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Rafael A. Porto

Publications and source records attributed to Rafael A. Porto.

At least 55 records · Page 3Linked to original sources
arXiv2015

B-modes and the Nature of Inflation

Observations of the cosmic microwave background do not yet determine whether inflation was driven by a slowly-rolling scalar field or involved another physical mechanism. In this paper we discuss the prospects of using the power spectra of scalar and tensor modes to probe the nature of inflation. We focus on the leading modification to the slow-roll dynamics, which entails a sound speed $c_s$ for the scalar fluctuations. We derive analytically a lower bound on $c_s$ in terms of a given tensor-to-scalar ratio $r$, taking into account the difference in the freeze-out times between the scalar and tensor modes. We find that any detection of primordial B-modes with $r > 0.01$ implies a lower bound on $c_s$ that is stronger than the bound derived from the absence of non-Gaussianity in the Planck data. For $r \gtrsim 0.1$, the bound would be tantalizingly close to a critical value for the sound speed, $(c_s)_\star = 0.47$ (corresponding to $(f_{\rm NL}^{\rm equil})_\star = -0.93$), which we show serves as a threshold for non-trivial dynamics beyond slow-roll. We also discuss how an order-one level of equilateral non-Gaussianity is a natural observational target for other extensions of the canonical paradigm.

hep-th↗
arXiv2015

Signs of Analyticity in Single-Field Inflation

The analyticity of response functions and scattering amplitudes implies powerful relations between low-energy observables and the underlying short-distance dynamics. These 'IR/UV' relations are rooted in basic physical principles, such as causality and unitarity. In this paper, we seek similar connections in inflation, relating cosmological observations to the physics responsible for the accelerated expansion. We assume that the inflationary theory is Lorentz invariant at short distances, but allow for non-relativistic interactions and a non-trivial speed of propagation at low energies. Focusing on forward scattering, we derive a 'sum rule' which equates a combination of low-energy parameters to an integral which is sensitive to the high-energy behavior of the theory. While for relativistic amplitudes unitarity is sufficient to prove positivity of the sum rule, this is not guaranteed in the non-relativistic case. We discuss the conditions under which positivity still applies, and show that they are satisfied by all known UV completions of single-field inflation. In that case, we obtain a consistency condition for primordial non-Gaussianity, which constrains the size and the sign of the equilateral four-point function in terms of the amplitude of the three-point function. The resulting bound rules out about half of the parameter space that is still allowed by current observations. Finding a violation of our consistency condition would point towards less conventional theories of inflation, or violations of basic physical principles.

hep-th↗
arXiv2015

On Soft Limits of Large-Scale Structure Correlation Functions

We study soft limits of correlation functions for the density and velocity fields in the theory of structure formation. First, we re-derive the (resummed) consistency conditions at unequal times using the eikonal approximation. These are solely based on symmetry arguments and are therefore universal. Then, we explore the existence of equal-time relations in the soft limit which, on the other hand, depend on the interplay between soft and hard modes. We scrutinize two approaches in the literature: The time-flow formalism, and a background method where the soft mode is absorbed into a locally curved cosmology. The latter has been recently used to set up (angular averaged) `equal-time consistency relations'. We explicitly demonstrate that the time-flow relations and `equal-time consistency conditions' are only fulfilled at the linear level, and fail at next-to-leading order for an Einstein de-Sitter universe. While applied to the velocities both proposals break down beyond leading order, we find that the `equal-time consistency conditions' quantitatively approximates the perturbative results for the density contrast. Thus, we generalize the background method to properly incorporate the effect of curvature in the density and velocity fluctuations on short scales, and discuss the reasons behind this discrepancy. We conclude with a few comments on practical implementations and future directions.

astro-ph.CO↗
arXiv2014

The Lagrangian-space Effective Field Theory of Large Scale Structures

We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of extended objects in Lagrangian space. In LEFT the resulting finite size effects are described using a multipole expansion parameterized by a set of time dependent coefficients and organized in powers of the ratio of the wavenumber of interest $k$ over the non-linear scale $k_{\rm NL}$. The multipoles encode the effects of the short distance modes on the long-wavelength universe and absorb UV divergences when present. There are no IR divergences in LEFT. Some of the parameters that control the perturbative approach are not assumed to be small and can be automatically resummed. We present an illustrative one-loop calculation for a power law universe. We describe the dynamics both at the level of the equations of motion and through an action formalism.

astro-ph.CO↗
arXiv2014

Analytic approximations, perturbation theory, effective field theory methods and their applications

We summarize the parallel session B4: 'Analytic approximations, perturbation theory effective field theory methods and their applications' and the joint session B2/B4: 'Approximate solutions to Einstein equations: Methods and Applications', of the GR20 & Amaldi10 conference in Warsaw, July 2013. The contributed talks reported significant advances on various areas of research in gravity.

gr-qc↗
arXiv2013

Gravitational self-force in the ultra-relativistic limit: The 'large-N' expansion

We study the gravitational self-force using the effective field theory formalism. We show that in the ultra-relativistic limit γ\to \infty, with γthe boost factor, many simplifications arise. Drawing parallels with the large N limit in quantum field theory, we introduce the parameter 1/N = 1/γ^2 and show that the effective action admits a well defined expansion in powers of λ= Nε, at each order in 1/N, where ε= E_m/M and E_m=γm is the (kinetic) energy of the small mass. Moreover, we show that diagrams with nonlinear bulk interactions first enter at O(λ^2/N^2) and only diagrams with nonlinearities in the worldline couplings, which are significantly easier to compute, survive in the large N/ultra-relativistic limit. Finally, we derive the self-force to O(λ^4/N) and provide expressions for some conservative quantities for circular orbits.

gr-qc↗
arXiv2013

On Squeezed Limits in Single-Field Inflation - Part I

The n-point correlation functions in single-field inflation obey a set of consistency conditions in the exact squeezed limit which are not present in multi-field models, and thus are powerful tools to distinguish between the two. However, these consistency conditions may be violated for a finite range of scales in single-field models, for example by departures from the Bunch-Davies state. These it excited states may be the consequence of interactions during inflation, or may be a remnant of the era that preceded inflation. In this paper we analyze the bispectrum, and show that in the regime of theoretical control the resulting signal in the squeezed limit remains undetectably small in all known models which continuously excite the state. We also show that the signal remains undetectably small if the initial state is related to the Bunch-Davies state by a Bogoliubov transformation and the energy density in the state is small enough so that the usual slow-roll conditions are obeyed. Bogoliubov states that lead to violations of the slow-roll conditions, as well as more general excited states, require more careful treatment and will be discussed in a separate publication.

hep-th↗
arXiv2012

Dissipation in the effective field theory for hydrodynamics: First order effects

We introduce dissipative effects in the effective field theory of hydrodynamics. We do this in a model-independent fashion by coupling the long-distance degrees of freedom explicitly kept in the effective field theory to a generic sector that "lives in the fluid", which corresponds physically to the microscopic constituents of the fluid. At linear order in perturbations, the symmetries, the derivative expansion, and the assumption that this microscopic sector is thermalized, allow us to characterize the leading dissipative effects at low frequencies via three parameters only, which correspond to bulk viscosity, shear viscosity, and--in the presence of a conserved charge--heat conduction. Using our methods we re-derive the Kubo relations for these transport coefficients.

hep-th↗
arXiv2012

Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order

Using the NRGR effective field theory formalism we calculate the remaining source multipole moments necessary to obtain the spin contributions to the gravitational wave amplitude to 2.5 Post-Newtonian (PN) order. We also reproduce the tail contribution to the waveform linear in spin at 2.5PN arising from the nonlinear interaction between the current quadrupole and the mass monopole.

gr-qc↗
arXiv2012

The consistency condition for the three-point function in dissipative single-clock inflation

We generalize the consistency condition for the three-point function in single field inflation to the case of dissipative, multi-field, single-clock models. We use the recently introduced extension of the effective field theory of inflation that accounts for dissipative effects, to provide an explicit proof to leading (non-trivial) order in the generalized slow roll parameters and mixing with gravity scales. Our results illustrate the conditions necessary for the validity of the consistency relation in situations with many degrees of freedom relevant during inflation, namely that there is a preferred clock. Departures from this condition in forthcoming experiments would rule out not only single field but also a large class of multi-field models.

hep-th↗
arXiv2012

Dissipative effects in the Effective Field Theory of Inflation

We generalize the effective field theory of single clock inflation to include dissipative effects. Working in unitary gauge we couple a set of composite operators in the effective action which is constrained solely by invariance under time-dependent spatial diffeomorphisms. We restrict ourselves to situations where the degrees of freedom responsible for dissipation do no contribute to the density perturbations at late time. The dynamics of the perturbations is then modified by the appearance of `friction' and noise terms, and assuming certain locality properties for the Green's functions of these composite operators, we show that there is a regime characterized by a large friction term γ>> H in which the ζ-correlators are dominated by the noise and the power spectrum can be significantly enhanced. We also compute the three point function <ζζζ> for a wide class of models and discuss under which circumstances large friction leads to an increased level of non-Gaussianities. In particular, under our assumptions, we show that strong dissipation together with the required non-linear realization of the symmetries implies |f_NL| ~ γ/(c_s^2H) >> 1. As a paradigmatic example we work out a variation of the `trapped inflation' scenario with local response functions and perform the matching with our effective theory. A detection of the generic type of signatures that result from incorporating dissipative effects during inflation, as we describe here, would teach us about the dynamics of the early universe and also extend the parameter space of inflationary models.

hep-th↗
arXiv2012

Absorption Effects due to Spin in the Worldline Approach to Black Hole Dynamics

We generalize the effective point particle approach to black hole dynamics to include spin. In this approach dissipative effects are captured by degrees of freedom localized on the wordline. The absorptive properties of the black hole are determined by correlation functions which can be matched with the graviton absorption cross section in the long wavelength approximation. For rotating black holes, superradiance is responsible for the leading contribution. The effective theory is then used to predict the power loss due to spin in the dynamics of non-relativistic binary systems. An enhancement of three powers of the relative velocity is found with respect to the non-rotating case. Then we generalize the results to other type of constituents in the binary system, such as rotating neutron stars. Finally we compute the power loss absorbed by a test spinning black hole in a given spacetime background.

hep-th↗
arXiv2011

Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order

Using effective field theory techniques we calculate the source multipole moments needed to obtain the spin contributions to the power radiated in gravitational waves from inspiralling compact binaries to third Post-Newtonian order (3PN). The multipoles depend linearly and quadratically on the spins and include both spin(1)spin(2) and spin(1)spin(1) components. The results in this paper provide the last missing ingredient required to determine the phase evolution to 3PN including all spin effects which we will report in a separate paper.

gr-qc↗
arXiv2010

Next to leading order spin-orbit effects in the motion of inspiralling compact binaries

Using effective field theory (EFT) techniques we calculate the next-to-leading order (NLO) spin-orbit contributions to the gravitational potential of inspiralling compact binaries. We use the covariant spin supplementarity condition (SSC), and explicitly prove the equivalence with previous results by Faye et al. in arXiv:gr-qc/0605139. We also show that the direct application of the Newton-Wigner SSC at the level of the action leads to the correct dynamics using a canonical (Dirac) algebra. This paper then completes the calculation of the necessary spin dynamics within the EFT formalism that will be used in a separate paper to compute the spin contributions to the energy flux and phase evolution to NLO.

gr-qc↗
arXiv2009

Next to Leading Order Spin(1)Spin(1) Effects in the Motion of Inspiralling Compact Binaries

Using effective field theory techniques we compute the next to leading order Spin(1)Spin(1) terms in the potential of spinning compact objects at third Post-Newtonian order, including sub-leading self-induced finite size effects. This result represents the last ingredient to complete the relevant spin potentials to 3PN order from which the equations of motion follow via a canonical formalism. As an example we include the precession equation.

gr-qc↗
arXiv2009

Relaxing the cosmological constant in the extreme ultra-infrared

We speculate on the dynamical critical behavior of gravity in the extreme ultra-infrared (EuIR) sector and a mechanism to relax the cosmological constant. We show that in the EuIR the cosmological constant term could be made irrelevant for values of the dynamical critical exponent z_EuIR greater than one. We discuss a possible realization of this idea that connects the relaxation of the cosmological constant to the ratio between the EuIR and IR scales, where the latter serves as the 'UV' cutoff of our (ultra long distance) effective theory, with z_IR ~ 1. For distances smaller than the IR regime Lorentz invariance emerges. We entertain the possibility that the effective description of the universe may not be Lorentz invariant at much larger scales. We discuss why local physics cannot detect the 'natural' value for the density of dark energy below the IR scale, and briefly comment on possible connections with holography.

hep-th↗
arXiv2009

The gravitational S-matrix

We investigate the hypothesized existence of an S-matrix for gravity, and some of its expected general properties. We first discuss basic questions regarding existence of such a matrix, including those of infrared divergences and description of asymptotic states. Distinct scattering behavior occurs in the Born, eikonal, and strong gravity regimes, and we describe aspects of both the partial wave and momentum space amplitudes, and their analytic properties, from these regimes. Classically the strong gravity region would be dominated by formation of black holes, and we assume its unitary quantum dynamics is described by corresponding resonances. Masslessness limits some powerful methods and results that apply to massive theories, though a continuation path implying crossing symmetry plausibly still exists. Physical properties of gravity suggest nonpolynomial amplitudes, although crossing and causality constrain (with modest assumptions) this nonpolynomial behavior, particularly requiring a polynomial bound in complex s at fixed physical momentum transfer. We explore the hypothesis that such behavior corresponds to a nonlocality intrinsic to gravity, but consistent with unitarity, analyticity, crossing, and causality.

hep-th↗