General Relativity and Cosmology: Unsolved Questions and Future Directions

Why Is the Mean Anomaly at Epoch Not Used in Tests of Non-Newtonian Gravity?

The mean anomaly at epoch η is one of the standard six Keplerian orbital elements in terms of which the motion of the two-body problem is parameterized. Along with the argument of pericenter ω, η experiences long-term rates of change induced, among other things, by general relativity and several modified models of gravity. Thus, in principle, it may be fruitfully adopted together with ω in several tests of post-Newtonian gravity performed with astronomical and astrophysical binary systems. This would allow us to enhance the gravitational signature we are interested in and to disentangle some competing disturbing effects acting as sources of systematic bias. Nonetheless, for some reasons unknown to the present author, η has never been used so far by astronomers in actual data reductions. This note aims to raise interest in the community about the possible practical use of such an orbital element or, at least, to induce experts in astronomical data processing to explicitly make clear if it is not possible to use η for testing gravitational models and, if this is the case, why.

Current and Future Tests of General Relativity

General Relativity (GR) holds a special place amongst all fundamental theories of physics: on one hand, it is the theory of all gravitational phenomena; on the other hand, it is also a theory of spacetime [...]

Cylindrical Gravastar Like-Structures in f(G) Gravity

The aim of this manuscript is to explore singularity-free solution for a specific self-gravitating highly dense object known as gravastar suggested by Mazur and Mottola, in the context of f(G) gravity theory. Gravastars are regarded as a possible alternate to black hole. To derive modified field equations and law of conservation related to Gauss-Bonnet gravity, we assume cylindrically symmetric irrotational configuration. Particular equation of states are used for the illustration of three sectors of gravastar model. Furthermore, we are intended to obtain a regular solution for our model and graphs will be used to elaborate various substantial characteristics of it.

Does standard cosmology really predict the cosmic microwave background?

In standard Big Bang cosmology, the universe expanded from a very dense, hot and opaque initial state. The light that was last scattered about 380,000 years later, when the universe had become transparent, has been redshifted and is now seen as thermal radiation with a temperature of 2.7 K, the cosmic microwave background (CMB). However, since light escapes faster than matter can move, it is prudent to ask how we, made of matter from this very source, can still see the light. In order for this to be possible, the light must take a return path of the right length. A curved return path is possible in spatially closed, balloon-like models, but in standard cosmology, the universe is “flat” rather than balloon-like, and it lacks a boundary surface that might function as a reflector. Under these premises, radiation that once filled the universe homogeneously cannot do so permanently after expansion, and we cannot see the last scattering event. It is shown that the traditional calculation of the CMB temperature is inappropriate and that light emitted by any source inside the Big Bang universe earlier than half its “conformal age” can only become visible to us via a return path. Although often advanced as the best evidence for a hot Big Bang, the CMB actually tells against a formerly smaller universe and so do also distant galaxies.

Additional Solar System Gravitational Anomalies

This article is motivated by uncertainty in experimental determinations of the gravitational constant, G, and numerous anomalies of up to 0.5 percent in Newtonian gravitational force on bodies within the solar system. The analysis sheds new light through six natural experiments within the solar system, which draw on published reports and astrophysical databases, and involve laboratory determinations of G, orbital dynamics of the planets and the moons of Earth and Mars, and non-gravitational acceleration (NGA) of ‘Oumuamua and comets. In each case, values are known for all variables in Newton’s Law F=G·M·mR2, except for the gravitational constant, G. Analyses determine the gravitational constant’s observed value, G^, which—across the six settings—varies with the mass of the smaller, moving body, m, so that G^=G×0.998+0.00016×lnm. While further work is required, this examination shows a scale-related Newtonian gravity effect at scales from benchtop to Solar System, which contributes to the understanding of symmetry in gravity and has possible implications for Newton’s Laws, dark matter, and formation of structure in the universe.

Cosmological Parameter Inference with Bayesian Statistics

Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In this paper, we review some fundamental concepts to understand Bayesian statistics and then introduce MCMC algorithms and samplers that allow us to perform the parameter inference procedure. We also introduce a general description of the standard cosmological model, known as the ΛCDM model, along with several alternatives, and current datasets coming from astrophysical and cosmological observations. Finally, with the tools acquired, we use an MCMC algorithm implemented in python to test several cosmological models and find out the combination of parameters that best describes the Universe.

Taxonomy of Dark Energy Models

The accelerated expansion of the Universe is one of the main discoveries of the past decades, indicating the presence of an unknown component: the dark energy. Evidence of its presence is being gathered by a succession of observational experiments with increasing precision in its measurements. However, the most accepted model for explaining the dynamic of our Universe, the so-called Lambda cold dark matter, faces several problems related to the nature of such energy component. This has led to a growing exploration of alternative models attempting to solve those drawbacks. In this review, we briefly summarize the characteristics of a (non-exhaustive) list of dark energy models as well as some of the most used cosmological samples. Next, we discuss how to constrain each model’s parameters using observational data. Finally, we summarize the status of dark energy modeling.

L2-CalSat: A Calibration Satellite for Ultra-Sensitive CMB Polarization Space Missions

In this work, the use of a calibration satellite (L2-CalSat) flying in formation with a Cosmic Microwave Background (CMB) polarization mission in an orbit located at the second Lagrange point, is proposed. The new generation of CMB telescopes are expected to reach unprecedented levels of sensitivity to allow a very precise measurement of the B-mode of polarization, the curl-like polarization component expected from gravitational waves coming from Starobinski inflationary models. Due to the CMB polarized signal weakness, the instruments must be subjected to very precise calibration processes before and after launching. Celestial sources are often used as external references for calibration after launch, but these sources are not perfectly characterized. As a baseline option, L2-CalSat is based on the CubeSat standard and serves as a perfectly known source of a reference signal to reduce polarization measurements uncertainty. A preliminary design of L2-CalSat is described and, according to the scanning strategy followed by the telescope, the influence of the relative position between the spacecrafts in the calibration process is studied. This new calibration element will have a huge impact on the performance of CMB space missions, providing a significant improvement in the measurements accuracy without requiring new and costly technological developments.

Einstein’s Geometrical versus Feynman’s Quantum-Field Approaches to Gravity Physics: Testing by Modern Multimessenger Astronomy

Modern multimessenger astronomy delivers unique opportunity for performing crucial observations that allow for testing the physics of the gravitational interaction. These tests include detection of gravitational waves by advanced LIGO-Virgo antennas, Event Horizon Telescope observations of central relativistic compact objects (RCO) in active galactic nuclei (AGN), X-ray spectroscopic observations of Fe Kα line in AGN, Galactic X-ray sources measurement of masses and radiuses of neutron stars, quark stars, and other RCO. A very important task of observational cosmology is to perform large surveys of galactic distances independent on cosmological redshifts for testing the nature of the Hubble law and peculiar velocities. Forthcoming multimessenger astronomy, while using such facilities as advanced LIGO-Virgo, Event Horizon Telescope (EHT), ALMA, WALLABY, JWST, EUCLID, and THESEUS, can elucidate the relation between Einstein’s geometrical and Feynman’s quantum-field approaches to gravity physics and deliver a new possibilities for unification of gravitation with other fundamental quantum physical interactions.

A Noncommutative Model of Cosmology with Two Metrics

We propose a bicosmology model which reduces to the classical analog of noncommutative quantum mechanics. From this point of view, one of the sources in the so modified Friedmann-Robertson- Walker equations is a kind of dark energy governed by a Chapligyn-like equation of state. The parameters of noncommutativity θ and B are interpreted in terms of the Planck area and a magnetic-like field, which presumably acts as a seed for magnetogenesis.

New Limit on Space-Time Variations in the Proton-to-Electron Mass Ratio from Analysis of Quasar J110325-264515 Spectra

Astrophysical tests of current values for dimensionless constants known on Earth, such as the fine-structure constant, α , and proton-to-electron mass ratio, μ = m p / m e , are communicated using data from high-resolution quasar spectra in different regions or epochs of the universe. The symmetry wavelengths of [Fe II] lines from redshifted quasar spectra of J110325-264515 and their corresponding values in the laboratory were combined to find a new limit on space-time variations in the proton-to-electron mass ratio, ∆ μ / μ = ( 0.096 ± 0.182 ) × 10 − 7 . The results show how the indicated astrophysical observations can further improve the accuracy and space-time variations of physics constants.

Do solar system experiments constrain scalar-tensor gravity?

It is now established that, contrary to common belief, (electro-)vacuum Brans-Dicke gravity does not reduce to general relativity (GR) for large values of the Brans-Dicke coupling ω . Since the essence of experimental tests of scalar-tensor gravity consists of providing lower bounds on ω , in light of the misguided assumption of the equivalence between the limit ω → ∞ and the GR limit of Brans-Dicke gravity, the parametrized post-Newtonian (PPN) formalism on which these tests are based could be in jeopardy. We show that, in the linearized approximation used by the PPN formalism, the anomaly in the limit to general relativity disappears. However, it survives to second (and higher) order and in strong gravity. In other words, while the weak gravity regime cannot tell apart GR and ω → ∞ Brans-Dicke gravity, when higher order terms in the PPN analysis of Brans-Dicke gravity are included, the latter never reduces to the one of GR in this limit. This fact is relevant for experiments aiming to test second order light deflection and Shapiro time delay.

The Legacy of Einstein’s Eclipse, Gravitational Lensing

A hundred years ago, two British expeditions measured the deflection of starlight by the Sun’s gravitational field, confirming the prediction made by Einstein’s General Theory of Relativity. One hundred years later many physicists around the world are involved in studying the consequences and use as a research tool, of the deflection of light by gravitational fields, a discipline that today receives the generic name of Gravitational Lensing. The present review aims to commemorate the centenary of Einstein’s Eclipse expeditions by presenting a historical perspective of the development and milestones on gravitational light bending, covering from early XIX century speculations, to its current use as an important research tool in astronomy and cosmology.

Monitoring Jovian Orbital Resonances of a Spacecraft: Classical and Relativistic Effects

Orbital resonances continue to be one of the most difficult problems in celestial mechanics. They have been studied in connection with the so-called Kirkwood gaps in the asteroid belt for many years. On the other hand, resonant trans-Neptunian objects are also an active area of research in Solar System dynamics, as are the recently discovered resonances in extrasolar planetary systems. A careful monitoring of the trajectories of these objects is hindered by the small size of asteroids or the large distances of the trans-Neptunian bodies. In this paper, we propose a mission concept, called CHRONOS (after the greek god of time), in which a spacecraft could be sent to with the initial condition of resonance with Jupiter in order to study the future evolution of its trajectory. We show that radio monitoring of these trajectories could allow for a better understanding of the initial stages of the evolution of resonant trajectories and the associated relativistic effects.

Cosmological Solutions from a Multi-Measure Model with Inflaton Field

In a recent work, we demonstrated that a modified gravity model in which a scalar “darkon” field is coupled to both the standard Riemannian metric and to another non-Riemannian volume form is compatible with observational data from Supernovae Type Ia. Here, we investigate a more complicated model with an additional “inflaton” scalar field. We demonstrate numerically that the model can qualitatively reproduce the Universe inflation epoch, matter dominated epoch, and present accelerating expansion in a seamless way. We show that such solutions occur only when the model parameters are within a very particular range. The main numerical problem we are faced with is reproducing the extremely small time of the inflation epoch. Here, we present how the variation of some parameters affects this time.

Modifications to Plane Gravitational Waves from Minimal Lorentz Violation

General Relativity predicts two modes for plane gravitational waves. When a tiny violation of Lorentz invariance occurs, the two gravitational wave modes are modified. We use perturbation theory to study the detailed form of the modifications to the two gravitational wave modes from the minimal Lorentz-violation coupling. The perturbation solution for the metric fluctuation up to the first order in Lorentz violation is discussed. Then, we investigate the motions of test particles under the influence of the plane gravitational waves with Lorentz violation. First-order deviations from the usual motions are found.

Analog black holes and energy extraction by super-radiance from Bose Einstein condensates (BEC) with constant density

This paper investigates the acoustic superradiance of the density and phase fluctuations from the single vortex state of a Bose-Einstein condensate, by employing full time-domain and asymptotic frequency domain numerical calculations. The draining bathtub model of an incompressible barotropic fluid is adopted to describe the vortex. The propagation of the axisymmetric density and phase fluctuations in the condensate are governed by the massless scalar Klein-Gordon wave equation, which establishes the rotating black-hole analogy. Hence, the amplified scattering of these fluctuations from the vortex comprise the superradiance effect. A particular coordinate transformation is applied to reveal the event horizon and the ergosphere termwise in the metric and the respective asymptotic spectral solutions. A comparative analysis of the time domain and asymptotic frequency domain results are given for a range of rotational speed of the vortex and the frequency of the impinging fluctuations. The agreement at low rotational speeds of the vortex is shown to be very good, which starts to deteriorate at higher rotational speeds due to increasing constraint violations of the time-domain calculations. We further demonstrate an asymptotic upper bound for the superradiance as a function of vortex rotational speed, provided that the vortex remains stable.

General Relativity Measurements in the Field of Earth with Laser-Ranged Satellites: State of the Art and Perspectives

Recent results of the LARASE research program in terms of model improvements and relativistic measurements are presented. In particular, the results regarding the development of new models for the non-gravitational perturbations that affect the orbit of the LAGEOS and LARES satellites are described and discussed. These are subtle and complex effects that need a deep knowledge of the structure and the physical characteristics of the satellites in order to be correctly accounted for. In the field of gravitational measurements, we present a new measurement of the relativistic Lense-Thirring precession with a 0.5 % precision. In this measurement, together with the relativistic effect we also estimated two even zonal harmonics coefficients. The uncertainties of the even zonal harmonics of the gravitational field of the Earth have been responsible, until now, of the larger systematic uncertainty in the error budget of this kind of measurements. For this reason, the role of the errors related to the model used for the gravitational field of the Earth in these measurements is discussed. In particular, emphasis is given to GRACE temporal models, that strongly help to reduce this kind of systematic errors.

Reasons in Favor of a Hubble-Lemaître-Slipher’s (HLS) Law

Based on historical facts, revisited from a present-day perspective, and on the documented opinions of the scientists involved in the discovery themselves, strong arguments are given in favor of a proposal to add prominent astronomer Vesto Slipher to the suggested addition of Georges Lemaître’s name to Hubble’s law on the expansion of the universe and thus eventually call it the Hubble–Lemaître–Slipher (HLS) law.

Seeing Black Holes: From the Computer to the Telescope

Astronomical observations are about to deliver the very first telescopic image of the massive black hole lurking at the Galactic Center. The mass of data collected in one night by the Event Horizon Telescope network, exceeding everything that has ever been done in any scientific field, should provide a recomposed image in 2018. All this, forty years after the first numerical simulations performed by the present author.

Perspectives on Constraining a Cosmological Constant-Type Parameter with Pulsar Timing in the Galactic Center

Independent tests aiming to constrain the value of the cosmological constant Λ are usually difficult because of its extreme smallness ( Λ ≃ 1 × 10 - 52 m - 2 , or 2 . 89 × 10 - 122 in Planck units ) . Bounds on it from Solar System orbital motions determined with spacecraft tracking are currently at the ≃ 10 - 43 – 10 - 44 m - 2 ( 5 – 1 × 10 - 113 in Planck units ) level, but they may turn out to be optimistic since Λ has not yet been explicitly modeled in the planetary data reductions. Accurate ( σ τ p ≃ 1 – 10 μ s ) timing of expected pulsars orbiting the Black Hole at the Galactic Center, preferably along highly eccentric and wide orbits, might, at least in principle, improve the planetary constraints by several orders of magnitude. By looking at the average time shift per orbit Δ δ τ ¯ p Λ , an S2-like orbital configuration with e = 0 . 8839 , P b = 16 yr would permit a preliminarily upper bound of the order of Λ ≲ 9 × 10 - 47 m - 2 ≲ 2 × 10 - 116 in Planck units if only σ τ p were to be considered. Our results can be easily extended to modified models of gravity using Λ -type parameters.

Testing General Relativity with Stellar Orbits around the Supermassive Black Hole in Our Galactic Center

We demonstrate that short-period stars orbiting around the supermassive black hole in our Galactic center can successfully be used to probe the gravitational theory in a strong regime. We use 19 years of observations of the two best measured short-period stars orbiting our Galactic center to constrain a hypothetical fifth force that arises in various scenarios motivated by the development of a unification theory or in some models of dark matter and dark energy. No deviation from general relativity is reported and the fifth force strength is restricted to an upper 95% confidence limit of |α|<0.016 at a length scale of λ=150 astronomical units. We also derive a 95% confidence upper limit on a linear drift of the argument of periastron of the short-period star S0-2 of |ω[over ˙]_{S0-2}|<1.6×10^{-3}  rad/yr, which can be used to constrain various gravitational and astrophysical theories. This analysis provides the first fully self-consistent test of the gravitational theory using orbital dynamic in a strong gravitational regime, that of a supermassive black hole. A sensitivity analysis for future measurements is also presented.