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Weak gravity conjecture can be formulated as a statement that gravity must be the weakest force, compared to the other interactions in low energy effective field theory (EFT). Several arguments in favor of this statement were presented from the side of string theory and black hole physics. However, it is still an open question whether the statement of weak gravity can be proven based on more general assumptions of causality, unitarity, and locality of the fundamental theory. These consistency requirements imply the dispersion relations for the scattering amplitudes which allow to bound the EFT coefficients. The main difficulty for obtaining these constraints in the presence of gravity is related to the graviton pole which makes the required dispersion relations divergent in the forward limit. In this work, we present a new way of deriving the bound on the ratio between the EFT cutoff scale and Planck mass from confronting the IR divergences from graviton pole and one-loop running of the EFT Wilson coefficient in front of the dimension-12 operator. Our method also allows the incorporation of full unitarity of partial wave expansion of the UV theory. We examine the EFT of a single shift-symmetric scalar in four dimensions and find that the maximal value of the cutoff scale of the EFT coupled to gravity must be lower than about $O(10)$ Planck mass., Comment: 22 pages, 3 figures

Implications of general properties of quantum field theory, such as causality, unitarity, and locality include constraints on the couplings of the effective field theory (EFT) coefficients. These constraints follow from the connections between the infrared (IR) and ultraviolet (UV) theory imposed by dispersion relations for four-particle amplitudes which formally allow us to express EFT couplings through the moments of positive-definite functions (imaginary parts of partial wave amplitudes) forming the EFT-hedron geometry. Previous studies of these positivity bounds were mainly focused on the weakly coupled EFTs, limiting the analysis to tree-level amplitudes of the IR theory. In this work, we extend the scope of positivity bounds including one-loop amplitudes, which is essential especially for the loops of massless particles. Examining a single scalar theory we found that the presence of massless loops cannot be reduced only to the running of EFT couplings because loops modify the crossing symmetry relations (null constraints). Our results demonstrate that while for small coupling constants, the one-loop bounds are in good agreement with the tree-level results, the allowed EFT parameter ranges can be significantly modified if a weak coupling assumption is not additionally imposed. In particular, we found that an upper bound on dimension-8 coupling becomes significantly stronger, and the dimension-12 coupling can be slightly negative which was thought to be forbidden by tree-level positivity bounds., Comment: 25 pages, 5 figures

Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards Quantum Gravity". The scope was to provide a coherent picture, from its foundation to forefront research, emphasizing connections between different areas. The lectures begin with perturbative quantum gravity and effective field theory. Subsequently, two ultraviolet-complete approaches are presented: asymptotically safe gravity and string theory. Finally, elements of quantum effects in black hole spacetimes are discussed., Comment: Lecture notes PhD school "Towards Quantum Gravity", Nordita Scientific Program "Quantum Gravity: from gravitational EFTs to UV complete approaches". 265 pages + references, 37 figures

The requirements of unitarity and causality lead to significant constraints on the Wilson coefficients of a EFT expansion, known as positivity bounds. Their standard derivation relies on the crucial assumption of polynomial boundedness on the growth of scattering amplitudes in the complex energy plane, which is a property satisfied by local QFTs, and by weakly coupled string theory in the Regge regime. The scope of this work is to clarify the role of locality by deriving generalized positivity bounds under the assumption of exponential boundedness, typical of non-local QFTs where the Froissart-Martin bound is usually not satisfied. Using appropriately modified dispersion relations, we derive new constraints and find regions in the EFT parameter space that do not admit a local UV completion. Furthermore, we show that there exist ETFs that satisfy IR causality and at the same time can admit a non-local UV completion, provided that the energy scale of non-locality is of the same order or smaller than the EFT cutoff. Finally, we provide explicit examples of non-perturbative amplitudes that simultaneously satisfy the properties of exponential boundedness, unitarity and causality. Our results have far-reaching implications for the question of the uniqueness of string theory as the only consistent ultraviolet completion beyond the framework of local QFT., Comment: 25 pages, 5 figures

Non-pertrubative quantum gravity formulated as a unitary four-dimensional theory suggests that certain amount of non-locality, such as infinite-derivative operators, can be present in the action, in both cases of Analytic Infinite Derivative gravity and Asymptotically Safe gravity. Such operators lead to the emergence of Background Induced States on top of any background deviating from the flat spacetime. Quasi-normal modes (QNMs) corresponding to these excitations are analyzed in the present paper with the use of an example of a static nearly Schwarzschild black hole. We mainly target micro-Black Holes, given that they are strongly affected by the details of UV completion for gravity, while real astrophysical black holes can be well described in EFT framework. We find that frequencies of QNMs are deviating from those in a General Relativity setup and, moreover, that the unstable QNMs are also possible. This leads to the necessity of constraints on gravity modifications or lower bounds on masses of the stable micro-Black Holes or both., Comment: 25 pages, 6 figures

We show how infinite derivative modifications of gravity impact on the stochastic background of Gravitational Waves from early Universe. The generic property of the ghost-free theory fixed on Minkowski space-time is the emergence of an infinite number of complex mass states when other classical backgrounds are considered. These additional states are shown to enhance the power spectrum of scalar perturbations generated during inflation. Current and future space-based and terrestrial interferometers offer indirect testing methods for the infinite derivative gravity action, enabling the exploration of new parameter spaces. In particular, we identify unconventional blue-tilted Gravitational Wave spectra, presenting a novel approach for testing infinite derivative quantum gravity in the future., Comment: 17 pages, 3 figures

The task of writing rap is challenging and involves producing complex rhyming schemes, yet meaningful lyrics. In this work, we propose Raply, a fine-tuned GPT-2 model capable of producing meaningful rhyming text in the style of rap. In addition to its rhyming capabilities, the model is able to generate less offensive content. It was achieved through the fine-tuning the model on a new dataset Mitislurs, a profanity-mitigated corpus. We evaluate the output of the model on two criteria: 1) rhyming based on the rhyme density metric; 2) profanity content, using the list of profanities for the English language. To our knowledge, this is the first attempt at profanity mitigation for rap lyrics generation.

We start from the assumption that the theory of gravity can be formulated in terms of 4-dimensional action, and there are only 2 graviton polarization states, as in general relativity. It can be a non-perturbative effective action discussed in the asymptotic safety program or the result of some other UV modification of the general relativity making it a complete theory. From these general grounds, we study the properties of the graviton two-point function on top of cosmological de-Sitter space. We find that the no-ghost requirement formulated for the flat background does not necessarily hold for the de-Sitter space where the graviton two-point function can have an infinite number of complex-conjugate poles. We show that under certain stability conditions, their appearance doesn't contradict any fundamental principle. We discuss their observational consequences for the tensor power spectrum from inflation and for the stochastic gravitational wave background., Comment: 6 pages, 2 figures

Although General Relativity predicts the presence of a singularity inside of a Black Hole, it is not a complete theory of gravity. A real structure of a Black Hole interior near an expected singularity depends on the UV completion of gravity. In this paper, we establish that the question whether singular spherically symmetric solutions are absent is governed by the functional form of a non-perturbative graviton propagator. We explicitly show in a framework of a ghost-free infinite derivative gravity that for the graviton propagator of an exponential form favored by the unitarity a singularity is not possible unless an unphysical situation when the total mass of the Black Hole is infinite is considered.

In the field of spoken language understanding, systems like Whisper and Multilingual Massive Speech (MMS) have shown state-of-the-art performances. This study is dedicated to a comprehensive exploration of the Whisper and MMS systems, with a focus on assessing biases in automatic speech recognition (ASR) inherent to casual conversation speech specific to the Portuguese language. Our investigation encompasses various categories, including gender, age, skin tone color, and geo-location. Alongside traditional ASR evaluation metrics such as Word Error Rate (WER), we have incorporated p-value statistical significance for gender bias analysis. Furthermore, we extensively examine the impact of data distribution and empirically show that oversampling techniques alleviate such stereotypical biases. This research represents a pioneering effort in quantifying biases in the Portuguese language context through the application of MMS and Whisper, contributing to a better understanding of ASR systems' performance in multilingual settings., Comment: EACL-2024 LT-EDI Workshop

The concept of early Universe inflation resolves several problems of hot Big Bang theory and quantitatively explains the origin of the inhomogeneities in the present Universe. However, it is not possible to arrange inflation in a scalar field model with renormalizable potential, such that it would not contradict the recent Planck data. For this reason, inflaton must have also higher derivative couplings suppressed at least by the Planck scale. We show that these couplings may be relevant during reheating and lead to non-negligible production of gravitons. We consider the possibility that the unitarity breaking scale for the model of inflation is lower than the Planck scale and compute production of gravitons during reheating, due to the inflaton decay to two gravitons and graviton bremsstrahlung process. The spectrum of produced gravitons is crucially dependent on reheating temperature and inflaton mass. We find that for low reheating temperature decay to gravitons lead to significant amount of dark radiation. Confronting this result with CMB constraints, we find reheating dependent bounds on the unitarity breaking scale. We also compare the obtained gravitational wave signals with the projected limits of future high frequency gravitational wave experiments.

Effective field theories (EFT) are strongly constrained by fundamental principles such as unitarity, locality, causality, and Lorentz invariance. In this paper, we consider the EFT of photons (or other $U(1)$ gauge field) and compare different approaches to obtain bounds on its Wilson coefficients. We present an analytic derivation of the implications of unitarity (linear and non-linear positivity bounds) and compare these constraints with the requirement of causal propagation of the photon modes around non-trivial backgrounds generated by external sources. We find that the low energy causality condition can give complementary constraints to the positivity bounds. Applying both constraints together can significantly reduce the allowed region of the photon EFT parameters., Comment: 37 pages + appendices and references, 23 figures

The classical Lagrangian of the Standard Model enjoys the symmetry of the full conformal group if the mass of the Higgs boson is put to zero. This is a hint that conformal symmetry may play a fundamental role in the ultimate theory describing Nature. The origin of scales, such as the Higgs vacuum expectation value (vev), may result from the spontaneous breakdown of the conformal symmetry by the dilaton field. In this work, we study whether this classical setup can be implemented in quantum theory and be phenomenologically viable by presenting an explicit construction where the exact conformal symmetry can be preserved and is anomaly free while being spontaneously broken. Not only the Higgs mass but also the genuine quantum scales like the QCD confinement radius are generated by the dilaton vev. We also discuss the extension of these ideas to the theories with dynamical gravity and show that the only finite subgroup of the local Weyl transformations which is anomaly free corresponds to the global scale symmetry. This means that the conformal invariance of the flat space theory is explicitly broken down to the scale symmetry by gravitational effects related to the Weyl anomaly.

The Standard Model Lagrangian has an approximate scale symmetry in the high-energy limit. This observation can be included in the fundamental principle of the ultimate theory of Nature as the requirement of the exact quantum scale invariance. In this setup, all low-energy particle phenomenology can be obtained as a result of the spontaneous breaking of scale symmetry leading to the presence of the extra massless scalar field -- the dilaton. We explore the scenario in which this field is capable of solving the strong CP-problem in QCD in a similar way as in QCD axion models. The dilaton, playing the role of the axion, is coupled to the QCD sector and acquires a mass term due to non-perturbative breaking of scale symmetry. We show that the dilaton can form dark matter after the low-scale inflation. As a proof of concept, we construct a model of Higgs-driven inflation consistently realising the axion-like dilaton dark matter production compatible with the CMB data., Comment: 32 pages, 8 figures; additional calculations, comments and references added, several plots upgraded, typos corrected

Gravity can be embedded into a renormalizable theory by means of adding quadratic in curvature terms. However, this at first leads to the presence of the Weyl ghost. It is possible to get rid of this ghost if the locality assumption is weakened and the propagator of the graviton is represented by an entire function of the d'Alembertian operator without new poles and zeros. Models of this type admit a cosmological solution describing the $R^2$, or Starobinsky, inflation. We study graviton production after inflation in this model and show that it is negligible despite the presence of the higher derivative operators which could potentially cause instabilities., Comment: We dedicate this paper to the memory of Valery Rubakov

In this Letter, we address the question of whether the conformal invariance can be considered as a global symmetry of a theory of fundamental interactions. To describe Nature, this theory must contain a mechanism of spontaneous breaking of the scale symmetry. Besides that, the fundamental theory must include gravity, whereas all known extensions of the conformal invariance to the curved space-time suffer from the Weyl anomaly. We show that conformal symmetry can be made free from the quantum anomaly only in the flat space. The presence of gravity would reduce the global symmetry group of the fundamental theory to the scale invariance only. We discuss how the effective Lagrangian respecting the scale symmetry can be used for the description of particle phenomenology and cosmology., Comment: An error in the generic solution for anomaly-free Weyl transformation is corrected. The updated conclusion is that gravity reduces conformal symmetry to the scale symmetry

In this work we explicitly show that the perturbative unitarity of analytic infinite derivative (AID) scalar field theories can be achieved using a modified prescription for computing scattering amplitudes. The crux of the new prescription is the analytic continuation of a result obtained in the Euclidean signature to the Minkowski external momenta. We intensively elaborate an example of a non-local $\phi^4$ model for various infinite derivative operators. General UV properties of amplitudes in non-local theories are discussed., Comment: 16 pages, 7 figures; revision matching the published version

We formulate Positivity Bounds for scattering amplitudes including exchange of massless particles. We generalize the standard construction through dispersion relations to include the presence of a branch cut along the real axis in the complex plane for the Maldestam variable $s$. In general, validity of these bounds require the cancellation of divergences in the forward limit of the amplitude, proportional to $t^{-1}$ and $\log(t)$. We show that this is possible in the case of gravitons if one assumes a Regge behavior of the amplitude at high energies below the Planck scale, as previously suggested in the literature, and that the concrete UV behaviour of the amplitude is uniquely determined by the structure of IR divergences. We thus extend previous results by including a sub-leading logarithmic term, which we show to be universal. The bounds that we present here have the potential of constraining very general models of modified gravity and EFTs of matter coupled to gravitation., Comment: 9 pages, 1 figure. Matches journal version

Higgs inflation is known to be a minimal extension of the Standard Model allowing for the description of the early Universe inflation. This model is considered as an effective field theory since it has a relatively low cutoff scale, thus requiring further extensions to be a valid description of the reheating phase. We present a novel unified approach to the problem of unitarization and UV completion of the Higgs inflation model without introducing new massive degrees of freedom. This approach is based on an analytic infinite derivative modification of the Higgs field kinetic term. We construct a unitary non-local UV completion of the original Higgs inflation model while the inflationary stage is kept stable with respect to quantum corrections., Comment: 22 pages, 15 pdf figures; v2: matches the published version

We study the consequences of (beyond) positivity of scattering amplitudes in the effective field theory description of the Higgs-Dilaton inflationary model. By requiring the EFT to be compatible with a unitary, causal, local and Lorentz invariant UV completion, we derive constraints on the Wilson coefficients of the first higher order derivative operators. We show that the values allowed by the constraints are consistent with the phenomenological applications of the Higgs-Dilaton model., Comment: 27 pages, 6 figures; matches the published version

Strong coupling in Higgs inflation at high energies hinders a joint description of inflation, reheating and low-energy dynamics. The situation may be improved with a proper UV completion of the model. A well-defined self-consistent way is to introduce an $R^2$-term into the action. In this modified model the strong coupling scale returns back to the Planck scale, which justifies the use of the perturbative methods in studies of the model dynamics after inflation. We investigate the reheating of the post-inflationary Universe, which involves two highly anharmonic oscillators strongly interacting with each other: homogeneous Higgs field and scalaron. We observe that in interesting regions of model parameter space these oscillations make longitudinal components of the weak gauge bosons tachyonic, triggering instant preheating at timescales much shorter than the Hubble time. The weak gauge bosons are heavy and decay promptly into light Standard Model particles, ensuring the onset of the radiation domination era right after inflation., Comment: 18 pages, 6 figures. Minor clarifications, corrected typo in eq. (38) and in Fig. 5 axes labels

We consider dark matter represented by the light scalar field whose coupling to the ordinary matter is extremely suppressed. We assume that this interaction can be described as the coupling of the square of the field to the energy-momentum tensor. We study the effect of this interaction on the evolution of dark matter scalar, as well as bounds on the model parameters that come from the variation of fundamental constants at the BBN., Comment: arXiv admin note: text overlap with arXiv:hep-ph/9602260 by other authors

We show that introducing $R^2$-term makes the Higgs-inflation and Higgs-dilaton inflation consistent models: the strong coupling energy scales in scalar, gauge and gravity sectors all are lifted up to the Planck scale., Comment: Journal version

We present a scale invariant extension of the Standard model allowing for the Kim-Shifman-Vainstein-Zakharov (KSVZ) axion solution of the strong CP problem in QCD. We add the minimal number of new particles and show that the Peccei-Quinn scalar might be identified with the complex dilaton field. Scale invariance, together with the Peccei-Quinn symmetry, is broken spontaneously near the Planck scale before inflation, which is driven by the Standard Model Higgs field. We present a set of general conditions which makes this scenario viable and an explicit example of an effective theory possessing spontaneous breaking of scale invariance. We show that this description works both for inflation and low-energy physics in the electroweak vacuum. This scenario can provide a self-consistent inflationary stage and, at the same time, successfully avoid the cosmological bounds on the axion. Our general predictions are the existence of coloured TeV mass fermion and the QCD axion. The latter has all the properties of the KSVZ axion but does not contribute to dark matter. This axion can be searched via it's mixing to a photon in an external magnetic field.

String scenarios generically predict that we live in a so called axiverse: the Universe with about a hundred of light axion species which are decoupled from the Standard Model particles. However, the axions can couple to the inflaton which leads to their production after inflation. Then, these axions remain in the expanding Universe contributing to the dark radiation component, which is severely bounded from present cosmological data. We place a general constraint on the axion production rate and apply it to several variants of reasonable inflaton-to-axion couplings. The limit merely constrains the number of ultralight axions and the relative strength of inflaton-to-axion coupling. It is valid in both large and small field inflationary models irrespectively of the axion energy scales and masses. Thus, the limit is complementary to those associated with the Universe overclosure and axion isocurvature fluctuations. In particular, a hundred of axions is forbidden if inflaton universally couples to all the fields at reheating. In the case of gravitational sector being responsible for the reheating of the Universe (which is a natural option in all inflationary models with modified gravity), the axion production can be efficient. We find that in the Starobinsky $R^2$-inflation even a single axion (e.g. the standard QCD-axion) is in tension with the Planck data, making the model inconsistent with the axiverse. The general conclusion is that an inflation with inefficient reheating mechanism and low reheating temperature may be in tension with the presence of light scalars.

We study the creation and evolution of cosmological perturbations in renormalizable quadratic gravity with a Weyl term. We adopt a prescription that implies the stability of the vacuum at the price of introducing a massive spin-two ghost state, leading to the loss of unitarity. The theory may still be predictive regardless the interpretation of non-unitary processes provided that their rate is negligible compared to the Universe expansion rate. This implies that the ghost is effectively stable. In such a setup, there are two scalar degrees of freedom excited during inflation. The first one is the usual curvature perturbation whose power spectrum appears to coincide with that of single-field inflation. The second one is a scalar component of the ghost encoded in the shift vector of the metric in the uniform inflaton gauge. The amplitudes of primordial tensor and vector perturbations are strongly suppressed. After inflation the ghost field starts to oscillate and its energy density shortly becomes dominant in the Universe. For all ghost masses allowed by laboratory constraints ghosts should have "overclosed" the Universe at temperatures higher than that of primordial nucleosynthesis. Thus, the model with the light Weyl ghost is ruled out., Comment: 26 pages, 1 figure, minor corrections, published version

The Starobinsky model of modified gravity suggested to explain dark energy may be also considered in the astrophysical context. Recently it has been pointed out that in contracting regions curvature oscillations around the GR value may lead to the production of high energy particles which contribute to the cosmic ray flux. We revisit these calculations in the Einstein frame and show that the continuous approximation for the matter density used in the original calculations is not valid. We show that this problem is generic in $F(R)$-gravity models introduced to describe the dark energy. We go beyond the approximation and find the rate of particle production to be negligible., Comment: 9 pages; v2: replaced with revised version; v3: extended discussion, new appendix with 3 figures added, journal version

We study the creation of high energy SM particles in the Starobinsky model of dark energy (a variant of F(R)-gravity) inside the regions contracting due to the Jeans instability. In this modification of gravity the additional degree of freedom -- scalaron -- behaves as a particle with mass depending on matter density. So when the mass changes light scalarons could be created at a non-adiabatic stage. Later scalaron mass grows and could reach large values, even the value of 10^{13} GeV, favored by early-time inflation. Heavy scalarons decay contributing to the cosmic ray flux. We analytically calculated the number density of created particles for the case of exponential (Jeans) contraction and found it negligibly small provided the phenomenologically viable and cosmologically interesting range of model parameters. We expect similar results for a generic model of F(R)-gravity mimicking cosmological constant., Comment: 11 pages; prepared for a special issue of JETP dedicated to the 60th birthday of Valery Rubakov

Recent cosmological data favour R^2-inflation and some amount of non-standard dark radiation in the Universe. We show that a framework of high energy scale invariance can explain these data. The spontaneous breaking of this symmetry provides gravity with the Planck mass and particle physics with the electroweak scale. We found that the corresponding massless Nambu--Goldstone bosons -- dilatons -- are produced at reheating by the inflaton decay right at the amount needed to explain primordial abundances of light chemical elements and anisotropy of the cosmic microwave background. Then we extended the discussion on the interplay with Higgs-inflation and on general class of inflationary models where dilatons are allowed and may form the dark radiation. As a result we put a lower limit on the reheating temperature in a general scale invariant model of inflation., Comment: 15 pages, 4 figures; v2: replaced with revised version recently published

We introduce conformal coupling of the Standard Model Higgs field to gravity and discuss the subsequent modification of $R^2$-inflation. The main observation is a lower temperature of reheating which happens mostly through scalaron decays into gluons due to the conformal (trace) anomaly. This modifies all predictions of the original $R^2$-inflation. To the next-to-leading order in slow roll parameters we calculate amplitudes and indices of scalar and tensor perturbations produced at inflation. The results are compared to the next-to-leading order predictions of $R^2$-inflation with minimally coupled Higgs field and of Higgs-inflation. We discuss additional features in gravity wave signal that may help to distinguish the proposed variant of $R^2$-inflation. Remarkably, the features are expected in the region available for study at future experiments like BBO and DECIGO. Finally, we check that (meta)stability of electroweak vacuum in the cosmological model is consistent with recent results of searches for the Higgs boson at LHC., Comment: 15 pages, 1 figure; replaced with journal version: tunnelling after inflation is studied