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$SU(\infty)$-QGR is a foundationally quantum approach to gravity. It assumes that Hilbert spaces of the Universe as a whole and its subsystems represent the symmetry group $SU(\infty)$. The Universe is divided to infinite number of subsystems based on an arbitrary finite rank symmetry group $G$, which arises due to quantum fluctuations and clustering of states. After selection of two arbitrary subsystems as clock and reference observer, subsystems acquire a relative dynamics, and gravity emerges as a $SU(\infty)$ Yang-Mills quantum field theory, defined on the (3+1)-dimensional parameter space of Hilbert spaces of the subsystems. As a Yang-Mills model $SU(\infty)$-QGR is renormalizable and despite prediction of a spin-1 field for gravity at quantum level, when QGR effects are not detectable, it is perceived similar to Einstein gravity. The aim of the present work is to make the foundation of $SU(\infty)$-QGR more mathematically rigorous and fill the gaps in the construction of the model reported in earlier works. In particular, we show that the global $SU(\infty)$ symmetry manifests itself through the entanglement of every subsystem with the rest of the Universe. Moreover, we demonstrate irrelevance of the geometry of parameter space, which can be gauged out by a $SU(\infty)$ gauge transformation up to an irrelevant constant. Therefore, $SU(\infty)$-QGR deviates from gauge-gravity duality models, because the perceived classical spacetime is neither quantized, nor considered to be non-commutative. In fact, using quantum uncertainty relations, we demonstrate that the classical spacetime and its perceived geometry present the average path of the ensemble of quantum states of subsystems in their parameter space. Thus, $SU(\infty)$-QGR explains both the dimension and signature of the classical spacetime. We also briefly discuss $SU(\infty)$-QGR specific models for dark energy., 50 pages+22 pages, 2 figures

International audience; We introduce a new logotropic model based on a complex scalar field with a logarithmic potential that unifies dark matter and dark energy. The scalar field satisfies a nonlinear wave equation generalizing the Klein-Gordon equation in the relativistic regime and the Schrödinger equation in the nonrelativistic regime. This model has an intrinsically quantum nature and returns the Λ cold dark matter (CDM) model in the classical limit ℏ→0. It involves a new fundamental constant of physics A/c2=2.10×10-26 g m-3 responsible for the late accelerating expansion of the Universe and superseding the Einstein cosmological constant Λ. The logotropic model is almost indistinguishable from the ΛCDM model at large (cosmological) scales but solves the CDM crisis at small (galactic) scales. It also solves the problems of the fuzzy dark matter model. Indeed, it leads to cored dark matter halos with a universal surface density Σ0th=5.85(A/4πG)1/2=133 M⊙/pc2. This universal surface density is predicted from the logotropic model without adjustable parameter and turns out to be close to the observed value Σ0obs=141-52+83 M⊙/pc2. We also argue that the quantities Ωdm,0 and Ωde,0, which are usually interpreted as the present proportions of dark matter and dark energy in the ΛCDM model, are equal to Ωdm,0th=11+e(1-Ωb,0)=0.2559 and Ωde,0th=e1+e(1-Ωb,0)=0.6955 in very good agreement with the measured values Ωdm,0obs=0.2589 and Ωde,0obs=0.6911 (their empirical ratio 2.669 is close to the Euler number e=2.71828…). We point out, however, important difficulties with the logotropic model, similar to those encountered by the generalized Chaplygin gas model. These problems are related to the difficulty of forming large-scale structures due to an increasing speed of sound as the Universe expands. We discuss potential solutions to these problems, stressing in particular the importance to perform a nonlinear study of structure formation.

Lattice field theory is a very powerful tool to study Feynman's path integral non-perturbatively. However, it usually requires Euclidean background metrics to be well-defined. On the other hand, a recently developed regularization scheme based on Fourier integral operator $\zeta$-functions can treat Feynman's path integral non-pertubatively in Lorentzian background metrics. In this article, we formally $\zeta$-regularize lattice theories with Lorentzian backgrounds and identify conditions for the Fourier integral operator $\zeta$-function regularization to be applicable. Furthermore, we show that the classical limit of the $\zeta$-regularized theory is independent of the regularization. Finally, we consider the harmonic oscillator as an explicit example. We discuss multiple options for the regularization and analytically show that they all reproduce the correct ground state energy on the lattice and in the continuum limit. Additionally, we solve the harmonic oscillator on the lattice in Minkowski background numerically.

Journal of high energy physics 04(4), 023 (2023). doi:10.1007/JHEP04(2023)023, We study the eikonal scattering of two gravitationally interacting bodies, in the regime of large angular momentum and large center of mass energy. We show that eikonal exponentiation of the scattering phase matrix is a direct consequence of the group contraction $SU(2)\to ISO(2)$, from rotations to the isometries of the plane, in the large angular momentum limit. We extend it to all orders in the scattering angle, and for all masses and spins. The emergence of the classical limit is understood in terms of the continuous-spin representations admitted by $ISO(2)$. We further investigate the competing classical vs quantum corrections to the leading classical eikonal scattering, and find several interesting examples where quantum corrections are more important than Post-Minkowskian's. As a case of study, we analyse the scattering of a photon off a massless neutral scalar field, up to next-to-leading order in the Newton constant, and to leading order in the fine structure constant. We investigate the causal structure of the eikonal regime and establish an infinite set of non-linear positivity bounds, of which positivity of time delay is the simplest., Published by SISSA, [Trieste]

We compute the four-momentum radiated during the scattering of two spinless bodies, at leading order in the Newton's contant $G$ and at all orders in the velocities, using the Effective Field Theory worldline approach. Following \cite{Mougiakakos:2021ckm}, we derive the conserved stress-energy tensor linearly coupled to gravity generated by localized sources, at leading and next-to-leading order in $G$, and from that the classical probability amplitude of graviton emission. The total emitted momentum is obtained by phase-space integration of the graviton momentum weighted by the modulo squared of the radiation amplitude. We recast this as a two-loop integral that we solve using techniques borrowed from particle physics, such as reverse unitarity, reduction to master integrals by integration-by-parts identities and canonical differential equations. The emitted momentum agrees with recent results obtained by other methods. Our approach provides an alternative way of directly computing radiated observables in the post-Minkowskian expansion without going through the classical limit of scattering amplitudes., Comment: 41 pages, corrected typos

We shed some light on the reason why the accidental flatness constraint appears in certain limits of the amplitudes of covariant loop quantum gravity. We show why this constraint is harmless, by displaying how analogous accidental constraints appear in transition amplitudes of simple systems, when certain limits are considered., Comment: 6 pages

The naive double-copy of (multi) loop amplitudes involving massive matter coupled to gauge theories will generically produce amplitudes in a gravitational theory that contains additional contributions from propagating antisymmetric tensor and dilaton states even at tree-level. We present a graph-based approach that combines the method of maximal cuts with double-copy construction to offer a systematic framework to isolate the pure Einstein-Hilbert gravitational contributions through loop level. Indeed this allows for a bootstrap of pure-gravitational results from the double-copy of massive scalar-QCD. We apply this to construct the novel result of the D-dimensional one-loop five-point QFT integrand relevant in the classical limit to generating observables associated with the radiative effects of massive black-hole scattering via pure Einstein-Hilbert gravity., Comment: 33 pages, 9 figures

We show how to compute classical wave observables using quantum scattering amplitudes. We discuss observables both with incoming and with outgoing waves. The required classical limits are naturally described by coherent states of massless bosons. We recompute the classic gravitational deflection of light, and also show how to rederive Thomson scattering. We introduce a new class of local observables, which includes the asymptotic electromagnetic and gravitational Newman--Penrose scalars. As an example, we compute a simple radiated waveform: the expectation of the electromagnetic field in charged-particle scattering. At leading order, the waveform is trivially related to the five-point scattering amplitude., Comment: 84 pages, 3 figures

Using $\mathcal N=8$ supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic two-loop amplitude. We employ the eikonal phase to obtain the physical deflection angle and to show how its non-relativistic (NR) and ultra-relativistic (UR) regimes are smoothly connected. Such a smooth interpolation rests on keeping contributions to the loop integrals originating from the full soft region, rather than restricting it to its potential sub-region. This task is efficiently carried out by using the method of differential equations with complete near-static boundary conditions. In contrast to the potential-region result, the physical deflection angle includes radiation-reaction contributions that are essential for recovering the finite and universal UR limit implied by general analyticity and crossing arguments. We finally discuss the real emission of massless states, which accounts for the imaginary part of the 3PM eikonal and for the dissipation of energy-momentum. Adopting a direct approach based on unitarity and on the classical limit of the inelastic tree-level amplitude, we are able to treat $\mathcal N=8$ and General Relativity on the same footing, and to complete the conservative 3PM eikonal in Einstein's gravity by the addition of the radiation-reaction contribution. We also show how this approach can be used to compute waveforms, as well as the differential and integrated spectra, for the different radiated massless fields., 88 pages, 7 figures, 2 ancillary files. v2: minor revisions, to appear in JHEP

Physical review letters 125(26), 261103 (2020). doi:10.1103/PhysRevLett.125.261103, We derive the conservative dynamics of non-spinning binaries to third~Post-Minkowskian order, using the Effective Field Theory (EFT) approach introduced in [2006.01184] together with the Boundary-to-Bound dictionary developed in [1910.03008, 1911.09130]. The main ingredient is the scattering angle, which we compute to ${\cal O}(G^3)$ via Feynman diagrams. Adapting to the EFT framework powerful tools from the amplitudes program, we show how all of the associated (massless) master integrals in the potential region are 'bootstrapped' to all orders in velocities via differential equations. Remarkably, the boundary conditions can be reduced to the same master integrals that appear in the EFT with Post-Newtonian sources at `two loop' order. For the sake of comparison, we reconstruct the Hamiltonian and, using the 'impetus formula', the classical limit of the (infrared-finite part of the) scattering amplitude at two loops. Our results are in perfect agreement with those in Bern et al. [1901.04424, 1908.01493]., Published by APS, College Park, Md.

Two properties of the radiation emitted by a relativistic electron in an external field, in the classical approximation, are presented in details: 1) spectral sum rules and their relationship with the sum rules for oscillator strength in atomic physics. Filtered sum rules can be used to remove infrared or ultraviolet divergences. 2) "half-naked electron" effects like the Landau- Pomeranchuk-Migdal and Ternovskij-Shul'ga-Fomin effects. These properties are best understood when introducing the apparent transverse velocity., 9 pages, 2 figures. Presented at "RREPS-19",Sept. 2019, Belgorod, Russia. This is the Accepted Manuscript version of an article accepted for publication in Journal of Instrumentation. Neither SISSA Medialab Srl nor IOP Publishing Ltd is responsible for any errors or omissions in this version of the manuscript or any version derived from it

Journal of high energy physics 2020(1), 72 (2020). doi:10.1007/JHEP01(2020)072, We introduce a — somewhat holographic — dictionary between gravitational observables for scattering processes (measured at the boundary) and adiabatic invariants for bound orbits (in the bulk), to all orders in the Post-Minkowskian (PM) expansion. Our map relies on remarkable connections between the relative momentum of the two­body problem, the classical limit of the scattering amplitude and the deflection angle in hyperbolic motion. These relationships allow us to compute observables for generic orbits (such as the periastron advance ∆Φ) through analytic continuation, via a radial action depending only on boundary data. A simplified (more geometrical) map can be obtained for circular orbits, enabling us to extract the orbital frequency as a function of the (conserved) binding energy, Ω(E), directly from scattering information. As an example, using the results in Bernet al. [36, 37], we readily derive Ω(E) and ∆Φ(J, E) to two-loop orders. We also provide closed-form expressions for the orbital frequency and periastron advance at tree-level and one-loop order, respectively, which capture a series of exact terms in the Post-Newtonian expansion. We then perform a partial PM resummation, using a no-recoil approximation for the amplitude. This limit is behind the map between the scattering angle for a test-particle and the two-body dynamics to 2PM. We show that it also captures a subset of higher order terms beyond the test-particle limit. While a (rather lengthy) Hamiltonian may be derived as an intermediate step, our map applies directly between gauge invariant quantities. Our findings provide a starting point for an alternative approach to the binary problem. We conclude with future directions and some speculations on the classical double copy., Published by SISSA, [Trieste]

We develop an Effective Field Theory (EFT) formalism to solve for the conservative dynamics of binary systems in gravity via Post-Minkowskian (PM) scattering data. Our framework combines a systematic EFT approach to compute the deflection angle in the PM expansion, together with the 'Boundary-to-Bound' (B2B) dictionary introduced in [1910.03008, 1911.09130]. Due to the nature of scattering processes, a remarkable reduction of complexity occurs both in the number of Feynman diagrams and type of integrals, compared to a direct EFT computation of the potential in a PM scheme. We provide two illustrative examples. Firstly, we compute all the conservative gravitational observables for bound orbits to 2PM, which follow from only one topology beyond leading order. The results agree with those in [1910.03008, 1911.09130], obtained through the 'impetus formula' applied to the classical limit of the one loop amplitude in Cheung et al. [1808.02489]. For the sake of comparison we reconstruct the conservative Hamiltonian to 2PM order, which is equivalent to the one derived in [1808.02489] from a matching calculation. Secondly, we compute the scattering angle due to tidal effects from the electric- and magnetic-type Love numbers at leading PM order. Using the B2B dictionary we then obtain the tidal contribution to the periastron advance. We also construct a Hamiltonian including tidal effects at leading PM order. Although relying on (relativistic) Feynman diagrams, the EFT formalism developed here does not involve taking the classical limit of a quantum amplitude, neither integrals with internal massive fields, nor additional matching calculations, nor spurious ('super-classical') infrared singularities. By construction, the EFT approach can be automatized to all PM orders.

Using the Effective Field Theory approach together with the Boundary-to-Bound map, we compute the next-to-leading order (NLO) Post-Minkowskian (PM) tidal effects in the conservative dynamics of compact binary systems. We derive the mass and current quadrupole and, for the first time, octupole corrections to the binding energy for circular orbits at ${\cal O}(G^3)$. Our results are consistent with the test-body limit as well as the existent Post-Newtonian literature. We also reconstruct a Hamiltonian incorporating tidal effects to NLO in the PM expansion and find complete agreement with the recent derivation of its quadrupolar part using the classical limit of scattering amplitudes.

51 pp. (2019)., We introduce a -- somewhat holographic -- dictionary between gravitational observables for scattering processes (measured at 'the boundary') and adiabatic invariants for bound orbits (in 'the bulk'), to all orders in the Post-Minkowskian (PM) expansion. Our map relies on remarkable connections between the relative momentum of the two-body problem, the classical limit of the scattering amplitude and the deflection angle in hyperbolic motion. These relationships allow us to compute observables for generic closed orbits, such as the periastron advance $\Delta\Phi$, from the unbound case through analytic continuation. A simplified (more geometrical) map can be obtained for circular orbits, enabling us to extract the orbital frequency as a function of the (conserved) binding energy, $\Omega(E)$, from scattering data. As an example, using the results in Bern et al. [1901.04424, 1908.01493], we readily derive $\Omega(E)$ and $\Delta\Phi(J,E)$ to two-loop orders. We also provide a closed-form expression for the orbital frequency and periastron advance at tree-level and one-loop order, respectively, which capture a series of exact terms in the Post-Newtonian expansion. We then perform a partial PM resummation, using a 'no-recoil' approximation for the amplitude. This limit is behind the map between the scattering angle for a test-particle and the two-body dynamics to 2PM. We show that it also captures a subset of higher order terms beyond the test-particle limit. While a (rather lengthy) Hamiltonian may be derived as an intermediate step, our map applies directly between gauge invariant quantities. Our findings provide a starting point for an alternative approach to the binary problem. We conclude with future directions and some speculations on the classical double copy.

The purely relaxational non-equilibrium dynamics of the quantum spherical model as described through a Lindblad equation is analysed. It is shown that the phenomenological requirements of reproducing the exact quantum equilibrium state as stationary solution and the associated classical Langevin equation in the classical limit $g\to 0$ fix the form of the Lindblad dissipators, up to an overall time-scale. In the semi-classical limit, the models' behaviour become effectively the one of the classical analogue, with a dynamical exponent $z=2$, and an effective temperature $T_{\rm eff}$, renormalised by the quantum coupling $g$. A distinctive behaviour is found for a quantum quench, at zero temperature, deep into the ordered phase $g\ll g_c(d)$, for $d>1$ dimensions. Only for $d=2$ dimensions, a simple scaling behaviour holds true, with a dynamical exponent $z=1$, while for dimensions $d\ne 2$, logarithmic corrections to scaling arise. The spin-spin correlator, the growing length scale and the time-dependent susceptibility show the existence of several logarithmically different length scales., 61 pages, 14 figures

We calculate the full probability density function (PDF) of inflationary curvature perturbations, even in the presence of large quantum backreaction. Making use of the stochastic-$\delta N$ formalism, two complementary methods are developed, one based on solving an ordinary differential equation for the characteristic function of the PDF, and the other based on solving a heat equation for the PDF directly. In the classical limit where quantum diffusion is small, we develop an expansion scheme that not only recovers the standard Gaussian PDF at leading order, but also allows us to calculate the first non-Gaussian corrections to the usual result. In the opposite limit where quantum diffusion is large, we find that the PDF is given by an elliptic theta function, which is fully characterised by the ratio between the squared width and height (in Planck mass units) of the region where stochastic effects dominate. We then apply these results to the calculation of the mass fraction of primordial black holes from inflation, and show that no more than $\sim 1$ $e$-fold can be spent in regions of the potential dominated by quantum diffusion. We explain how this requirement constrains inflationary potentials with two examples., Comment: 30 pages without appendices (total 42 pages), 9 figures, matches published version in JCAP where one typo in the equation given in the last line of page 23 has also been corrected

Letters in mathematical physics 104(5), 527 - 551 (2014). doi:10.1007/s11005-014-0684-3, We revisit the definition of the 6j-symbols from the modular double of U_q(sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories., Published by Springer Science + Business Media B.V, Dordrecht [u.a.]

Physical review / D 72(4), 043504 (2005). doi:10.1103/PhysRevD.72.043504, We investigate the cosmology of a recently proposed deformation of Einstein gravity, emerging from quantum gravity heuristics. The theory is constructed to have de Sitter space as a vacuum solution, and thus to be relevant to the accelerating universe. However, this solution turns out to be unstable, and the true phase space of cosmological solutions is significantly more complex, displaying two late-time power-law attractors -- one accelerating and the other dramatically decelerating. It is also shown that non-accelerating cosmologies sit on a separatrix between the two basins of attraction of these attractors. Hence it is impossible to pass from a decelerating cosmology to an accelerating one, as required in standard cosmology for consistency with nucleosynthesis and structure formation and compatibility with the data inferred from supernovae Ia. We point out that alternative models of the early universe, such as the one investigated here might provide possible ways to circumvent these requirements., Published by Inst., Woodbury, NY

Journal of high energy physics 11(11), 106 (2020). doi:10.1007/JHEP11(2020)106, We develop an Effective Field Theory (EFT) formalism to solve for the conservative dynamics of binary systems in gravity via Post-Minkowskian (PM) scattering data. Our framework combines a systematic EFT approach to compute the deflection angle in the PM expansion, together with the ‘Boundary-to-Bound’ (B2B) dictionary introduced in [1, 2]. Due to the nature of scattering processes, a remarkable reduction of complexity occurs both in the number of Feynman diagrams and type of integrals, compared to a direct EFT computation of the potential in a PM scheme. We provide two illustrative examples. Firstly, we compute all the conservative gravitational observables for bound orbits to 2PM, which follow from only one topology beyond leading order. The results agree with those in [1, 2], obtained through the ‘impetus formula’ applied to the classical limit of the one loop amplitude in Cheung et al. [3]. For the sake of comparison we reconstruct the conservative Hamiltonian to 2PM order, which is equivalent to the one derived in [3] from a matching calculation. Secondly, we compute the scattering angle due to tidal effects from the electric- and magnetic-type Love numbers at leading PM order. Using the B2B dictionary we then obtain the tidal contribution to the periastron advance. We also construct a Hamiltonian including tidal effects at leading PM order. Although relying on (relativistic) Feynman diagrams, the EFT formalism developed here does not involve taking the classical limit of a quantum amplitude, neither integrals with internal massive fields, nor additional matching calculations, nor spurious (‘super-classical’) infrared singularities. By construction, the EFT approach can be automatized to all PM orders., Published by SISSA, [Trieste]

We study causality in gravitational systems beyond the classical limit. Using on-shell methods, we consider the one-loop corrections from charged particles to the photon energy-momentum tensor - the self-stress - that controls the quantum interaction between two on-shell photons and one off-shell graviton. The self-stress determines in turn the phase shift and time delay in the scattering of photons against a spectator particle of any spin in the eikonal regime. We show that the sign of the $\beta$-function associated to the running gauge coupling is related to the sign of time delay at small impact parameter. Our results show that, at first post-Minkowskian order, asymptotic causality, where the time delay experienced by any particle must be positive, is respected quantum mechanically. Contrasted with asymptotic causality, we explore a local notion of causality, where the time delay is longer than the one of gravitons, which is seemingly violated by quantum effects., Comment: v3: added references, fixed numerics in Fig.5, found analytic asymptotic behaviors, matching journal version

Physical review / D 102(12), 124025 (2020). doi:10.1103/PhysRevD.102.124025, Using the Effective Field Theory approach together with the Boundary-to-Bound map, we compute the next-to-leading order (NLO) Post-Minkowskian (PM) tidal effects in the conservative dynamics of compact binary systems. We derive the mass and current quadrupole and, for the first time, octupole corrections to the binding energy for circular orbits at ${\cal O}(G^3)$. Our results are consistent with the test-body limit as well as the existent Post-Newtonian literature. We also reconstruct a Hamiltonian incorporating tidal effects to NLO in the PM expansion and find complete agreement with the recent derivation of its quadrupolar part using the classical limit of scattering amplitudes., Published by Inst.302363, Melville, NY

Multiparametric families of hypergeometric $\tau$-functions of KP or Toda type serve as generating functions for weighted Hurwitz numbers, providing weighted enumerations of branched covers of the Riemann sphere. A graphical interpretation of the weighting is given in terms of constellations mapped onto the covering surface. The theory is placed within the framework of topological recursion, with the Baker function at ${\bf t} ={\bf 0}$ shown to satisfy the quantum spectral curve equation, whose classical limit is rational. A basis for the space of formal power series in the spectral variable is generated that is adapted to the Grassmannian element associated to the $\tau$-function. Multicurrent correlators are defined in terms of the $\tau$-function and shown to provide an alternative generating function for weighted Hurwitz numbers. Fermionic VEV representations are provided for the adapted bases, pair correlators and multicurrent correlators. Choosing the weight generating function as a polynomial, and restricting the number of nonzero "second" KP flow parameters in the Toda $\tau$-function to be finite implies a finite rank covariant derivative equation with rational coefficients satisfied by a finite "window" of adapted basis elements. The pair correlator is shown to provide a Christoffel-Darboux type finite rank integrable kernel, and the WKB series coefficients of the associated adjoint system are computed recursively, leading to topological recursion relations for the generators of the weighted Hurwitz numbers., Comment: 30 pages, 2 figures. References updated. Weighting of constellations revised. Weighting of Hurwitz numbers corrected