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We discuss ensemble averages of two-dimensional conformal field theories associated with an arbitrary indefinite lattice with integral quadratic form $Q$. We provide evidence that the holographic dual after the ensemble average is the three-dimensional Abelian Chern-Simons theory with kinetic term determined by $Q$. The resulting partition function can be written as a modular form, expressed as a sum over the partition functions of Chern-Simons theories on lens spaces. For odd lattices, the dual bulk theory is a spin Chern-Simons theory, and we identify several novel phenomena in this case. We also discuss the holographic duality prior to averaging in terms of Maxwell-Chern-Simons theories., Comment: 38 pages, 1 figure

Given a number field $K$ with a Hecke character $\chi$, for each place $\nu$ we study the free scalar field theory whose kinetic term is given by the regularized Vladimirov derivative associated to the local component of $\chi$. These theories appear in the study of $p$-adic string theory and $p$-adic AdS/CFT correspondence. We prove a formula for the regularized Vladimirov derivative in terms of the Fourier conjugate of the local component of $\chi$. We find that the Green's function is given by the local functional equation for Zeta integrals. Furthermore, considering all places $\nu$, the CFT two-point functions corresponding to the Green's functions satisfy an adelic product formula, which is equivalent to the global functional equation for Zeta integrals. In particular, this points out a role of Tate's thesis in adelic physics.

From the field equations corresponding to a four-dimensional brane embedded in the five-dimensional spacetime of the Einstein–Chern–Simons theory for gravity, we find cosmological solutions that describe an accelerated expansion for a flat universe. Apart from a quintessence-type evolution scheme, we obtain a transient phantom evolution, which is not ruled out by the current observational data. Additionally, a bouncing solution is shown. The introduction of a kinetic term in the action shows a de Sitter behavior although the energy density is not constant. A quintessence behavior is also found. We conjecture on a possible geometric origin of dark energy coming from this action.

We consider the gauged model of Siegel type chiral boson with a Lorentz non-covariant mass-like term for the gauge fields which is found to be equivalent to a model of boson where the kinetic term is like the kinetic term of Floreanini-Jackiw type chiral boson. We carry out the quantization of gauge non-invariant version this model in both the Lagrangian and Hamiltonian formulation. The quantization of the gauge-invariant version of this model in the extended phase space also has been carried out in the Lagrangian formulation. The gauge-invariant version of this model in the extended phase space is found to map onto the physical phase space with the appropriate gauge fixing condition. BRST symmetry associated with this model has been studied with different gauge fixing terms. It has been shown that the same model shows off-shell as well as on-shell BRST invariance depending on the choice of gauge fixing term.

We study quadratic gravity $R^2+R_{[\mu\nu]}^2$ in the Palatini formalism where the connection and the metric are independent. This action has a {\it gauged} scale symmetry (also known as Weyl gauge symmetry) of Weyl gauge field $v_\mu= (\tilde\Gamma_\mu-\Gamma_\mu)/2$, with $\tilde\Gamma_\mu$ ($\Gamma_\mu$) the trace of the Palatini (Levi-Civita) connection, respectively. The underlying geometry is non-metric due to the $R_{[\mu\nu]}^2$ term acting as a gauge kinetic term for $v_\mu$. We show that this theory has an elegant spontaneous breaking of gauged scale symmetry and mass generation in the absence of matter, where the necessary scalar field ($\phi$) is not added ad-hoc to this purpose but is "extracted" from the $R^2$ term. The gauge field becomes massive by absorbing the derivative term $\partial_\mu\ln\phi$ of the Stueckelberg field ("dilaton"). In the broken phase one finds the Einstein-Proca action of $v_\mu$ of mass proportional to the Planck scale $M\sim \langle\phi\rangle$, and a positive cosmological constant. Below this scale $v_\mu$ decouples, the connection becomes Levi-Civita and metricity and Einstein gravity are recovered. These results remain valid in the presence of non-minimally coupled scalar field (Higgs-like) with Palatini connection and the potential is computed. In this case the theory gives successful inflation and a specific prediction for the tensor-to-scalar ratio $0.007\leq r \leq 0.01$ for current spectral index $n_s$ (at $95\%$CL) and N=60 efolds. This value of $r$ is mildly larger than in inflation in Weyl quadratic gravity of similar symmetry, due to different non-metricity. This establishes a connection between non-metricity and inflation predictions and enables us to test such theories by future CMB experiments., Comment: 22 pages, 2 figures, LaTeX

Using the Noether symmetry approach, we investigate $$f( \mathcal{R} , \varphi ,\chi)$$ theories of gravity, where $$ \mathcal{R} $$ is the scalar curvature, $$ \varphi $$ is the scalar field, and $$\chi$$ is the kinetic term of $$ \varphi $$ . Based on the Lagrangian for $$f( \mathcal{R} , \varphi ,\chi)$$ gravity, we obtain the determining equations. We consider $$f( \mathcal{R} , \varphi ,\chi)$$ models of a flat Friedmann–Robertson–Walker universe. Using the obtained solutions, we find conserved quantities. In the framework of this scenario, the continuity equation is extremely important for analyzing the energy density and pressure. Using the first integral of motion, we present a graphical analysis of the energy density, pressure component, and parameter of the equation of state. The negativity of the pressure observed in the considered cases in fact suggests that this theory can describe a Noether universe with dark matter.

We consider a scalar field $\phi$ whose coupling to the kinetic term of a non-abelian gauge field is set at an UV scale $M$. Then the confinement of the gauge sector will induce a $\phi$-dependent vacuum energy which generates a dimensionful potential for the scalar. It provides a good example of dynamical generation of a new physics scale below $M$ through the vacuum expectation value $\langle \phi \rangle$. This mechanism may shed light on the origin of dark matter, or spontaneous symmetry breaking applicable to the electroweak symmetry., Comment: 4 pages, 3 figures

The U(1) vector multiplet theory with the Fayet-Iliopoulos (FI) term is one of the oldest and simplest models for spontaneously broken rigid supersymmetry. Lifting the FI term to supergravity requires gauged $R$-symmetry, as was first demonstrated in 1977 by Freedman within ${\cal N}=1$ supergravity. There exists an alternative to the standard FI mechanism, which is reviewed in this conference paper. It is obtained by replacing the FI model with a manifestly gauge-invariant action such that its functional form is determined by two arbitrary real functions of a single complex variable. One of these functions generates a superconformal kinetic term for the vector multiplet, while the other yields a generalised FI term. Coupling such a vector multiplet model to supergravity does not require gauging of the $R$-symmetry. These generalised FI terms are consistently defined for any off-shell formulation for ${\cal N}=1$ supergravity, and are compatible with a supersymmetric cosmological term., Contribution to the Proceedings of the Workshop "Supersymmetries and Quantum Symmetries" (SQS'2019, 26 August - August 31, 2019). V2: References have been reformated into the internationally recognised standard

We investigate extensions for the Schrodinger equation, by considering different non-linear dependencies on the kinetic term, which admit the standard probabilistic interpretation for the wave-function. For one of the cases, we show that the Heisenberg equation is invariant in form and a modified Hamilton-Jacobi equation emerges from the semi-classical approximation for the wave-function. Furthermore, we find solutions assuming time scaling functions different from the standard case and observe nonstandard relaxation processes for the wave-function.

We describe how to reconstruct generalized scalar-tensor gravity (GSTG) theory, which admits exact solutions for physical type of the potentials. Our consideration deals with cosmological inflationary models based on GSTG with non-minimal coupling of a (non-canonical) scalar field to the Ricci scalar. The basis of proposed approach to the analysis of these models is a priori specified relation between the Hubble parameter $H$ and a function of non-minimal coupling $F=1+\delta F$ as $H\propto\sqrt{F}$. Deviations from Einstein gravity $\delta F$ induce a corresponding deviations of the potential $\delta V$ from a constant value and modify the dynamics from pure de Sitter exponential expansion. We analyze the models with exponential power-law evolution of the scale factor and we find the equations of influence of non-minimal coupling, choosing it in the special form, on the potential and kinetic energies. Such consideration allows us to substitute the physical potential into obtained equations and then to calculate the non-minimal coupling function and kinetic term that are define GSTG parameters. With this method, we reconstruct GSTG for polynomial, exponential, Higgs, Higgs-Starobinsky and Coleman-Weinberg potentials. Special attention we pay to parameters of cosmological perturbations and prove correspondence obtained solutions to observational data from Planck., Comment: 15 pages

This paper proposes a theory for understanding perceptual learning processes within the general framework of laws of nature. Artificial neural networks are regarded as systems whose connections are Lagrangian variables, namely, functions depending on time. They are used to minimize the cognitive action, an appropriate functional index that measures the agent interactions with the environment. The cognitive action contains a potential and a kinetic term that nicely resemble the classic formulation of regularization in machine learning. A special choice of the functional index, which leads to the fourth-order differential equations-Cognitive Action Laws (CAL)-exhibits a structure that mirrors classic formulation of machine learning. In particular, unlike the action of mechanics, the stationarity condition corresponds with the global minimum. Moreover, it is proven that typical asymptotic learning conditions on the weights can coexist with the initialization provided that the system dynamics is driven under a policy referred to as information overloading control. Finally, the theory is experimented for the problem of feature extraction in computer vision.

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) approach, we discuss mainly the fermionic (i.e. off-shell nilpotent) (anti-)BRST, (anti-)co-BRST and some discrete dual-symmetries of the appropriate Lagrangian densities for a two (1+1)-dimensional (2D) modified Proca (i.e. a massive Abelian 1-form) theory without any interaction with matter fields. One of the novel observations of our present investigation is the existence of some kinds of restrictions in the case of our present St\"{u}ckelberg-modified version of the 2D Proca theory which is not like the standard Curci-Ferrari (CF)-condition of a non-Abelian 1-form gauge theory. Some kinds of similarities and a few differences between them have been pointed out in our present investigation. To establish the sanctity of the above off-shell nilpotent (anti-)BRST and (anti-)co-BRST symmetries, we derive them by using our newly proposed (anti-)chiral superfield formalism where a few specific and appropriate sets of invariant quantities play a decisive role. We express the (anti-)BRST and (anti-)co-BRST conserved charges in terms of the superfields that are obtained after the applications of (anti-)BRST and (anti-)co-BRST invariant restrictions and prove their off-shell nilpotency and absolute anticommutativity properties, too. Finally, we make some comments on (i) the novelty of our restrictions/obstructions, and (ii) the physics behind the negative kinetic term associated with the pseudo-scalar field of our present theory., Comment: LaTeX file, 58 pages, Journal reference given

We apply the tools of the dynamical system theory in order to revisit and uncover the structure of a nongravitational interaction between pressureless dark matter and dark energy described by a scalar field $\phi$. For a coupling function $Q = -(\alpha d\rho_m/dt + \beta d\rho_\phi/dt )$, where t is the cosmic time, we have found that it can be rewritten in the form $Q = 3H (\alpha \rho_m + \beta (d\phi/dt)^2 )/(1-\alpha +\beta)$, so that its dependence on the dark matter density and on the kinetic term of the scalar field is linear and proportional to the Hubble parameter. We analyze the scenarios $\alpha=0$, $\alpha = \beta$ and $\alpha = -\beta$, separately and in order to describe the cosmological evolution we have calculated various observables. A notable result of this work is that, unlike for the noninteracting scalar field with exponential potential where five critical points appear, in the case studied here, with the exception of the matter dominated solution, the remaining singular points are transformed into scaling solutions enriching the phase space. It is shown that for $\alpha \neq 0$, a separatrix arises modifying prominently the structure of the phase space. This represents a novel feature no mentioned before in the literature., Comment: 16 pages, 9 figures, 7 tables

The fractional dark energy (FDE) model describes the accelerated expansion of the Universe through a nonrelativistic gas of particles with a noncanonical kinetic term. This term is proportional to the absolute value of the three-momentum to the power of $3w$, where $w$ is simply the dark energy equation of state parameter, and the corresponding energy leads to an energy density that mimics the cosmological constant. In this paper we expand the fractional dark energy model considering a non-zero chemical potential and we show that it may thermodynamically describe a phantom regime. The Planck constraints on the equation of state parameter put upper limits on the allowed value of the ratio of the chemical potential to the temperature. In the second part, we investigate the system of fractional dark energy particles with negative absolute temperatures (NAT). NAT are possible in quantum systems and in cosmology, if there exists an upper bound on the energy. This maximum energy is one ingredient of the FDE model and indicates a connection between FDE and NAT, if FDE is composed of fermions. In this scenario, the equation of state parameter is equal to minus one and, using cosmological observations, we find that the transition from positive to negative temperatures is allowed at any redshift larger than one., Comment: 11 pages, updated version with constraints from observations, references added

In this work, a cosmological model is considered having two scalar fields minimally coupled to gravity with a mixed kinetic term. The model is characterized by the coupling function and the potential function which are assumed to depend on one of the scalar fields. Instead of choosing these functions phenomenologically here, they are evaluated assuming the existence of Noether symmetry. By appropriate choice of a point transformation in the augmented space, one of the variables in the Lagrangian becomes cyclic and the evolution equations become much simpler to have solutions. Finally, the solutions are analyzed from cosmological view point., 12 pages, 3 figures

We investigate static and spherically symmetric stars disformally coupled to a scalar field. The scalar field is assumed to be shift symmetric, and hence the conformal and disformal factors of the metric coupled to matter are dependent only on the kinetic term of the scalar field. Assuming that the scalar field is linearly dependent on time, we consider a general shift-symmetric scalar-tensor theory and a general form of the matter energy-momentum tensor that allows for the anisotropic pressure and the heat flux in the radial direction. This is a natural starting point in light of how the gravitational field equations and the energy-momentum tensor transform under a disformal transformation. By inspecting the structure of the hydrostatic equilibrium equation in the presence of the derivative-dependent conformal and disformal factors, we show that the energy density and tangential pressure must vanish at the surface of a star. This fact is used to prove the disformal invariance of the surface of a star, which was previously subtle and unclear. We then focus on the shift-symmetric k-essence disformally coupled to matter, and study the interior and exterior metric functions and scalar-field profile in more detail. It is found that there are two branches of the solution depending on the velocity of the scalar field. The disformally-related metric functions of the exterior spacetime are also discussed., Comment: 12 pages, 4 figures

It is shown that the inflationary model is the result of the symmetry of the generalized F(R,T,X,φ)-cosmological model using the Noether symmetry. It leads to a solution, a particular case of which is Starobinsky’s cosmological model. It is shown that even in the more particular case of cosmological models F(R,X,φ) and F(T,X,φ) the Monge–Ampère equation is still obtained, one of the solutions including the Starobinsky model. For these models, it is shown that one can obtain both power-law and exponential solutions for the scale factor from the Euler–Lagrange equations. In this case, the scalar field φ has similar time dependences, exponential and exponential. The resulting form of the Lagrangian of the model allows us to consider it as a model with R2 or X2. However, it is also shown that previously less studied models with a non-minimal relationship between R and X are important, as one of the possible models. It is shown that in this case the power-law model can have a limited evolutionary period with a negative value of the kinetic term.

An alternative scenario about the phenomenology of primordial Universe is k-inflation. According to this concept, inflation can be achieved by nonstandard kinetic term of scalar field, namely the inflaton. In this project we focus on k-essence models in the presence of a higher order and a linear kinetic term. Furthermore, the inflationary phenomenology with a Dirac-Born-Infeld scalar field is briefly examined, which arises from quantum theories of gravity such as superstring theory. Our approach about the inflationary era is that it can be described in the context of Einstein's gravity involving quantum corrections such as the Chern-Simons string inspired parity violating gravitational term. The equations of motion namely, the Friedmann equation, the Raychadhuri equation and the Klein-Gordon equation for an expanding background are extracted from the gravitational action utilizing the variational principle. The consequential system of differential equations with respect to Hubble's parameter and the inflaton field was quite perplexed in order to be solved with an analytic way. Therefore, the slow-roll conditions during inflationary era were imposed and terms with minor numerically contribution were neglected. From the overall phenomenological analysis it is proved that, models with exotic kinetic terms can generate viable results in consistency with the latest Planck data. Finally, the presence of Chern-Simons quantum corrections shifts the primordial spectral tensor index to blue. Even though blue gravitational waves have yet to be observed, if detected, compatibility with the aforementioned theory can be achieved., Accepted in International Journal of Modern Physics A. arXiv admin note: text overlap with arXiv:2107.09457

We employ the "complexity equals action" conjecture to investigate the action growth rate for the charged and neutral AdS black branes of a holographic toy model consisting of Einstein-Maxwell theory in $d + 1$-dimensional bulk spacetime with $d - 1$ massless scalar fields which is called Einstein-Maxwell-Axion (EMA) theory. From the holographic point of view, the scalar fields source a spatially dependent field theory with momentum relaxation on the boundary, which is dual to the homogeneous and isotropic black branes. We find that the growth rate of the holographic complexity within the Wheeler-DeWitt (WDW) patch saturates the corresponding Lloyd's bound at the late time limit. Especially for the neutral AdS black branes, it will be shown that the complexity growth rate at late time vanishes for a particular value of relaxation parameter $\beta_{max}$ where the temperature of the black hole is minimal. Then, we investigate the transport properties of the holographic dual theory in the minimum temperature. A non-linear contribution of the axion field kinetic term in the context of k-essence model in the four-dimensional spacetime is considered as well. We also study the time evolution of the holographic complexity for the dyonic AdS black branes in this model., Comment: 31 pages, 6 figures, Version accepted for publication in PRD

Within the framework of inflationary model with field-dependent kinetic term for quartic and natural potentials, we investigate generation of the primordial black holes (PBHs) and induced gravitational waves (GWs). In this setup, we consider a kinetic function as $G(\phi)=g_I(\phi)\big(1+g_{II}(\phi)\big)$ and show that in the presence of first term $g_I(\phi)$ both quartic and natural potentials, in contrast to the standard model of inflation, can be consistent, with the 68\% CL of Planck observations. Besides, the second term $g_{II}(\phi)$ can cause a significant enhancement in the primordial curvature perturbations at the small scales which results the PBHs formation. For the both potentials, we obtain an enhancement in the scalar power spectrum at the scales $k\sim10^{12}~\rm Mpc^{-1}$, $10^{8}~\rm Mpc^{-1}$, and $10^{5}~\rm Mpc^{-1}$, which causes PBHs production in mass scales around $10^{-13}M_{\odot}$, $10^{-5}M_{\odot}$, and $10 M_{\odot}$, respectively. Observational constraints confirm that PBHs with a mass scale of $10^{-13}M_{\odot}$ can constitute the total of dark matter in the universe. Furthermore, we estimate the energy density parameter of induced GWs which can be examined by the observation. Also we conclude that it can be parametrized as a power-law function $\Omega_{\rm GW}\sim (f/f_c)^n$, where the power index equals $n=3-2/\ln(f_c/f)$ in the infrared limit $f\ll f_{c}$., Comment: 25 pages, 7 figures, 5 tables

In this short note, we present the dynamics of a general scalar–tensor model, and in particular a scalar Einstein–Gauss–Bonnet model with a non-minimal coupling between gravity and the kinetic term of the scalar field. For the sake of simplicity, two f(R) models are studied separately, an exponential and a power-law, accompanied by either an exponential or quartic scalar potential and a strictly exponential Gauss–Bonnet scalar coupling function known for being a suitable candidate for describing both the early and the late time. By introducing the general framework of a late-time study for an arbitrary scalar–tensor model, we find that the aforementioned models are capable of producing compatible with the Planck data observations and are in a relatively good agreement with the $$\Lambda $$ CDM model and the GW170817 event as the tensor perturbation velocity is equal to unity in natural units for the whole are of values of redshift studied if certain parameters are properly designated. A brief comment on the appearance of dark energy oscillations which appear for the case of power-law f(R) and the overall viability of the model is also made.

The generalized SU(2) Proca theory (GSU2P) is a variant of the well known generalized Proca theory where the vector field belongs to the Lie algebra of the SU(2) group of global transformations under which the action is made invariant. New interesting possibilities arise in this framework because of the existence of new interactions of purely non-Abelian character and new configurations of the vector field resulting in spatial spherical symmetry and the cosmological dynamics being driven by the propagating degrees of freedom. We study the two-dimensional phase space of the system that results when the cosmic triad configuration is employed in the Friedmann-Lemaitre-Robertson-Walker background and find an attractor curve whose attraction basin both covers almost all the allowed region and does not include a Big-Bang singularity. Such an attractor curve corresponds to a primordial inflationary solution that has the following characteristic properties: 1.) it is a de Sitter solution whose Hubble parameter is regulated by a generalized version of the SU(2) group coupling constant, 2.) it is constant-roll including, as a limiting case, the slow-roll variety, 3.) a number of e-folds $N > 60$ is easily reached, 4.) it has a graceful exit into a radiation dominated period powered by the canonical kinetic term of the vector field and the Einstein-Hilbert term. The free parameters of the action are chosen such that the tensor sector of the theory is the same as that of general relativity at least up to second-order perturbations, thereby avoiding the presence of ghost and Laplacian instabilities in the tensor sector as well as making the gravity waves propagate at light speed. This is a proof of concept of the interesting properties we could find in this scenario when the coupling constants be replaced by general coupling functions and more terms be discovered in the GSU2P., LaTeX file in WileYMSP-template style, 28 pages, 20 figures. Version published in Annalen der Physik. Dedicated to Carlos J. Quimbay Herrera, Marta A. Losada Falk, and David H. Lyth

We present a detailed and pedagogical analysis of recent cosmological data, including CMB, BAO, SnIa and the recent local measurement of $H_0$. We thus obtain constraints on the parameters of standard dark energy parameterizations, including $\Lambda CDM$, and $H(z)$ deformation models such as $wCDM$ (constant equation of state $w$ of dark energy), and the CPL model (corresponding to the evolving dark energy equation-of-state parameter $w(z) = w_0 + w_a \frac{z}{1+z}$). The fitted parameters include the dark matter density $\Omega_{0m}$, the SnIa absolute magnitude $M$, the Hubble constant $H_0$ and the dark energy parameters (e.g., $w$ for $wCDM$). All models considered lead to a best-fit value of $M$ that is inconsistent with the locally determined value obtained by Cepheid calibrators ($M$ tension). We then use the best-fit dark energy parameters to reconstruct the quintessence Lagrangian that would be able to reproduce these best-fit parameterizations. Due to the derived late phantom behavior of the best-fit dark energy equation-of-state parameter $w(z)$, the reconstructed quintessence models have a negative kinetic term and are therefore plagued with instabilities., Comment: 69 pages,4 tables,33 figures. Based on the BSc thesis of AT. Published in Universe 7 (2021) 8, 300. The numerical analysis files that were used for the production of the figures may be downloaded from: https://github.com/TasosTheodoropoulos/M_crisis

This analysis explores the solutions for wormhole in [Formula: see text] gravity, where [Formula: see text], and [Formula: see text] represent the kinetic term, scalar potential, and Ricci scalar, respectively. For this study, we use the spherically symmetric spacetime with the anisotropic source of matter. Further, we use the linear equation of state to complete this current investigation in the background of conformal symmetry motion. By plugging non-zero conformal Killing vectors, we discuss the feasible phantom wormhole configurations. Under the linear equation of state, the stability of wormhole solutions with specific values of parameters is also checked by using the Tolman–Oppenheimer–Volkoff equation. Further, the energy conditions are also discussed with conformal motions. Moreover, it is concluded that our inquired solutions are physically viable in [Formula: see text] gravity.

Study the behaviour and the evolution of the cosmological field equations in an homogeneous and anisotropic spacetime with two scalar fields coupled in the kinetic term. Specifically, the kinetic energy for the scalar field Lagrangian is that of the Chiral model and defines a two-dimensional maximally symmetric space with negative curvature. For the background space we assume the locally rotational spacetime which describes the Bianchi I, the Bianchi III and the Kantowski-Sachs anisotropic spaces. We work on the $H$% -normalization and we investigate the stationary points and their stability. For the exponential potential we find a new exact solution which describes an anisotropic inflationary solution. The anisotropic inflation is always unstable, while future attractors are the scaling inflationary solution or the hyperbolic inflation. For scalar field potential different from the exponential, the de Sitter universe exists., 17 pages, 2 figures, published in Eur. Phys. J. Plus

In the context of massive gravity theories, we study holographic flows driven by a relevant scalar operator and interpolating between a UV 3-dimensional CFT and a trans-IR Kasner universe. For a large class of scalar potentials, the Cauchy horizon never forms in presence of a non-trivial scalar hair, although, in absence of it, the black hole solution has an inner horizon due to the finite graviton mass. We show that the instability of the Cauchy horizon triggered by the scalar field is associated to a rapid collapse of the Einstein-Rosen bridge. The corresponding flows run smoothly through the event horizon and at late times end in a spacelike singularity at which the asymptotic geometry takes a general Kasner form dominated by the scalar hair kinetic term. Interestingly, we discover deviations from the simple Kasner universe whenever the potential terms become larger than the kinetic one. Finally, we study the effects of the scalar deformation and the graviton mass on the Kasner singularity exponents and show the relationship between the Kasner exponents and the entanglement and butterfly velocities probing the black hole dynamics. Differently from the holographic superconductor case, we can prove explicitly that Josephson oscillations in the interior of the BH are absent., v2: matching the revised version published in JHEP

We construct a new covariant action for "flat" self-dual gravity in four spacetime dimensions. The action has just one term, but when expanded around an appropriate background gives rise to a kinetic term and a cubic interaction. Upon imposing the light-cone gauge, the action reproduces the expected chiral interaction of Siegel. The new action is in many ways analogous to the known covariant action for self-dual Yang-Mills theory. There is also a sense in which the new self-dual gravity action exhibits the double copy of self-dual Yang-Mills structure., Comment: 18 pages

In five dimensions we consider a general shift symmetric and parity preserving scalar tensor action that contains up to second order covariant derivatives of the scalar field. A rotating stealth black hole solution is constructed where the metric is given by the Myers-Perry spacetime with equal momenta and the scalar field is identified with the Hamilton-Jacobi potential. This nontrivial scalar field has an extra hair associated with the rest mass of the test particle, and the solution does not require any fine tuning of the coupling functions of the theory. Interestingly enough, we show that the disformal transformation, generated by this scalar field, and with a constant degree of disformality, leaves invariant (up to diffeomorphisms) the Myers-Perry metric with equal momenta. This means that the hair of the scalar field, along with the constant disformality parameter, can be consistently absorbed into further redefinitions of the mass and of the single angular parameter of the disformed metric. These results are extended in higher odd dimensions with a Myers-Perry metric for which all the momenta are equal. The key of the invariance under disformal transformation of the metric is mainly the cohomogeneity-1 character of the Myers-Perry metric with equal momenta. Starting from this observation, we consider a general class of cohomogeneity-1 metrics in arbitrary dimension, and we list the conditions ensuring that this class of metrics remain invariant (up to diffeomorphisms) under a disformal transformation with a constant degree of disformality and with a scalar field with constant kinetic term. The extension to the Kerr-(A)dS case is also considered where it is shown that rotating stealth solutions may exist provided some fine tuning of the coupling functions of the scalar tensor theory., Comment: 19 pages (added new references)

Non-canonical scalar fields with the Lagrangian ${\cal L} = X^\alpha - V(\phi)$, possess the attractive property that the speed of sound, $c_s^{2} = (2\,\alpha - 1)^{-1}$, can be exceedingly small for large values of $\alpha$. This allows a non-canonical field to cluster and behave like warm/cold dark matter on small scales. We demonstrate that simple potentials including $V = V_0\coth^2{\phi}$ and a Starobinsky-type potential can unify dark matter and dark energy. Cascading dark energy, in which the potential cascades to lower values in a series of discrete steps, can also work as a unified model. In all of these models the kinetic term $X^\alpha$ plays the role of dark matter, while the potential term $V(\phi)$ plays the role of dark energy., Comment: 19 pages, 9 figures. Comprehensively revised and expanded. New section on Cascading dark energy

Chaotic inflation is inconsistent with the observational constraint at 68\% CL. Here, we show that the enhancement mechanism with a peak function in the noncanonical kinetic term not only helps the chaotic model $V(\phi)=V_0\phi^{1/3}$ satisfy the observational constraint at large scales but also enhances the primordial scalar power spectrum by seven orders of magnitude at small scales. The enhanced curvature perturbations can produce primordial black holes of different masses and secondary gravitational waves with different peak frequencies. We also show that the non-Gaussianities of curvature perturbations have little effect on the abundance of primordial black holes and energy density of the scalar-induced secondary gravitational waves., Comment: 17 pages,2 tables, 5 figures. Minor changes to match the version published on SCPMA(SCIENCE CHINA Physics, Mechanics & Astronomy)

Dilatonic black hole dyon-like solutions are overviewed in the gravitational 4D model with a scalar field, two 2-forms, two dilatonic coupling constants λi ≠ 0, i = 1, 2, obeying λ1 ≠ − λ2, and the sign parameter e = ±1 before the scalar field kinetic term. Here e = −1 corresponds to a phantom scalar field. The solutions are defined up to solutions of two master equations for two moduli functions, when $$\lambda_i^2 \neq 1/2$$ for e = −1. Several integrable cases, corresponding to the Lie algebras A1 + A1, A2, B2 = C2 and G2 are considered. Some physical parameters of the solutions are derived: the gravitational mass, scalar charge, Hawking temperature, black hole area entropy and PPN parameters β and γ. Bounds on the gravitational mass and scalar charge, based on a certain conjecture, are presented.

The Swampland Distance Conjecture (SDC) constraints the dynamics emerging at infinite distances in field space of any effective field theory consistent with quantum gravity. It provides a relation between the cut-off in energies and the field range which, as we show, in the context of inflation it yields a universal upper bound on the inflaton excursion in terms of the tensor-to-scalar ratio, measured at typical CMB scales. In this note, we investigate the interplay between the SDC and the emergent inflationary physics around infinite distances singularities in string theory, with a special look at its significance for the $\alpha$-attractor scenario of inflation. We show that the conjecture itself suggests that inflation may arise as an infinite distance phenomenon with the asymptotic kinetic structure typical of $\alpha$-attractors. Furthermore, we argue that a proper string realisation of these cosmological models in Calabi-Yau manifolds should occur around infinite field distance singularities. However, such constructions typically imply that inflation should not take place in the limit where the inflaton kinetic term develops a pole but rather in the opposite regime. Finally, we study the constraints that the SDC poses on $\alpha$-attractors and show that they still leave considerable room for compatibility with observations., Comment: 15 pages, 3 figures; v2: comments and references added

The generalized Brans-Dicke (abbreviated as GBD) theory is obtained by replacing the Ricci scalar $R$ in the original Brans-Dicke (BD) action with an arbitrary function $f(R)$. Comparing with other theories, some interesting properties have been found or some problems existing in other theories could be solved in the GBD theory. For example, (1) the state parameter of geometrical dark energy in the GBD model can cross over the phantom boundary $w=-1$, without bearing the problems existing in the quintom model (e.g. the problem of negative kinetic term and the fine-tuning problem, etc); (2) $f(R)$ theory is equivalent to the BD theory with a potential (BDV) with the couple parameter $\omega=0$, where the kinetic term of field in the equivalent BDV theory is absent. While the scalar fields in the GBD own the non-disappeared kinetic term, when one compares the GBD theory with the $f(R)$ theory. In this paper, we continue to investigate the GBD theory. Using the method of the weak-field approximation, we explore the linearized physics in the GBD theory. The linearized equations of the gravitational field and two scalar fields are given. We investigate their solutions in the linearized theory for a point mass. It is shown that the problem of the $\gamma$ (parametrized post-Newtonian parameter) value in the $f(R)$ theory could be solved in the GBD theory, where the theoretical $\gamma$ value in the GBD theory can be consistent with the observational results. At last, we study the gravitational waves physics in the vacuum for the GBD theory. It is found that the gravitational radiation in the GBD theory has new freedoms beyond the two standard modes in the general relativity theory., Comment: 11 pages, no figure. arXiv admin note: text overlap with arXiv:1803.00365

We consider modified f(R) gravity with a kinetic curvature scalar, which can be reduced to a chiral cosmological model of special kind. A detailed derivation is presented for the action of a chiral cosmological model as an equivalent to a gravitational model with higher derivatives with respect to the Ricci scalar using Lagrange multipliers and a transition from the Jordan frame to the Einstein one. The equations of the model are written in the spatially flat Friedmann-Robertson-Walker metric on the basis of the constructed chiral cosmological model. Examples of solutions are found, corresponding to a special choice of the field χ = χ* = const, and its fixed value $$\chi_0=-\sqrt{3/2}\;\text{ln}2$$ . For this value of χ0, in the case of the canonical inclusion of the kinetic component of the Ricci scalar, we have obtained a nonlinear second-order differential equation with respect to H, which is not amenable to analytic solution. Therefore we implement a transition to a noncanonical form of the kinetic term. Using a fixed value of χ0, an exact solution is obtained for power-law inflation. We have considered a transition from the de Sitter and power-law solutions specified in the Jordan frame to the Einstein frame for comparison with the results obtained in f(R) gravity with higher derivatives. It is proved that there is a Weyl conformal transformation which transforms the de Sitter and power-law solutions in one frame to similar solutions in the other.

We argue that a new type of extremely light axion is generically present in the type IIB part of the string theory landscape. Its mass is suppressed by the third power of the warp factor of a strongly warped region (Klebanov-Strassler throat), suggesting the name thraxion. Our observation is based on the generic presence of several throats sharing the same 2-cycle. This cycle shrinks to zero volume at the end of each throat. It is hence trivial in homology and the corresponding $C_2$ axion is massive. However, the mass is warping-suppressed since, if one were to cut off the strongly warped regions, a proper 2-cycle would re-emerge. Since the kinetic term of the axion is dominated in the UV, an even stronger, quadratic mass suppression results. Moreover, if the axion is excited, the angular modes of the throats backreact. This gives our effective $C_2$ axion a finite monodromy and flattens its potential even further. Eventually, the mass turns out to scale as the third power of the warp factor. We briefly discuss possible implications for phenomenology and potential violations of the Weak Gravity Conjecture for axions. Moreover we identify a mechanism for generating super-Planckian axionic field ranges which we call drifting monodromies. However, in the examples we consider, the potential oscillates on sub-Planckian distances in field space, preventing us from building a natural inflation model on the basis of this idea., 40 pages + appendices, 11 figures; v2: added references; v3: new section 2.5, published in JHEP