up considerably even for ${\tilde \sigma}$ as small as $\gtrsim 10^{-7}$. For ${\tilde \sigma} \gtrsim \frac{9}{16}$, particle production is dominated by the scattering of the inflaton condensate, either through single graviton exchange or the contact interaction between $\phi$ and $\chi$. In this regime, the range of allowed masses and reheating temperatures is maximal. For $0.004 < {\tilde \sigma} < 50$, constraints from isocurvature fluctuations are satisfied, and the production from parametric resonance can be neglected., Comment: 13 pages, 4 Figures

We consider the decay of the inflaton in Starobinsky-like models arising from either an $R+R^2$ theory of gravity or $N=1$ no-scale supergravity models. If Standard Model matter is simply introduced to the $R + R^2$ theory, the inflaton (which appears when the theory is conformally transformed to the Einstein frame) couples to matter predominantly in Standard Model Higgs kinetic terms. This will typically lead to a reheating temperature of $\sim 3 \times 10^9$~GeV. However, if the Standard Model Higgs is conformally coupled to curvature, the decay rate may be suppressed and vanishes for a conformal coupling $\xi = 1/6$. Nevertheless, inflaton decays through the conformal anomaly leading to a reheating temperature of order $10^8$~GeV. The Starobinsky potential may also arise in no-scale supergravity. In this case, the inflaton decays if there is a direct coupling of the inflaton to matter in the superpotential or to gauge fields through the gauge kinetic function. We also discuss the relation between the theories and demonstrate the correspondence between the no-scale models and the conformally coupled $R+R^2$ theory (with $\xi = 1/6$)., Comment: 21 pages, 2 figures, Contribution to Universe Special Issue: Particle Physics and Cosmology: A Themed Issue in Honour of Professor Dimitri Nanopoulos

In this article we study the internal controllability of 1D linear hyperbolic balance laws when the number of controls is equal to the number of state variables. The controls are supported in space in an arbitrary open subset. Our main result is a complete characterization of the minimal control time for the exact controllability property.

Monochromatic gamma-ray signals constitute a potential smoking gun signature for annihilating or decaying dark matter particles that could relatively easily be distinguished from astrophysical or instrumental backgrounds. We provide an updated assessment of the sensitivity of the Cherenkov Telescope Array (CTA) to such signals, based on observations of the Galactic centre region as well as of selected dwarf spheroidal galaxies. We find that current limits and detection prospects for dark matter masses above 300 GeV will be significantly improved, by up to an order of magnitude in the multi-TeV range. This demonstrates that CTA will set a new standard for gamma-ray astronomy also in this respect, as the world's largest and most sensitive high-energy gamma-ray observatory, in particular due to its exquisite energy resolution at TeV energies and the adopted observational strategy focussing on regions with large dark matter densities. Throughout our analysis, we use up-to-date instrument response functions, and we thoroughly model the effect of instrumental systematic uncertainties in our statistical treatment. We further present results for other potential signatures with sharp spectral features, e.g.~box-shaped spectra, that would likewise very clearly point to a particle dark matter origin., Comment: 44 pages JCAP style (excluding author list and references), 19 figures; minor changes to match published version

Given a CNF formula $\varphi$ with clauses $C_1, \dots, C_m$ over a set of variables $V$, a truth assignment $\mathbf{a} : V \to \{0, 1\}$ generates a binary sequence $\sigma_\varphi(\mathbf{a})=(C_1(\mathbf{a}), \ldots, C_m(\mathbf{a}))$, called a signature of $\varphi$, where $C_i(\mathbf{a})=1$ if clause $C_i$ evaluates to 1 under assignment $\mathbf{a}$, and $C_i(\mathbf{a})=0$ otherwise. Signatures and their associated generation problems have given rise to new yet promising research questions in algorithmic enumeration. In a recent paper, B\'erczi et al. interestingly proved that generating signatures of a CNF is tractable despite the fact that verifying a solution is hard. They also showed the hardness of finding maximal signatures of an arbitrary CNF due to the intractability of satisfiability in general. Their contribution leaves open the problem of efficiently generating maximal signatures for tractable classes of CNFs, i.e., those for which satisfiability can be solved in polynomial time. Stepping into that direction, we completely characterize the complexity of generating all, minimal, and maximal signatures for XOR-CNFs., Comment: 21 pages, 5 figures

We consider the effects of a bare mass term for the inflaton, when the inflationary potential takes the form $V(\phi)= \lambda \phi^k$ about its minimum with $k \ge 4$. We concentrate on $k=4$, but discuss general cases as well. Further, we assume $\lambda \phi_{\rm end}^2 \gg m_\phi^2$, where $\phi_{\rm end}$ is the inflaton field value when the inflationary expansion ends. We show that the presence of a mass term (which may be present due to radiative corrections or supersymmetry breaking) can significantly alter the reheating process, as the equation of state of the inflaton condensate changes from $w_\phi=\frac{1}{3}$ to $w_\phi=0$ when $\lambda \phi^2$ drops below $m_\phi^2$. We show that for a mass $m_\phi \gtrsim T_{\rm RH}/250$, the mass term will dominate at reheating. We compute the effects on the reheating temperature for cases where reheating is due to inflaton decay (to fermions, scalars, or vectors) or to inflaton scattering (to scalars or vectors). For scattering to scalars and in the absence of a decay, we derive a strong upper limit to the inflaton bare mass $m_\phi < 350~{\rm MeV} (T_{\rm RH}/10^{10}~{\rm GeV})^{3/5}$, as there is always a residual inflaton background which acts as cold dark matter. We also consider the effect of the bare mass term on the fragmentation of the inflaton condensate., Comment: 16 pages, 10 figures

The inflationary reheating phase begins when accelerated expansion ends. As all Standard Model particles are coupled to gravity, gravitational interactions will lead to particle production. This includes the thermal bath, dark matter and gravitational radiation. Here, we compute the spectrum of gravitational waves from the inflatoncondensate during the initial phase of reheating. As particular examples of inflation, we consider the Starobinsky model and T-models, all of which are in good phenomenological agreement with CMB anisotropy measurements. The T-models are distinguished by the shape of the potential about its minimum and can be approximated by $V \sim \phi^k$, where $\phi$ is the inflaton. Interestingly, the shape of the gravitational wave spectrum (when observed) can be used to distinguish among the models considered. As we show, the Starobinsky model and T-models with $k=2$, provide very different spectra when compared to models with $k=4$ or $k>4$. Observation of multiple harmonics in the spectrum can be interpreted as a direct measurement of the inflaton mass. Furthermore, the cutoff in frequency can be used to determine the reheating temperature., Comment: 11 pages, 4 figures

Adequate representations of brittle deformation (fracturing and faulting) are essential ingredients of long term tectonic simulations. Such models commonly rely on Mohr Coulomb plasticity coupled with prescribed softening of cohesion and/or friction with accumulated plastic strain. This approach captures fundamental properties of brittle failure, but is overly sensitive to empirical softening parameters that cannot be determined experimentally. Here we design a brittle constitutive law that captures key processes of brittle deformation, and can be straightforwardly implemented in standard geodynamic models. In our Sub Critically Altered Maxwell (SCAM) flow law, brittle failure begins with the accumulation of distributed brittle damage, which represents the sub critical lengthening of tensile micro cracks prompted by slip on pre existing shear defects. Damage progressively and permanently weakens the rock's elastic moduli, until cracks catastrophically interact and coalesce up to macroscopic failure. The model's micromechanical parameters can be fully calibrated against rock deformation experiments, alleviating the need for ad hoc softening parameters. Upon implementing the SCAM flow law in 2 D plane strain simulations of rock deformation experiments, we find that it can produce Coulomb oriented shear bands which originate as damage bands. SCAM models can also be used to extrapolate rock strength from laboratory to tectonic strain rates, and nuance the use of Byerlee's law as an upper bound on lithosphere stresses. We further show that SCAM models can be upscaled to simulate tectonic deformation of a 10 km thick brittle plate over millions of years. These features make the SCAM rheology a promising tool to further investigate the complexity of brittle behavior across scales.