A test of general relativity using radio links with the Cassini spacecraft

Teleparallel gravity: from theory to cosmology

Teleparallel gravity (TG) has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we give a comprehensive introduction to how teleparallel geometry is developed as a gauge theory of translations together with all the other properties of gauge field theory. This relates the geometry to the broader metric-affine approach to forming gravitational theories where we describe a systematic way of constructing consistent teleparallel theories that respect certain physical conditions such as local Lorentz invariance. We first use TG to formulate a teleparallel equivalent of general relativity (GR) which is dynamically equivalent to GR but which may have different behaviors for other scenarios, such as quantum gravity. After setting this foundation, we describe the plethora of modified teleparallel theories of gravity that have been proposed in the literature. We attempt to connect them together into general classes of covariant gravitational theories. Of particular interest, we highlight the recent proposal of a teleparallel analogue of Horndeski gravity which offers the possibility of reviving all of the regular Horndeski contributions. In the second part of the Review, we first survey works in teleparallel astrophysics literature where we focus on the open questions in this regime of physics. We then discuss the cosmological consequences for the various formulations of TG. We do this at background level by exploring works using various approaches ranging from dynamical systems to Noether symmetries, and more. Naturally, we then discuss perturbation theory, firstly by giving a concise approach in which this can be applied in TG theories and then apply it to a number of important theories in the literature. Finally, we examine works in observational and precision cosmology across the plethora of proposal theories. This is done using some of the latest observations and is used to tackle cosmological tensions which may be alleviated in teleparallel cosmology. We also introduce a number of recent works in the application of machine learning to gravity, we do this through deep learning and Gaussian processes, together with discussions about other approaches in the literature.

A way forward for fundamental physics in space

Space-based research can provide a major leap forward in the study of key open questions in the fundamental physics domain. They include the validity of Einstein’s Equivalence principle, the origin and the nature of dark matter and dark energy, decoherence and collapse models in quantum mechanics, and the physics of quantum many-body systems. Cold-atom sensors and quantum technologies have drastically changed the approach to precision measurements. Atomic clocks and atom interferometers as well as classical and quantum links can be used to measure tiny variations of the space-time metric, elusive accelerations, and faint forces to test our knowledge of the physical laws ruling the Universe. In space, such instruments can benefit from unique conditions that allow improving both their precision and the signal to be measured. In this paper, we discuss the scientific priorities of a space-based research program in fundamental physics.

MICROSCOPE Mission: Final Results of the Test of the Equivalence Principle

The MICROSCOPE mission was designed to test the weak equivalence principle (WEP), stating the equality between the inertial and the gravitational masses, with a precision of 10^{-15} in terms of the Eötvös ratio η. Its experimental test consisted of comparing the accelerations undergone by two collocated test masses of different compositions as they orbited the Earth, by measuring the electrostatic forces required to keep them in equilibrium. This was done with ultrasensitive differential electrostatic accelerometers onboard a drag-free satellite. The mission lasted two and a half years, cumulating five months worth of science free-fall data, two-thirds with a pair of test masses of different compositions-titanium and platinum alloys-and the last third with a reference pair of test masses of the same composition-platinum. We summarize the data analysis, with an emphasis on the characterization of the systematic uncertainties due to thermal instabilities and on the correction of short-lived events which could mimic a WEP violation signal. We found no violation of the WEP, with the Eötvös parameter of the titanium and platinum pair constrained to η(Ti,Pt)=[-1.5±2.3(stat)±1.5(syst)]×10^{-15} at 1σ in statistical errors.

Internet of Spacecraft for Multi-Planetary Defense and Prosperity

Recent years have seen unprecedentedly fast-growing prosperity in the commercial space industry. Several privately funded aerospace manufacturers, such as Space Exploration Technologies Corporation (SpaceX) and Blue Origin have transformed what we used to know about this capital-intense industry and gradually reshaped the future of human civilization. As private spaceflight and multi-planetary immigration gradually become realities from science fiction (sci-fi) and theory, both opportunities and challenges will be presented. In this article, we first review the progress in space exploration and the underlying space technologies. Next, we revisit the K-Pg extinction event and the Chelyabinsk event and predict extra-terrestrialization, terraformation, and planetary defense, including the emerging near-Earth object (NEO) observation and NEO impact avoidance technologies and strategies. Furthermore, a framework for the Solar Communication and Defense Networks (SCADN) with advanced algorithms and high efficacy is proposed to enable an Internet of distributed deep-space sensing, communications, and defense to cope with disastrous incidents such as asteroid/comet impacts. Furthermore, perspectives on the legislation, management, and supervision of founding the proposed SCADN are also discussed in depth.

Is the Hubble Crisis Connected with the Extinction of Dinosaurs?

It has recently been suggested that a gravitational transition of the effective Newton’s constant Geff by about 10%, 50–150 Myrs ago could lead to the resolution of both the Hubble crisis and the growth tension of the standard ΛCDM model. Hints for such an abrupt transition with weaker gravity at times before the transition, have recently been identified in Tully–Fisher galactic mass-velocity data, and also in Cepheid SnIa calibrator data. Here we use Monte-Carlo simulations to show that such a transition could significantly increase (by a factor of 3 or more) the number of long period comets (LPCs) impacting the solar system from the Oort cloud (semi-major axis of orbits ≳104AU). This increase is consistent with observational evidence from the terrestrial and lunar cratering rates, indicating that the impact flux of kilometer sized objects increased by at least a factor of 2 over that last 100 Myrs compared to the long term average. This increase may also be connected with the Chicxulub impactor event that produced the Cretaceous–Tertiary (K-T) extinction of 75% of life on Earth (including dinosaurs) about 66 Myrs ago. We use Monte-Carlo simulations to show that for isotropic Oort cloud comet distribution with initially circular orbits, random velocity perturbations (induced e.g., by passing stars and/or galactic tidal effects), lead to a deformation of the orbits that increases significantly when Geff increases. A 10% increase in Geff leads to an increase in the probability of the comets to enter the loss cone and reach the planetary region (pericenter of less than 10 AU) by a factor that ranges from 5% (for velocity perturbation much smaller than the comet initial velocity) to more than 300% (for total velocity perturbations comparable with the initial comet velocity).

Hyperbolic Inflation in the Jordan Frame

We consider a multi-scalar field model in the Jordan frame, which can be seen as a two-scalar field model where the Brans–Dicke field interacts in the kinetic part with the second scalar field. This theory under a conformal transformation reduces to the hyperbolic inflation. We show that scaling solutions and the de Sitter universe are provided by the theory. In the study of asymptotic dynamics, we determine an attractor where all the fluid sources contribute in the cosmological fluid. This attractor is always a spiral, and it can be seen as the analogue of the hyperbolic inflation in the Jordan frame.

Classical and Quantum f(R) Cosmology: The Big Rip, the Little Rip and the Little Sibling of the Big Rip

The big rip, the little rip and the little sibling of the big rip are cosmological doomsdays predicted by some phantom dark-energy models that could describe the future evolution of our universe. When the universe evolves towards either of these future cosmic events, all bounded structures and, ultimately, space–time itself are ripped apart. Nevertheless, it is commonly believed that quantum gravity effects may smooth or even avoid these classically predicted singularities. In this review, we discuss the classical and quantum occurrence of these riplike events in the scheme of metric f(R) theories of gravity. The quantum analysis is performed in the framework of f(R) quantum geometrodynamics. In this context, we analyze the fulfilment of the DeWitt criterion for the avoidance of these singular fates. This review contains as well new unpublished work (the analysis of the equation of state for the phantom fluid and a new quantum treatment of the big rip and the little sibling of the big rip events).

Probing Gravitational Waves from Pulsars in Brans–Dicke Theory

This paper comprises the theoretical background for the data analysis of gravitational waves (GWs) from spinning neutron stars in Brans–Dicke (BD) theory. Einstein’s general theory of relativity (GR) predicts only two tensor polarization states, but a generic metric theory of gravity can also possess scalar and vector polarization states. The BD theory attempts to modify the GR by varying gravitational constant G, and it has three polarization states. The first two states are the same as in GR, and the third one is scalar polarization. We derive the response of a laser interferometric detector to the GW signal from a spinning neutron star in BD theory. We obtain a statistic based on the maximum likelihood principle to identify the signal in BD theory in the detector’s noise. This statistic generalizes the well known F-statistic used in the case of GR. We perform Monte Carlo simulations in Gaussian noise to test the detectability of the signal and the accuracy of estimation of its parameters.

Gravitational Measurements in Higher Dimensions

We attempt to study three significant tests of general relativity in higher dimensions, both in commutative and non-commutative spaces. In the context of non-commutative geometry, we will consider a solution of Einstein’s equation in higher dimensions, with a source given by a static, spherically symmetric Gaussian distribution of mass. The resulting metric would describe a regular or curvature singularity free black hole in higher dimensions. The metric should smoothly interpolate between Schwarzschild geometry at large distance, and de-Sitter spacetime at short distance. We will consider gravitational redshift, lensing, and time delay in each sector. It will be shown that, compared to the four-dimensional spacetime, there can be significant modifications due to the presence of extra dimensions and the non-commutative corrected black holes. Finally, we shall attempt to obtain a lower bound on the size of the extra dimensions and on the mass needed to form a black hole in different dimensions.

Gravity Tests with Radio Pulsars

The discovery of the first binary pulsar in 1974 has opened up a completely new field of experimental gravity. In numerous important ways, pulsars have taken precision gravity tests quantitatively and qualitatively beyond the weak-field slow-motion regime of the Solar System. Apart from the first verification of the existence of gravitational waves, binary pulsars for the first time gave us the possibility to study the dynamics of strongly self-gravitating bodies with high precision. To date there are several radio pulsars known which can be utilized for precision tests of gravity. Depending on their orbital properties and the nature of their companion, these pulsars probe various different predictions of general relativity and its alternatives in the mildly relativistic strong-field regime. In many aspects, pulsar tests are complementary to other present and upcoming gravity experiments, like gravitational-wave observatories or the Event Horizon Telescope. This review gives an introduction to gravity tests with radio pulsars and its theoretical foundations, highlights some of the most important results, and gives a brief outlook into the future of this important field of experimental gravity.

Structure of Neutron Stars in Massive Scalar-Tensor Gravity

We compute families of spherically symmetric neutron-star models in two-derivative scalar-tensor theories of gravity with a massive scalar field. The numerical approach we present allows us to compute the resulting spacetimes out to infinite radius using a relaxation algorithm on a compactified grid. We discuss the structure of the weakly and strongly scalarized branches of neutron-star models thus obtained and their dependence on the linear and quadratic coupling parameters α0, β0 between the scalar and tensor sectors of the theory, as well as the scalar mass μ. For highly negative values of β0, we encounter configurations resembling a “gravitational atom”, consisting of a highly compact baryon star surrounded by a scalar cloud. A stability analysis based on binding-energy calculations suggests that these configurations are unstable and we expect them to migrate to models with radially decreasing baryon density and scalar field strength.

Early Dark Energy from Massive Neutrinos as a Natural Resolution of the Hubble Tension

The Hubble tension can be significantly eased if there is an early component of dark energy that becomes active around the time of matter-radiation equality. Early dark energy models suffer from a coincidence problem-the physics of matter-radiation equality and early dark energy are completely disconnected, so some degree of fine-tuning is needed in order for them to occur nearly simultaneously. In this Letter, we propose a natural explanation for this coincidence. If the early dark energy scalar couples to neutrinos then it receives a large injection of energy around the time that neutrinos become nonrelativistic. This is precisely when their temperature is of order of their mass, which, coincidentally, occurs around the time of matter-radiation equality. Neutrino decoupling therefore provides a natural trigger for early dark energy by displacing the field just before matter-radiation equality. We discuss various theoretical aspects of this proposal, potential observational signatures, and future directions for its study.

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.

Black Holes and Wormholes in Extended Gravity

We discuss black hole type solutions and wormhole type ones in the effective gravity models. Such models appear during the attempts to construct the quantum theory of gravity. The mentioned solutions, being, mostly, the perturbative generalisations of well-known ones in general relativity, carry out additional set of parameters and, therefore could help, for example, in the studying of the last stages of Hawking evaporation, in extracting the possibilities for the experimental or observational search and in helping to constrain by astrophysical data.

StarNAV: Autonomous Optical Navigation of a Spacecraft by the Relativistic Perturbation of Starlight

Future space exploration missions require increased autonomy. This is especially true for navigation, where continued reliance on Earth-based resources is often a limiting factor in mission design and selection. In response to the need for autonomous navigation, this work introduces the StarNAV framework that may allow a spacecraft to autonomously navigate anywhere in the Solar System (or beyond) using only passive observations of naturally occurring starlight. Relativistic perturbations in the wavelength and direction of observed stars may be used to infer spacecraft velocity which, in turn, may be used for navigation. This work develops the mathematics governing such an approach and explores its efficacy for autonomous navigation. Measurement of stellar spectral shift due to the relativistic Doppler effect is found to be ineffective in practice. Instead, measurement of the change in inter-star angle due to stellar aberration appears to be the most promising technique for navigation by the relativistic perturbation of starlight.

Parametrizing Theories of Gravity on Large and Small Scales in Cosmology

We present a link between parametrizations of alternative theories of gravity on large and small scales in cosmology. This relationship is established using theoretical consistency conditions only. We find that in both limits the "slip" and "effective Newton's constant" can be written in terms of a set of four functions of time, two of which are direct generalizations of the α and γ parameters from post-Newtonian physics. This generalizes previous work that has constructed frameworks for testing gravity on small scales, and is to the best of our knowledge the first time that a link between parametrizations of gravity on such very different scales has been established. We expect our result to facilitate the imposition of observational constraints, by drastically reducing the number of functional degrees of freedom required to consistently test gravity on multiple scales in cosmology.

Stochastic gravitational wave backgrounds

A stochastic background of gravitational waves could be created by the superposition of a large number of independent sources. The physical processes occurring at the earliest moments of the universe certainly created a stochastic background that exists, at some level, today. This is analogous to the cosmic microwave background, which is an electromagnetic record of the early universe. The recent observations of gravitational waves by the Advanced LIGO and Advanced Virgo detectors imply that there is also a stochastic background that has been created by binary black hole and binary neutron star mergers over the history of the universe. Whether the stochastic background is observed directly, or upper limits placed on it in specific frequency bands, important astrophysical and cosmological statements about it can be made. This review will summarize the current state of research of the stochastic background, from the sources of these gravitational waves to the current methods used to observe them.

Testing general relativity in cosmology

We review recent developments and results in testing general relativity (GR) at cosmological scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the dark energy associated with it. However, with the advent of precision cosmology, it has also become a well-motivated endeavor by itself to test gravitational physics at cosmic scales. We overview cosmological probes of gravity, formalisms and parameterizations for testing deviations from GR at cosmological scales, selected modified gravity (MG) theories, gravitational screening mechanisms, and computer codes developed for these tests. We then provide summaries of recent cosmological constraints on MG parameters and selected MG models. We supplement these cosmological constraints with a summary of implications from the recent binary neutron star merger event. Next, we summarize some results on MG parameter forecasts with and without astrophysical systematics that will dominate the uncertainties. The review aims at providing an overall picture of the subject and an entry point to students and researchers interested in joining the field. It can also serve as a quick reference to recent results and constraints on testing gravity at cosmological scales.

Universality of free fall from the orbital motion of a pulsar in a stellar triple system

Einstein's theory of gravity-the general theory of relativity¹-is based on the universality of free fall, which specifies that all objects accelerate identically in an external gravitational field. In contrast to almost all alternative theories of gravity², the strong equivalence principle of general relativity requires universality of free fall to apply even to bodies with strong self-gravity. Direct tests of this principle using Solar System bodies^3,4 are limited by the weak self-gravity of the bodies, and tests using pulsar-white-dwarf binaries^5,6 have been limited by the weak gravitational pull of the Milky Way. PSR J0337+1715 is a hierarchical system of three stars (a stellar triple system) in which a binary consisting of a millisecond radio pulsar and a white dwarf in a 1.6-day orbit is itself in a 327-day orbit with another white dwarf. This system permits a test that compares how the gravitational pull of the outer white dwarf affects the pulsar, which has strong self-gravity, and the inner white dwarf. Here we report that the accelerations of the pulsar and its nearby white-dwarf companion differ fractionally by no more than 2.6 × 10^-6. For a rough comparison, our limit on the strong-field Nordtvedt parameter, which measures violation of the universality of free fall, is a factor of ten smaller than that obtained from (weak-field) Solar System tests^3,4 and a factor of almost a thousand smaller than that obtained from other strong-field tests^5,6.

A precise extragalactic test of General Relativity

Einstein’s theory of gravity, General Relativity, has been precisely tested on Solar System scales, but the long-range nature of gravity is still poorly constrained. The nearby strong gravitational lens ESO 325-G004 provides a laboratory to probe the weak-field regime of gravity and measure the spatial curvature generated per unit mass, γ. By reconstructing the observed light profile of the lensed arcs and the observed spatially resolved stellar kinematics with a single self-consistent model, we conclude that γ = 0.97 ± 0.09 at 68% confidence. Our result is consistent with the prediction of 1 from General Relativity and provides a strong extragalactic constraint on the weak-field metric of gravity.

New Class of Quasinormal Modes of Neutron Stars in Scalar-Tensor Gravity

Detection of the characteristic spectrum of pulsating neutron stars can be a powerful tool not only to probe the nuclear equation of state but also to test modifications to general relativity. However, the shift in the oscillation spectrum induced by modified theories of gravity is often small and degenerate with our ignorance of the equation of state. In this Letter, we show that the coupling to additional degrees of freedom present in modified theories of gravity can give rise to new families of modes, with no counterpart in general relativity, which could be sufficiently well resolved in frequency space to allow for clear detection. We present a realization of this idea by performing a thorough study of radial oscillations of neutron stars in massless scalar-tensor theories of gravity. We anticipate astrophysical scenarios where the presence of this class of quasinormal modes could be probed with electromagnetic and gravitational wave measurements.

New General Relativistic Contribution to Mercury's Perihelion Advance

We point out the existence of a new general relativistic contribution to the perihelion advance of Mercury that, while smaller than the contributions arising from the solar quadrupole moment and angular momentum, is 100 times larger than the second-post-Newtonian contribution. It arises in part from relativistic "crossterms" in the post-Newtonian equations of motion between Mercury's interaction with the Sun and with the other planets, and in part from an interaction between Mercury's motion and the gravitomagnetic field of the moving planets. At a few parts in 10^{6} of the leading general relativistic precession of 42.98 arcseconds per century, these effects are likely to be detectable by the BepiColombo mission to place and track two orbiters around Mercury, scheduled for launch around 2018.

Rejecting or Accepting Parameter Values in Bayesian Estimation

This article explains a decision rule that uses Bayesian posterior distributions as the basis for accepting or rejecting null values of parameters. This decision rule focuses on the range of plausible values indicated by the highest density interval of the posterior distribution and the relation between this range and a region of practical equivalence (ROPE) around the null value. The article also discusses considerations for setting the limits of a ROPE and emphasizes that analogous considerations apply to setting the decision thresholds for p values and Bayes factors.

Cosmology and fundamental physics with the Euclid satellite

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015-2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid's Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.