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We give a detailed exposition of the formalism of kinetic field theory (KFT) with emphasis on the perturbative determination of observables. KFT is a statistical nonequilibrium classical field theory based on the path integral formulation of classical mechanics, employing the powerful techniques developed in the context of quantum field theory to describe classical systems. Unlike previous work on KFT, we perform the integration over the probability distribution of initial conditions in the very last step. This significantly improves the clarity of the perturbative treatment and allows for physical interpretation of intermediate results. We give an introduction to the general framework, but focus on the application to interacting N-body systems. Specializing the results to cosmic structure formation, we reproduce the linear growth of the cosmic density fluctuation power spectrum on all scales from microscopic, Newtonian particle dynamics alone., Physical Review D, 106 (6), ISSN:1550-7998, ISSN:0556-2821, ISSN:1550-2368

We study the effects of particle production on the evolution of the inflaton field in an axion monodromy model with the goal of discovering in which situations the resulting dynamics will be consistent with the swampland constraints. In the presence of a modulated potential the evolving background field (solution of the inflaton homogeneous in space) induces the production of long wavelength inflaton fluctuation modes. However, this either has a negligible effect on the inflaton dynamics (if the field spacing between local minima of the modulated potential is large), or else it traps the inflaton in a local minimum and leads to a graceful exit problem. On the other hand, the production of moduli fields at enhanced symmetry points can lead to a realization of trapped inflation consistent with the swampland constraints, as long as the coupling between the inflaton and the moduli fields is sufficiently large., The European Physical Journal C, 81 (2), ISSN:1434-6044, ISSN:1434-6052

The construction of general derivative self-interactions for a massive Proca field relies on the well-known condition for constrained systems of having a degenerate Hessian. The nature of the existing constraints algebra will distinguish among different classes of interactions. Proca-Nuevo interactions enjoy a nontrivial constraint by mixing terms of various order whereas generalized Proca interactions satisfy the degeneracy condition order by order for each individual Lagrangian. In both cases the vector field propagates at most 3 degrees of freedom. It has been shown that the scattering amplitudes of Proca-Nuevo arising at the tree level always differ from those of the generalized Proca, implying their genuinely different nature and a lack of relation by local field redefinitions. In this work, we show the quantum stability of the Proca-Nuevo theory below a specific UV cutoff. Although Proca-Nuevo and generalized Proca are different inherently in their classical structure, both have the same high energy behavior when quantum corrections are taken into account. The arising counterterms have the exact same structure and scaling. This might indicate that whatever UV completion they may come from, we expect it to be of similar nature. ISSN:1550-7998 ISSN:0556-2821 ISSN:1550-2368

We systematically study the field equations of f (Q) gravity for spherically symmetric and stationary metric-affine spacetimes. Such spacetimes are described by a metric as well as a flat and torsionless affine connection. In the symmetric teleparallel equivalent of general relativity (STEGR), the connection is pure gauge and hence unphysical. However, in the nonlinear extension f (Q), it is promoted to a dynamical field which changes the physics. Starting from a general metric-affine geometry, we construct the most general static and spherically symmetric forms of the metric and the affine connection. We then use these symmetry reduced geometric objects to prove that the field equations of f (Q) gravity admit general relativity (GR) solutions as well as beyond-GR solutions, contrary to what has been claimed in the literature. We formulate precise criteria, under which conditions it is possible to obtain GR solutions and under which conditions it is possible to obtain beyond-GR solutions. We subsequently construct several perturbative corrections to the Schwarzschild solution for different choices of f(Q), which in particular include a hair stemming from the now dynamical affine connection. We also present an exact beyond-GR vacuum solution. Lastly, we apply this method of constructing spherically symmetric and stationary solutions to f(T) gravity, which reproduces similar solutions but without a dynamical connection. ISSN:1550-7998 ISSN:0556-2821 ISSN:1550-2368

The equivalence principle and its universality enables the geometrical formulation of gravity. In the standard formulation of General Relativity (GR) a la Einstein, the gravitational interaction is geometrized in terms of the spacetime curvature. However, if we embrace the geometrical character of gravity, two alternative, though equivalent, formulations of GR emerge in flat spacetimes, in which gravity is fully ascribed either to torsion or to non-metricity. The latter allows a much simpler formulation of GR oblivious to the affine spacetime structure, the Coincident General Relativity (CGR). The entropy of a black hole can be computed using the Euclidean path integral approach, which strongly relies on the addition of boundary or regulating terms in the standard formulation of GR. A more fundamental derivation can be performed using Wald's formula, in which the entropy is directly related to Noether charges and is applicable to general theories with diffeomorphism invariance. In this work we extend Wald's Noether charge method for calculating black hole entropy to spacetimes endowed with non-metricity. Using this method, we show that CGR with an improved action principle gives the same entropy as the well-known entropy in standard GR. Furthermore the first law of black hole thermodynamics holds and an explicit expression for the energy appearing in the first law is obtained., Classical and Quantum Gravity, 39 (23), ISSN:0264-9381, ISSN:1361-6382

We show that an S-Brane which arises in the inside of the black hole horizon when the Weyl curvature reaches the string scale induces a continuous transition between the inside of the black hole and the beginning of a new universe. This provides a simultaneous resolution of both the black hole and Big Bang singularities. In this context, the black hole information loss problem is also naturally resolved., 9 pages, 3 figures; essay written for the Gravity Research Foundation 2021 Awards for Essays on Gravitation, awarded Honorable Mention

Warp drives in Einstein's general theory of relativity provide a unique mechanism for manned interstellar travel. It is well-known that the classical superluminal soliton spacetimes require negative energy densities, likely sourced by quantum processes of the uncertainty principle. It has even been claimed by few that negative energy densities are a requirement of superluminal motion. However, recent studies suggest this may not be the case. A general decomposition of the defining variables and the corresponding decomposition of the Eulerian energy are studied. A geometrical interpretation of the Eulerian energy is found, shedding new light on superluminal solitons generated by realistic energy distributions. With this new interpretation, it becomes a relatively simple matter to generate solitonic configurations, within a certain subclass, that respect the positive energy constraint. Using this newfound interpretation, a superluminal solitonic spacetime is presented that possesses positive semi-definite energy. A modest numerical analysis is carried out on a set of example configurations, finding total energy requirements four orders of magnitude smaller than the solar mass. Extraordinarily, the example configurations are generated by purely positive energy densities, a tremendous improvement on the classical configurations. The geometrical interpretation of the Eulerian energy thus opens new doors to generating realistic warp fields for laboratory study and potential future manned interstellar travel., 20 pages, 2 figures, matches now the journal version

Local determinations of the Hubble constant $H_0$ favour a higher value than Planck based on CMB and $\Lambda$CDM. Through a model-independent expansion, we show that low redshift ($z \lesssim 0.7$) data comprising baryon acoustic oscillations (BAO), cosmic chronometers and Type Ia supernovae has a preference for Quintessence models that lower $H_0$ relative to $\Lambda$CDM. In addition, we confirm that an exponential coupling to dark matter cannot alter this conclusion in the same redshift range. Our results leave open the possibility that a coupling in the matter-dominated epoch, potentially even in the dark ages, may yet save $H_0$ from sinking in the string theory Swampland., Comment: 4 pages; v2 comments, references added; v3 appendix added on CPL, matches published version

We establish radiative stability of generalized Proca effective field theories. While standard power-counting arguments would conclude otherwise, we find non-trivial cancellations of leading order corrections by explicit computation of divergent one-loop diagrams up to four-point. These results are crosschecked against an effective action based generalized Schwinger–DeWitt method. Further, the cancellations are understood as coming from the specific structure of the theory through a decoupling limit analysis which at the same time allows for an extension of the results to higher orders.

Current and upcoming cosmological experiments open a new era of precision cosmology, thus demanding accurate theoretical predictions for cosmological observables. Because of the complexity of the codes delivering such predictions, reaching a high level of numerical accuracy is challenging. Among the codes already fulfilling this task, PyCosmo is a Python-based framework providing solutions to the Einstein–Boltzmann equations and accurate predictions for cosmological observables. We present the first public release of the code, which is valid in ΛCDM cosmology. The novel aspect of this version is that the user can work within a Python framework, either locally or through an online platform, called PyCosmo Hub. In this work we first describe how the observables are implemented. Then, we check the accuracy of the theoretical predictions for background quantities, power spectra and Limber and beyond-Limber angular power spectra by comparison with other codes: the Core Cosmology Library (CCL), CLASS, HMCode and iCosmo. In our analysis we quantify the agreement of PyCosmo with the other codes, for a range of cosmological models, monitored through a series of unit tests. PyCosmo, conceived as a multi-purpose cosmology calculation tool in Python, is designed to be interactive and user-friendly. The PyCosmo Hub is accessible from this link: https://cosmology.ethz.ch/research/software-lab/PyCosmo.html. On this platform the users can perform their own computations using Jupyter Notebooks without the need of installing any software, access to the results presented in this work and benefit from tutorial notebooks illustrating the usage of the code. The link above also redirects to the code release and documentation., Astronomy and Computing, 36, ISSN:2213-1337

We discuss the most general field equations for cosmological spacetimes for theories of gravity based on non-linear extensions of the non-metricity scalar and the torsion scalar. Our approach is based on a systematic symmetry-reduction of the metric-affine geometry which underlies these theories. While for the simplest conceivable case the connection disappears from the field equations and one obtains the Friedmann equations of General Relativity, we show that in $f(\mathbb{Q})$ cosmology the connection generically modifies the metric field equations and that some of the connection components become dynamical. We show that $f(\mathbb{Q})$ cosmology contains the exact General Relativity solutions and also exact solutions which go beyond. In $f(\mathbb{T})$~cosmology, however, the connection is completely fixed and not dynamical., Comment: 17 pages, no figures

We perform the ADM decomposition of a five-parameter family of quadratic non-metricity theories and study their conjugate momenta. After systematically identifying all possible conditions which can be imposed on the parameters such that different sets of primary constraints arise, we find that the five-parametric theory space can be compartmentalized into nine different sectors, based on the presence or absence of primary constraints. This classification allows to dismiss certain classes of theories as unphysical and invites further investigations into the remaining sectors, which may contain phenomenologically interesting modifications of General Relativity., Journal of High Energy Physics, 2021 (2), ISSN:1126-6708, ISSN:1029-8479

Proca-Nuevo is a non-linear theory of a massive spin-1 field which enjoys a non-linearly realized constraint that distinguishes it among other generalized vector models. We show that the theory may be extended by the addition of operators of the Generalized Proca class without spoiling the primary constraint that is necessary for consistency, allowing to interpolate between Generalized Proca operators and Proca-Nuevo ones. The constraint is maintained on flat spacetime and on any fixed curved background. Upon mixing extended Proca-Nuevo dynamically with gravity, we show that the constraint gets broken in a Planck scale suppressed way. We further prove that the theory may be covariantized in models that allow for consistent and ghost-free cosmological solutions. We study the models in the presence of perfect fluid matter, and show that they describe the correct number of dynamical variables and derive their dispersion relations and stability criteria. We also exhibit, in a specific set-up, explicit hot Big Bang solutions featuring a late-time self-accelerating epoch, and which are such that all the stability and subluminality conditions are satisfied and where gravitational waves behave precisely as in General Relativity., Comment: 34 pages + appendices, 8 figures

The standard model of cosmology, the $\Lambda$CDM model, describes the evolution of the Universe since the Big Bang with just a few parameters, six in its basic form. Despite being the simplest model, direct late-time measurements of the Hubble constant compared with the early-universe measurements result in the so-called $H_0$ tension. It is claimed that a late time resolution is predestined to fail when different cosmological probes are combined. In this work, we shake the ground of this belief with a very simple model. We show how, in the context of cubic vector Galileon models, the Hubble tension can naturally be relieved using a combination of CMB, BAO and SNe observations without using any prior on $H_0$ . The tension can be reduced even further by including the local measurement of the Hubble constant., Comment: 19 pages, 9 figures

The universal character of the gravitational interaction provided by the equivalence principle motivates a geometrical description of gravity. The standard formulation of General Relativity \`a la Einstein attributes gravity to the spacetime curvature, to which we have grown accustomed. However, this perception has masked the fact that two alternative, though equivalent, formulations of General Relativity in flat spacetimes exist, where gravity can be fully ascribed either to torsion or to non-metricity. The latter allows a simpler geometrical formulation of General Relativity that is oblivious to the affine spacetime structure. Generalisations along this line permit to generate teleparallel and symmetric teleparallel theories of gravity with exceptional properties. In this work we explore modified gravity theories based on non-linear extensions of the non-metricity scalar. After presenting some general properties and briefly studying some interesting background cosmologies (including accelerating solutions with relevance for inflation and dark energy), we analyse the behaviour of the cosmological perturbations. Tensor perturbations feature a re-scaling of the corresponding Newton's constant, while vector perturbations do not contribute in the absence of vector sources. In the scalar sector we find two additional propagating modes, hinting that $f(Q)$ theories introduce, at least, two additional degrees of freedom. These scalar modes disappear around maximally symmetric backgrounds because of the appearance of an accidental residual gauge symmetry corresponding to a restricted diffeomorphism. We finally discuss the potential strong coupling problems of these maximally symmetric backgrounds caused by the discontinuity in the number of propagating modes., Comment: 15 pages, 1 figure. V2 Published version. Added clarifications and three new appendices

The geometrical formulation of gravity is not unique and can be set up in a variety of spacetimes. Even though the gravitational sector enjoys this freedom of different geometrical interpretations, consistent matter couplings have to be assured for a steady foundation of gravity. In generalised geometries, further ambiguities arise in the matter couplings unless the minimal coupling principle (MCP) is adopted that is compatible with the principles of relativity, universality and inertia. In this work, MCP is applied to all Standard Model gauge fields and matter fields in a completely general (linear) affine geometry. This is also discussed from an effective field theory perspective. It is found that the presence of torsion generically leads to theoretical problems. However, symmetric teleparallelism, wherein the affine geometry is integrable and torsion-free, is consistent with MCP. The generalised Bianchi identity is derived and shown to determine the dynamics of the connection in a unified fashion. Also, the parallel transport with respect to a teleparallel connection is shown to be free of second clock effects., 17 pages

In this Letter, we consider the model-independent reconstruction of the expansion and growth functions from the Pantheon supernova data. The method relies on developing the expansion function in terms of shifted Chebyshev polynomials and determining the coefficients of the polynomials by a maximum-likelihood fit to the data. Having obtained the expansion function in a model-independent way, we can then also determine the growth function without assuming a particular model. We then compare the results with the predictions of two classes of Dark Energy models, firstly a class of quintessence scalar field models consistent with the trans-Planckian censorship and swampland conjectures, and secondly a class of generalized Proca vector field models. We determine constraints on the parameters which appear in these models. © 2020 The Author(s), Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 812

We investigate the nonlinear growth of large-scale structure in the generalised Proca theory, in which a self-interacting massive vector field plays the role of driving the acceleration of the cosmic expansion. Focusing to the Proca Lagrangian at cubic order -- the cubic vector Galileon model -- we derive the simplified equations for gravity as well as the longitudinal and transverse modes of the vector field under the weak-field and quasi-static approximations, and implement them in a modified version of the ECOSMOG N-body code. Our simulations incorporate the Vainshtein screening effect, which reconciles the fifth force propagated by the longitudinal mode of the cubic vector Galileon model with local tests of gravity. The results confirm that for all scales probed by the simulation, the transverse mode has a negligible impact on structure formation in a realistic cosmological setup. It is well known that in this model the strength of the fifth force is controlled by a free model parameter, which we denote as beta_3. By running a suite of cosmological simulations for different values of beta_3, we show that this parameter also determines the effectiveness of the Vainshtein screening. The model behaves identically to the cubic scalar Galileon for beta_3 going to zero, in which the fifth force is strong in unscreened regions but is efficiently screened in high-density regions. In the opposite limit, beta_3 going to infinity, the model approaches its `quintessence' counterpart, which has a vanishing fifth force but a modified expansion history compared to LambdaCDM. This endows the model with rich phenomenology, which will be investigated in future works., Comment: 32 pages, 7 figures, version to appear in JCAP

In this work we revisit the topological mass generation of 2-forms and establish a connection to the unique derivative coupling arising in the quartic Lagrangian of the systematic construction of massive 2-form interactions, relating in this way BF theories to Galileon-like theories of 2-forms. In terms of a massless 1-form A and a massless 2-form B, the topological term manifests itself as the interaction B∧F, where F=dA is the field strength of the 1-form. Such an interaction leads to a mechanism of generation of mass, usually referred to as “topological generation of mass” in which the single degree of freedom propagated by the 2-form is absorbed by the 1-form, generating a massive mode for the 1-form. Using the systematical construction in terms of the Levi-Civita tensor, it was shown that, apart from the quadratic and quartic Lagrangians, Galileon-like derivative self-interactions for the massive 2-form do not exist. A unique quartic Lagrangian εμνρσεαβγσ∂μBαρ∂νBβγ arises in this construction in a way that it corresponds to a total derivative on its own but ceases to be so once an overall general function is introduced. We show that it exactly corresponds to the same interaction of topological mass generation. Based on the decoupling limit analysis of the interactions, we make supporting arguments for the uniqueness of such a topological mass term and absence of the Galileon-like interactions. Finally, we discuss some preliminary applications in cosmology., Physical Review D, 102 (6), ISSN:1550-7998, ISSN:0556-2821, ISSN:1550-2368

We consider the prospect of detecting cubic Galileons through their imprint on gravitational wave signals from a triple system. Namely, we consider a massive Black Hole (BH) surrounded by a binary system of two smaller BHs. We assume that the three BHs acquire a conformal coupling to the scalar field whose origin could be due to cosmology or to the galactic environment. In this case, the massive BH has a Vainshtein radius which englobes the smaller ones and suppresses the scalar effects on the motion of the binary system. On the other hand the two binaries can be outside each other's redressed Vainshtein radius calculated in the background of the central BH, allowing for a perturbative treatment of their dynamics. Despite the strong Vainshtein suppression, we find that the scalar effects on the binary system are slightly enhanced with respect to the static case and a significant amount of power can be emitted in the form of the Galileon scalar field, hence actively participating in the inspiralling phase. We compute the modification to the GW phase and show that it can lead to a detectable signal for large enough effective scalar coupling., Comment: 29 pages, 1 figure. Version accepted for publication in JCAP

It has been suggested that low energy effective field theories should satisfy given conditions in order to be successfully embedded into string theory. In the case of a single canonically normalized scalar field this translates into conditions on its potential and the derivatives thereof. In this Letter we revisit small field hilltop models of eternal inflation including stochastic effects and study the compatibility of the swampland constraints with entropy considerations. We show that these stochastic inflation scenarios either violate entropy bounds or the swampland criterion on the slope of the scalar field potential. Furthermore, we illustrate that such models are faced with a graceful exit problem: any patch of space which exits the region of eternal inflation is either not large enough to explain the isotropy of the cosmic microwave background, or has a spectrum of fluctuations with an unacceptably large red tilt., The European Physical Journal C, 80 (9), ISSN:1434-6044, ISSN:1434-6052

Gravitational wave (GW) oscillations occur whenever there are additional tensor modes interacting with the perturbations of the metric coupled to matter. These extra modes can arise from new spin-2 fields (as in e.g. bigravity theories) or from non-trivial realisations of the cosmological principle induced by background vector fields with internal symmetries (e.g. Yang-Mills, gaugids or multi-Proca). We develop a general cosmological framework to study such novel features due to oscillations. The evolution of the two tensor modes is described by a linear system of coupled second order differential equations exhibiting friction, velocity, chirality and mass mixing. We follow appropriate schemes to obtain approximate solutions for the evolution of both modes and show the corresponding phenomenology for different mixings. Observational signatures include modulations of the wave-form, oscillations of the GW luminosity distance, anomalous GW speed and chirality. We discuss the prospects of observing these effects with present and future GW observatories such as LIGO/VIRGO and LISA., 36 pages, 9 figures. Matches JCAP version

Recently, it has been argued that application of the weak gravity conjecture (WGC) to spin-2 fields implies a universal upper bound on the cutoff of the effective theory for a single spin-2 field. We point out here that these arguments are largely spurious, because of the absence of states carrying spin-2 Stückelberg U(1) charge, and because of incorrect scaling assumptions. Known examples such as Kaluza-Klein theory that respect the usual WGC do so because of the existence of a genuine U(1) field under which states are charged, as in the case of the Stückelberg formulation of spin-1 theories, for which there is an unambiguously defined U(1) charge. Theories of bigravity naturally satisfy a naive formulation of the WGC, MW, Physical Review D, 100 (10), ISSN:1550-7998, ISSN:0556-2821, ISSN:1550-2368