arXiv subjects

Rafael A. Porto

Publications and source records attributed to Rafael A. Porto.

At least 37 records · Page 2Linked to original sources

arXiv2020

Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order

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.

hep-th↗

arXiv2020

From Boundary Data to Bound States

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 orbits (such as the periastron advance $ΔΦ$) 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 Bern et al. [1901.04424, 1908.01493], we readily derive $Ω(E)$ and $ΔΦ(J,E)$ 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.

hep-th↗

arXiv2020

From Boundary Data to Bound States II: Scattering Angle to Dynamical Invariants (with Twist)

We recently introduced in [1910.03008] a "boundary-to-bound" dictionary between gravitational scattering data and observables for bound states of non-spinning bodies. In this paper, we elaborate further on this (holographic) map. We start by deriving the following -- remarkably simple -- formula relating the periastron advance to the scattering angle: $ΔΦ(J,{\cal E}) =χ(J,{\cal E}) + χ(-J,{\cal E})$, via analytic continuation in angular momentum and binding energy. Using explicit expressions from [1910.03008], we confirm its validity to all orders in the Post-Minkowskian (PM) expansion. Furthermore, we reconstruct the radial action for the bound state directly from the knowledge of the scattering angle. The radial action enables us to write compact expressions for dynamical invariants in terms of the deflection angle to all PM orders, which can also be written as a function of the PM-expanded amplitude. As an example, we reproduce our result in [1910.03008] for the periastron advance, and compute the radial and azimuthal frequencies and redshift variable to two-loops. Agreement is found in the overlap between PM and Post-Newtonian (PN) schemes. Last but not least, we initiate the study of our dictionary including spin. We demonstrate that the same relation between deflection angle and periastron advance applies for aligned-spin contributions, with $J$ the (canonical) total angular momentum. Explicit checks are performed to display perfect agreement using state-of-the-art PN results in the literature. Using the map between test- and two-body dynamics, we also compute the periastron advance up to quadratic order in the spin, to one-loop and to all orders in velocity. We conclude with a discussion on the generalized "impetus formula" for spinning bodies and black holes as "elementary particles".

hep-th↗

arXiv2020

Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics

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.

hep-th↗

arXiv2020

The Effective Field Theory of Large Scale Structure at Three Loops

We study the power spectrum of dark matter density fluctuations in the framework of the Effective Field Theory of Large Scale Structures (EFTofLSS) up to three loop orders. In principle, several counter-terms may be needed to handle the short-distance sensitivity in perturbation theory. However, we show that a small number of extra coefficients are sufficient to match numerical simulations with percent accuracy when a generic renormalization prescription is implemented (allowing for running of the individual counter-terms). We show that the level of accuracy increases with respect to the two loop results, up to $k \simeq 0.4\, h$Mpc$^{-1}$ at redshift $z=0$, although the overall improvement is somewhat marginal. At the same time, we argue there is evidence that the behavior of the loop expansion in the EFTofLSS is typical of an asymptotic series, already on the brink of its maximum predictive power (at $z=0$). Hence, the inclusion of higher orders will likely deteriorate the matching to data, even at moderate values of $k$. Part of the reason for this behavior is due to large contributions to the (renormalized) power spectrum at three loop order from mildly non-linear scales, even after the UV counter-terms are included. In conclusion, the EFTofLSS to three loop orders provides the best approximation to the (deterministic part of the) power spectrum in the weakly non-linear regime at $z=0$, and higher loops are not expected to improve our level of accuracy.

astro-ph.CO↗

arXiv2020

Signals of a Quantum Universe

Structure in the Universe is widely believed to have originated from quantum fluctuations during an early epoch of accelerated expansion. Yet, the patterns we observe today do not distinguish between quantum or classical primordial fluctuations; current cosmological data is consistent with either possibility. We argue here that a detection of primordial non-Gaussianity can resolve the present situation, and provide a litmus-test for the quantum origin of cosmic structure. Unlike in quantum mechanics, vacuum fluctuations cannot arise in classical theories and therefore long-range classical correlations must result from (real) particles in the initial state. Similarly to flat-space scattering processes, we show how basic principles require these particles to manifest themselves as poles in the $n$-point functions, in the so-called folded configurations. Following this observation, and assuming fluctuations are (i) correlated over large scales, and (ii) generated by local evolution during an inflationary phase, we demonstrate that: the absence of a pole in the folded limit of non-Gaussian correlators uniquely identifies the quantum vacuum as the initial state. In the same spirit as Bell's inequalities, we discuss how this can be circumvented if locality is abandoned. We also briefly discuss the implications for simulations of a non-Gaussian universe.

hep-th↗

arXiv2019

Gravitational Collider Physics

We study the imprints of new ultralight particles on the gravitational-wave signals emitted by binary black holes. Superradiant instabilities may create large clouds of scalar or vector fields around rotating black holes. The presence of a binary companion then induces transitions between different states of the cloud, which become resonantly enhanced when the orbital frequency matches the energy gap between the states. We find that the time dependence of the orbit significantly impacts the cloud's dynamics during a transition. Following an analogy with particle colliders, we introduce an S-matrix formalism to describe the evolution through multiple resonances. We show that the state of the cloud, as it approaches the merger, carries vital information about its spectrum via time-dependent finite-size effects. Moreover, due to the transfer of energy and angular momentum between the cloud and the orbit, a dephasing of the gravitational-wave signal can occur which is correlated with the positions of the resonances. Notably, for intermediate and extreme mass ratio inspirals, long-lived floating orbits are possible, as well as kicks that yield large eccentricities. Observing these effects, through the precise reconstruction of waveforms, has the potential to unravel the internal structure of the boson clouds, ultimately probing the masses and spins of new particles.

gr-qc↗

arXiv2019

Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian

We complete the derivation of the conservative dynamics of binary systems to fourth Post-Newtonian (4PN) order in the effective field theory (EFT) approach. We present a self-contained (ambiguity-free) computation of the renormalized Lagrangian, entirely within the confines of the PN expansion. While we confirm the final results reported in the literature, we clarify several issues regarding intermediate infrared (IR) and ultraviolet (UV) divergences, as well as the renormalization procedure. First, we properly identify the IR and UV singularities using (only) dimensional regularization and the method of regions, which are the pillars of the EFT formalism. This requires a careful study of scaleless integrals in the potential region, as well as conservative contributions from radiation modes due to tail effects. As expected by consistency, the UV divergences in the near region (due to the point-particle limit) can be absorbed into two counter-terms in the worldline effective theory. The counter-terms can then be removed by field redefinitions, such that the renormalization scheme-dependence has no physical effect to 4PN order. The remaining IR poles, which are spurious in nature, are unambiguously removed by implementing the zero-bin subtraction in the EFT approach. The procedure transforms the IR singularities into UV counter-parts. As anticipated, the left-over UV poles explicitly cancel out against UV divergences in conservative terms from radiation-reaction, uniquely determining the gravitational potential. Similar artificial IR/UV poles, which are intimately linked to the split into regions, are manifest at lower orders. Starting at 4PN, both local- and nonlocal-in-time contributions from the radiation region enter in the conservative dynamics. Neither additional regulators nor ambiguity-parameters are introduced at any stage of the computations.

gr-qc↗

arXiv2018

Probing Ultralight Bosons with Binary Black Holes

We study the gravitational-wave (GW) signatures of clouds of ultralight bosons around black holes (BHs) in binary inspirals. These clouds, which are formed via superradiance instabilities for rapidly rotating BHs, produce distinct effects in the population of BH masses and spins, and a continuous monochromatic GW signal. We show that the presence of a binary companion greatly enriches the dynamical evolution of the system, most remarkably through the existence of resonant transitions between the growing and decaying modes of the cloud (analogous to Rabi oscillations in atomic physics). These resonances have rich phenomenological implications for current and future GW detectors. Notably, the amplitude of the GW signal from the clouds may be reduced, and in many cases terminated, much before the binary merger. The presence of a boson cloud can also be revealed in the GW signal from the binary through the imprint of finite-size effects, such as spin-induced multipole moments and tidal Love numbers. The time dependence of the cloud's energy density during the resonance leads to a sharp feature, or at least attenuation, in the contribution from the finite-size terms to the waveforms. The observation of these effects would constrain the properties of putative ultralight bosons through precision GW data, offering new probes of physics beyond the Standard Model.

gr-qc↗

arXiv2017

Radiation reaction for spinning bodies in effective field theory I: Spin-orbit effects

We compute the leading Post-Newtonian (PN) contributions at linear order in the spin to the radiation-reaction acceleration and spin evolution for binary systems, which enter at fourth PN order. The calculation is carried out, from first principles, using the effective field theory framework for spinning compact objects, in both the Newton-Wigner and covariant spin supplementary conditions. A non-trivial consistency check is performed on our results by showing that the energy loss induced by the resulting radiation-reaction force is equivalent to the total emitted power in the far zone, up to so-called "Schott terms." We also find that, at this order, the radiation reaction has no net effect on the evolution of the spins. The spin-spin contributions to radiation reaction are reported in a companion paper.

gr-qc↗

arXiv2017

Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects

We compute the leading Post-Newtonian (PN) contributions at quadratic order in the spins to the radiation-reaction acceleration and spin evolution for binary systems, entering at four-and-a-half PN order. Our calculation includes the back-reaction from finite-size spin effects, which is presented for the first time. The computation is carried out, from first principles, using the effective field theory framework for spinning extended objects. At this order, nonconservative effects in the spin-spin sector are independent of the spin supplementary conditions. A non-trivial consistency check is performed by showing that the energy loss induced by the resulting radiation-reaction force is equivalent to the total emitted power in the far zone. We find that, in contrast to the spin-orbit contributions (reported in a companion paper), the radiation reaction affects the evolution of the spin vectors once spin-spin effects are incorporated.

gr-qc↗

arXiv2017

On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems

We discuss the source of the apparent ambiguities arising in the calculation of the dynamics of binary black holes within the Post-Newtonian framework. Divergences appear in both the near and far zone calculations, and may be of either ultraviolet (UV) or infrared (IR) nature. The effective field theory (EFT) formalism elucidates the origin of the singularities which may introduce apparent ambiguities. In particular, the only (physical) 'ambiguity parameters' that necessitate a matching calculation correspond to unknown finite size effects, which first appear at fifth Post-Newtonian (5PN) order for non-spinning bodies. We demonstrate that the ambiguities linked to IR divergences in the near zone, that plague the recent derivations of the binding energy at 4PN order, both in the ADM and 'Fokker-action' approach, can be resolved by implementing the so-called 'zero-bin' subtraction in the EFT framework. The procedure yields ambiguity-free results without the need of additional information beyond the PN expansion.

gr-qc↗

arXiv2017

The Lamb shift and the gravitational binding energy for binary black holes

We show that the correction to the gravitational binding energy for binary black holes due to the tail effect resembles the Lamb shift in the Hydrogen atom. In both cases a 'conservative' effect arises from interactions with 'radiation' modes, and moreover an explicit cancelation between near and far zone divergences is at work. In addition, regularization scheme-dependence may introduce ambiguity parameters. This is remediated, within an effective field theory approach, by the implementation of the zero-bin subtraction. We illustrate the procedure explicitly for the Lamb shift, by performing an ambiguity-free derivation within the framework of non-relativistic electrodynamics. We also derive the renormalization group equations from which we reproduce Bethe logarithm (at order $α_e^5 \log α_e$), and likewise the contribution to the gravitational potential from the tail effect (proportional to $v^8 \log v$).

gr-qc↗

arXiv2017

The Music of the Spheres: The Dawn of Gravitational Wave Science

The LIGO results are among the greatest experimental achievements of all times. Time and again scientists have compared this feat to Galileo pointing his telescope to the sky, offering instead an 'ear' to the cosmos. After the remarkable landmark of detection, the physics community will soon turn into the study of the properties of the sources, addressing fundamental questions in astrophysics and cosmology. A combined numerical and analytic effort to tackle the binary problem is of paramount importance in light of the nascent program of multi-messenger astronomy. The century of gravitational wave science is in the making, and many discoveries are yet to come in the advent of a new era of 'precision gravity'.

physics.pop-ph↗

arXiv2016

The Tune of Love and the Nature(ness) of Spacetime

The black hole information paradox is among the most outstanding puzzles in physics. I argue here there is yet another black hole quandary which, in light of the recent direct detection of gravitational waves by Advanced LIGO, reveals a new window to probe the nature of spacetime in the forthcoming era of 'precision gravity.'

gr-qc↗

arXiv2016

The Effective Field Theorist's Approach to Gravitational Dynamics

We review the effective field theory (EFT) approach to gravitational dynamics. We focus on extended objects in long-wavelength backgrounds and gravitational wave emission from spinning binary systems. We conclude with an introduction to EFT methods for the study of cosmological large scale structures.

hep-th↗

arXiv2016

The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution

We use the effective field theory (EFT) framework to calculate the tail effect in gravitational radiation reaction, which enters at 4PN order in the dynamics of a binary system. The computation entails a subtle interplay between the near (or potential) and far (or radiation) zones. In particular, we find that the tail contribution to the effective action is non-local in time, and features both a dissipative and a `conservative' term. The latter includes a logarithmic ultraviolet (UV) divergence, which we show cancels against an infrared (IR) singularity found in the (conservative) near zone. The origin of this behavior in the long-distance EFT is due to the point-particle limit -shrinking the binary to a point- which transforms a would-be infrared singularity into an ultraviolet divergence. This is a common occurrence in an EFT approach, which furthermore allows us to use renormalization group (RG) techniques to resum the resulting logarithmic contributions. We then derive the RG evolution for the binding potential and total mass/energy, and find agreement with the results obtained imposing the conservation of the (pseudo) stress-energy tensor in the radiation theory. While the calculation of the leading tail contribution to the effective action involves only one diagram, five are needed for the one-point function. This suggests logarithmic corrections may be easier to incorporate in this fashion. We conclude with a few remarks on the nature of these IR/UV singularities, the (lack of) ambiguities recently discussed in the literature, and the completeness of the analytic Post-Newtonian framework.

gr-qc↗

arXiv2016

On the Soft Limit of the Large Scale Structure Power Spectrum: UV Dependence

We derive a non-perturbative equation for the large scale structure power spectrum of long-wavelength modes. Thereby, we use an operator product expansion together with relations between the three-point function and power spectrum in the soft limit. The resulting equation encodes the coupling to ultraviolet (UV) modes in two time-dependent coefficients, which may be obtained from response functions to (anisotropic) parameters, such as spatial curvature, in a modified cosmology. We argue that both depend weakly on fluctuations deep in the UV. As a byproduct, this implies that the renormalized leading order coefficient(s) in the effective field theory (EFT) of large scale structures receive most of their contribution from modes close to the non-linear scale. Consequently, the UV dependence found in explicit computations within standard perturbation theory stems mostly from counter-term(s). We confront a simplified version of our non-perturbative equation against existent numerical simulations, and find good agreement within the expected uncertainties. Our approach can in principle be used to precisely infer the relevance of the leading order EFT coefficient(s) using small volume simulations in an `anisotropic separate universe' framework. Our results suggest that the importance of these coefficient(s) is a $\sim 10 \%$ effect, and plausibly smaller.

astro-ph.CO↗