arXiv subjects

Maurício O. Calvão

Publications and source records attributed to Maurício O. Calvão.

13 recordsLinked to original sources

arXiv2024

A unified approach to coupled homogeneous linear wave propagation in generic gravity

Wave propagation is a common occurrence in all of physics. A linear approximation provides a simpler way to describe various fields related to observable phenomena in laboratory physics as well as astronomy and cosmology, allowing us to probe gravitation through its effect on the trajectories of particles associated with those fields. This paper proposes a unified framework to describe the wave propagation of a set of interacting tensor fields that obey coupled homogeneous linear second-order partial differential equations for arbitrary curved spacetimes, both Lorentzian and metric-affine. We use JWKB Ansätze for all fields, written in terms of a perturbation parameter proportional to a representative wavelength among them, deriving a set of hierarchical algebraic and differential equations that link the fields' phases and different order amplitudes. This allows us to reobtain the well-known laws of geometrical optics and beyond geometrical optics in a generalized form, showing that these laws are independent of the rank of the fields involved. This is true as long as what we refer to as the kinetic tensor of a given field satisfies a set of diagonality conditions, which further imply a handful of simplifications on the transport equations obtained in the subleading orders of the JWKB Ansätze. We explore these results in several notable examples in Lorentzian and metric-affine spacetimes, illustrating the reach of our derivations in general relativity, reduced Horndeski theories, spacetimes with completely antisymmetric torsion and Weyl spacetimes. The formalism presented herein lays the groundwork for the study of rays associated with different types of waves in curved spacetimes and provides the tools to compute modifications to their brightness evolution laws, consequential distance duality relations, and beyond geometrical optics phenomena.

gr-qc↗

arXiv2024

Gravitational wave energy momentum-tensor in reduced Horndeski theories

We generalize, imposing the field equations only at dominant order, the Isaacson formula for the gravitational wave (GW) energy-momentum tensor (EMT) to the class of Horndeski theories in which the tensor modes travel at the speed of light (reduced Horndeski theories) and scalar waves are present. We discuss important particular cases such as: theories where scalar waves are also luminal and theories in which the transverse-traceless gauge can be achieved in an arbitrary open set. The vanishing of the trace of the gravitational wave energy-momentum tensor is obtained for theories in which all wave perturbations propagate at the speed of light. The trace is shown not to vanish trivially in other cases. We obtain, as a particular case of our general result, the GW EMTs, in a Brans-Dicke theory, both in the Einstein frame, recovering previous results in the literature, and in the Jordan frame, thereby showing the GW EMT is not conformally invariant. We further prove that there exists a subclass of reduced Horndeski theories where, in contrast to general relativity, the divergence of the GW EMT does not vanish even after the imposition of the full equations of motion, assuming an eikonal solution.

gr-qc↗

arXiv2023

Testing gravity with gravitational wave friction and gravitational slip

Gravitational waves (GWs) emitted by binary sources are interesting signals for testing gravity on cosmological scales since they allow measurements of the luminosity distance. When followed by electromagnetic counterparts, in particular, they enable a reconstruction of the GW-distance-redshift relation. In the context of several modified gravity (MG) theories, even when requiring that the speed of propagation is equal to that of light, this GW distance differs from the standard electromagnetic luminosity distance due to the presence of a modified friction in the GW propagation. The very same source of this friction, which is the running of an effective Planck mass, also affects the scalar sector generating gravitational slip, i.e. a difference between the scalar potentials, an observable that can be inferred from large-scale structure (LSS) probes. In this work, we use a model within effective field theories for dark energy to exemplify precisely the fact that, at the linear perturbation level, parametrizing a single function is already enough to generate simultaneous deviations in the GW distance and the slip. By simulating multi-messenger GW events that might be detected by the Einstein Telescope in the future, we compare the constraining power of the two observables on this single degree of freedom. We then combine forecasts of a Euclid-like survey with GW simulations, coming to the conclusion that, when using Planck data to better constrain the cosmological parameters, those future data on the scalar and tensor sectors are competitive to probe such deviations from General Relativity, with LSS giving stronger (but more model-dependent) results than GWs.

astro-ph.CO↗

arXiv2022

Gravitational wave stochastic background in reduced Horndeski theories

We generalize to reduced Horndeski theories of gravity, where gravitational waves (GWs) travel at the speed of light, the expression of a statistically homogeneous and unpolarized stochastic gravitational wave background (SGWB) signal measured as the correlation between the individual signals detected by two interferometers in arbitrary configurations. We also discuss some results found in the literature regarding cosmological distances in modified theories, namely, the simultaneous validity of a duality distance relation for GW signals and of the coincidence between the gravitational wave luminosity distance, based on the energy flux, and the distance inferred from the wave amplitude. This discussion allows us to conclude that the spectral energy density per unit solid angle of an astrophysical SGWB signal has the same functional dependency with the luminosity of each emitting source as in General Relativity (GR). Using the generalized expression of the GW energy-momentum tensor and the modified propagation law for the tensor modes, we conclude that the energy density of a SGWB maintains the same functional relation with the scale factor as in GR, provided that the modified theory coincides with GR in a given hypersurface of constant time. However, the relation between the detected signal and the spectral energy density is changed by the global factor $G_4(φ(t_0))$, thus potentially serving as a probe for modified gravity theories.

gr-qc↗

arXiv2021

New dynamical system approach to Palatini $f(R)$ theories and its application to exponential gravity

The approach of dynamical systems is a useful tool to investigate the cosmological history that follows from modified theories of gravity. It provides qualitative information on the typical background solutions in a parametrized family of models, through the computation of the fixed points and their characters (attractor, repeller or saddle), allowing, for instance, the knowledge of which regions on the parameter space of the models generate the desired radiation, matter and dark energy dominated eras. However, the traditional proposal for building dynamical systems for an $f(R)$ theory in the Palatini formalism assumes the invertibility of a function that depends on the specific Lagrangian functional form, which is not true, for example, for the particular theory of exponential gravity ($f(R)=R-αR_*(1-e^{-R/R_*})$). In this work, we propose an alternative choice of variables to treat $f(R)$ models in their Palatini formulation, which do include exponential gravity. We derive some general results that can be applied to a given model of interest and present a complete description of the phase space for exponential gravity. We show that Palatini exponential gravity theories have a final attractor critical point with an effective equation of state parameter $w_{\text{eff}} = -1$ (for $α>1$), $w_{\text{eff}} = -2/3$ (for $α=1$) and $w_{\text{eff}} = 0$ (for $α<1$). Finally, our analytical results are compared with numerical solutions of the field equations.

gr-qc↗

arXiv2021

Influence of gravitational waves upon light in the Minkowski background: from null geodesics to interferometry

We have recently derived a manifestly covariant evolution law, under the geometrical optics approximation of the vacuum Maxwell's equations, for the electric field along null geodesics in a general spacetime, relative to an arbitrary set of instantaneous observers [arXiv:2004.03496]. As one of its applications, we derive here the final detected intensity signal arising from a prototypical laser interferometric gravitational wave (GW) Michelson-Morley detector, comoving with transverse traceless (TT) observers, valid for both long and short GW wavelengths. One of our main results is the presentation of the integrated null geodesic parametric equations exchanged between two TT observers in terms of explicitly observable quantities and the profile of the plane GW packet. This allows us to revisit the derivation of the consequential radar distance and Doppler shift, taking the opportunity to discuss some related subtle conceptual issues and how they might affect the interferometric process. Another achievement is the calculation of the electric field in each arm up to the detection event, for any relative orientations of the arms and the GW direction. The main quantitative result is the new expression for the final interference pattern, for normal GW incidence, which turns out to have three contributions: (i) the well-known traditional one due to the difference in optical paths, and two new ones due to (ii) the Doppler effect, and (iii) the divergence of the laser beams. The quantitative relevance of the last two contributions is compared to the traditional one and shown to be negligible within the geometrical optics regime of light. Although in general further contributions from the non-parallel transport of the polarization vector are expected, again in the case of GW normal incidence, such a vector is indeed parallel transported, and those contributions are absent.

gr-qc↗

arXiv2021

Gravitational wave propagation in $f(R)$ models: New parametrizations and observational constraints

Modified gravity (MG) theories predict, in general, that the ratio of gravitational wave (GW) to electromagnetic (EM) luminosity distances, $Ξ$, differs from its general relativity (GR) value of unity at cosmological scales, thus providing another perturbative probe to MG. In this paper, we introduce new phenomenological parametrizations for both the Friedmann-Lemaître-Robertson-Walker (FLRW) background evolution of $f(R)$ models, via the dark energy equation of state parameter, $w_{\text{DE}}$, and for $Ξ$ in this class of theories. We simulate a mock dataset for the Einstein Telescope (ET) of 1000 GW signals from binary neutron star (BNS) mergers and redshift information from their EM counterpart, exploring the consequent constraints on the relevant gravitational, cosmological and phenomenological parameters. As a model of particular interest, we take $γ$-gravity theory and investigate whether it could be distinguished from GR's $Λ$CDM model. We then combine our results with actual data from type Ia supernovae (SNIa) and combined baryon acoustic oscillations (BAO) and cosmic microwave background (CMB) observations. Additionally, we also investigate the potential bounds to $f_{R0}$ for any viable $f(R)$ whose background evolution is indistinguishable from the standard model of cosmology above a certain redshift, showing that, for a $Λ$CDM fiducial model, ET data would provide $|f_{R0}|<10^{-2}$ at a 95\% level. We conclude altogether that probing the redshift evolution of the GW luminosity distance from detections of the ET in its first running decade will not substantially help constraining $f(R)$ theories of gravity.

gr-qc↗

arXiv2021

Influence of gravitational waves upon light. Part I. Null geodesics, radar distance and frequency shift

We explore different facets of the action of linearized gravitational waves in Minkowski spacetime background upon light, under the electromagnetic geometrical optics limit, covering the main aspects: light trajectory perturbations, radar distance and light frequency shift. For this purpose, we consider observers comoving with the transverse traceless gauge coordinates. We compute the parametrized null geodesics exchanged between two of these observers, presenting explicitly the constants of motion as functions of observables, determining therefrom both the radar distance between the observers and the electromagnetic round-trip frequency shift caused by the gravitational wave. Also, a comparison is made between these results and what one would obtain by using a frequently adopted hybrid model in which the spatial trajectory of light is unchanged. Finally, we revisit and provide an explanation, resorting to the constancy of the phase along a light ray, to the fundamental puzzling question of how one is able to detect gravitational waves by means of interferometry if both light wavelength and detector arms are stretched.

gr-qc↗

arXiv2021

Influence of gravitational waves upon light. Part II. Electric field propagation and interference pattern in a gravitational wave detector

In this second article of the series, we apply our recently derived equation for the electric field propagation along light rays [arXiv:2004.03496], valid on the electromagnetic geometrical optics limit, to the special case of a toy interferometer used to detect gravitational waves in a flat background. Such an equation shows that, assuming the detector is in the transverse-traceless frame, which has a local shearing relative motion due to the gravitational wave perturbations, the electric field does not propagate as in an inertial reference frame in Minkowski spacetime. We present the electric field at the end of the interferometric process, for arbitrary arm configurations with respect to the plane gravitational wave packet propagation direction. Then, for normal incidence, we compute the interference pattern and, in addition to the usual term associated with the difference in path traveled by light in the arms, we deduce two new contributions to the final intensity, arising from: (i) the round-trip electromagnetic frequency shift and (ii) the divergence of the light beam. Their quantitative relevance is compared to the traditional contribution and shown to be typically negligible due to the geometrical optics regime of light. Moreover, a non-parallel transport of the polarization vector takes place, in general, because of the gravitational wave, a feature which could generate further contributions. However, we conclude that for the normal incidence case such vector is parallel transported, preventing this kind of correction.

gr-qc↗

arXiv2020

Evolution of the electric field along null rays for arbitrary observers and spacetimes

We derive, in a manifestly covariant and electromagnetic gauge independent way, the evolution law of the electric field $E^α= Ee^α (e^αe_α=1)$, relative to an arbitrary set of instantaneous observers along a null geodesic ray, for an arbitrary Lorentzian spacetime, in the geometrical optics limit of Maxwell's equations in vacuum. We show that, in general, neither the magnitude $E$ nor the direction $e^α$ of the electric field (here interpreted as the observed polarization of light) are parallel transported along the ray. For an extended reference frame around the given light ray, we express the evolution of the direction $e^α$ in terms of the frame's kinematics, proving thereby that its expansion never spoils parallel transport, which bears on the unbiased inference of intrinsic properties of cosmological sources, such as, for instance, the polarization field of the cosmic microwave background (CMB). As an application of the newly derived laws, we consider a simple setup for a gravitational wave (GW) interferometer, showing that, despite the (kinematic) shear induced by the GW, the change in the final interference pattern is negligible since it turns out to be of the order of the ratio of the GW and laser frequencies.

gr-qc↗

arXiv2017

How does light move in a generic metric-affine background?

Light is the richest information retriever for most physical systems, particularly so for astronomy and cosmology, in which gravitation is of paramount importance, and also for solid state defects and metamaterials, in which some effects can be mimicked by non-Euclidean or even non-Riemannian geometries. Thus, it is expedient to probe light motion in geometrical backgrounds alternative to that of general relativity. Here we investigate this issue in generic metric-affine theories and derive (i) the expression, in the geometrical optics (eikonal) limit, for light trajectories, showing that they still are null (extremal) geodesics and thus, in general, no longer autoparallels, (ii) a generic {formula} to obtain the relation between source (galaxy) and reception (observer) angular size (area) distances, generalizing Etherington's original distance reciprocity relation (DRR), and then applying it to two particular representative non-Riemannian geometries. First in metric-compatible, completely antisymmetric torsion geometries, the generalized DRR is not changed at all, and then in Weyl integrable spacetimes, the generalized DRR assumes a specially simple expression.

gr-qc↗

arXiv2014

Standardization of type Ia supernovae

Type Ia supernovae (SNe Ia) have been intensively investigated due to its great homogeneity and high luminosity, which make it possible to use them as standardizable candles for the determination of cosmological parameters. In 2011, the physics Nobel prize was awarded for the discovery of the accelerating expansion of the Universe through observations of distant supernovae. This is a pedagogical article, aimed at those starting their study of that subject, in which we dwell on some topics related to the analysis of SNe Ia and their use in luminosity distance estimators. Here we investigate their spectral properties and light curve standardization, paying careful attention to the fundamental quantities directly related to the SNe Ia observables. Finally, we describe our own step-by-step implementation of a classical light curve fitter, the stretch, applying it to real data from the Carnegie Supernova Project.

astro-ph.CO↗

arXiv2014

Photometric type Ia supernova surveys in narrow band filters

We study the characteristics of a narrow band type Ia supernova survey through simulations based on the upcoming Javalambre Physics of the accelerating universe Astrophysical Survey (J-PAS). This unique survey has the capabilities of obtaining distances, redshifts, and the SN type from a single experiment thereby circumventing the challenges faced by the resource-intensive spectroscopic follow-up observations. We analyse the flux measurements signal-to-noise ratio and bias, the supernova typing performance, the ability to recover light curve parameters given by the SALT2 model, the photometric redshift precision from type Ia supernova light curves and the effects of systematic errors on the data. We show that such a survey is not only feasible but may yield large type Ia supernova samples (up to 250 supernovae at $z<0.5$ per month of search) with low core collapse contamination ($\sim 1.5$ per cent), good precision on the SALT2 parameters (average $σ_{m_B}=0.063$, $σ_{x_1}=0.47$ and $σ_c=0.040$) and on the distance modulus (average $σ_μ=0.16$, assuming an intrinsic scatter $σ_{\mathrm{int}}=0.14$), with identified systematic uncertainties $σ_{\mathrm{sys}}\lesssim 0.10 σ_{\mathrm{stat}}$. Moreover, the filters are narrow enough to detect most spectral features and obtain excellent photometric redshift precision of $σ_z=0.005$, apart from $\sim$ 2 per cent of outliers. We also present a few strategies for optimising the survey's outcome. Together with the detailed host galaxy information, narrow band surveys can be very valuable for the study of supernova rates, spectral feature relations, intrinsic colour variations and correlations between supernova and host galaxy properties, all of which are important information for supernova cosmological applications.

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