Space tests of relativistic gravity with precision clocks and atom interferometers

Precision clocks and interferometers in space can test relativistic gravity with extremely high sensitivity. Yet, only a single such test has been performed, namely the celebrated flight of a hydrogen maser in a sub-orbital trajectory in 1976 (GP-A mission). This paper suggests some of the obstacles to space flight of precision instruments, and describes how the emergence of new technology might offer a pathway for removing those obstacles. A brief review of emerging technologies is made, and new mission concepts based on them are described. Some of the technologies that can impact more tests of relativistic gravity in space at a more distant future are also described.     

Special relativistic Newtonian gravity

Newtonian gravity is modified minimally to obtain a Lorentz covariant theory of gravity in a background flat space. Gravity is assumed to appear as a potential. Constraint Hamiltonian dynamics is used to determine particle trajectories in a manifestly covariant fashion. The resulting theory is significantly different from the general theory of relativity. However, all known experimental results (precession of planetary orbits, bending of the path of light near the sun, and gravitational spectral shift) are still explained by this theory.     

A relativistic gravity train

A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can attain speeds arbitrarily close to the speed of light; generalizing the electrostatic and gravitational cases requires special and general relativity, respectively. We find exact closed-form relations between the position, proper time, and coordinate time in both cases, and find that they are no longer harmonic, with oscillation periods that depend on the amplitude. In the highly relativistic limit of both cases, the particle spends almost all of its proper time near the turning points, but almost all of the coordinate time moving through the bulk of the ball. Buchdahl’s theorem imposes nontrivial constraints on the general-relativistic case, as a ball of given density can only attain a finite maximum radius before collapsing into a black hole. This article is intended to be pedagogical, and should be accessible to those who have taken an undergraduate course in general relativity.     

Tests of relativistic gravity in space

We review the foundations of Einstein’s general theory of relativity, discuss recent progress in the tests of relativistic gravity, and present motivations for new generation of high-accuracy gravitational experiments. We discuss the advances in our understanding of fundamental physics anticipated in the near future and evaluate discovery potential of the recently proposed gravitational experiments.     

Cosmological tests of gravity

Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher-dimensional approaches and chameleon/f(R) theories. We classify these models in terms of the screening mechanisms that enable such theories to approach general relativity on small scales (and thus satisfy solar system constraints). We describe general features of the modified Friedman equation in such theories.The second half of this review describes experimental tests of gravity in light of the new theoretical approaches. We summarize the high precision tests of gravity on laboratory and solar system scales. We describe in some detail tests on astrophysical scales ranging from ∼ kpc (galaxy scales) to ∼ Gpc (large-scale structure). These tests rely on the growth and inter-relationship of perturbations in the metric potentials, density and velocity fields which can be measured using gravitational lensing, galaxy cluster abundances, galaxy clustering and the integrated Sachs-Wolfe effect. A robust way to interpret observations is by constraining effective parameters, such as the ratio of the two metric potentials. Currently tests of gravity on astrophysical scales are in the early stages — we summarize these tests and discuss the interesting prospects for new tests in the coming decade.     

Bouncing scenario of general relativistic hydrodynamics in extended gravity

In this paper,we have framed bouncing cosmological model of the Universe in the presence of general relativistic hydrodynamics in an extended theory of gravity.The metric assumed here is the flat Friedmann–Robertson–Walker space–time and the stress energy tensor is of perfect fluid.Since general relativity(GR)has certain issues with late time cosmic speed up phenomena,here we have introduced an additional matter geometry coupling that described the extended gravity to GR.The dynamical parameters are derived and analyzed.The dynamical behavior of the equation of state parameter has been analyzed.We have observed that the bouncing behavior is mostly controlled by the coupling parameter.     

Numerical tests of causal relativistic dissipative fluid dynamics

We present numerical methods to solve the Israel–Stewart (IS) equations of causal relativistic dissipative fluid dynamics with bulk and shear viscosities. We then test these methods studying the Riemann problem in (1+1)- and (2+1)-dimensional geometry. The numerical schemes investigated here are applicable to realistic (3+1)-dimensional modeling of a relativistic dissipative fluid.     

A laboratory test of Mach's principle and strong-field relativistic gravity

A laboratory experiment that tests the validity of Mach's principle — the relativity and gravitational induction of inertia — and relativistic gravity in strong-field circumstances is described. It consists of looking for a stationary shift in the apparent weight of an object when a transient mass fluctuation is induced in one of its parts, that part then being subjected to a pulsed thrust. The transient mass fluctuation induced is of the order of a few tens of milligrams, and the stationary weight shift observed is several milligrams. Details of the apparatus used (capable of detecting an effect at the level of about a tenth of a milligram) are presented. Procedural protocols are laid out. The results obtained — signals some 10 to 15 times the standard error in magnitude — confirm to better than order of magnitude that the predicted effect is indeed present. The consequences of this confirmation of Mach's principle and relativistic gravity are briefly addressed. In particular, it is pointed out that in light of these results radical timelessness seems to be the correct way to understand reality and, from the practical point-of-view, it may prove possible to make traversable wormholes whenever we choose to devote sufficient resources to that end.     

Experimental demonstration of relativistic electron cooling

We report on an experimental demonstration of electron cooling of high-energy antiprotons circulating in a storage ring. In our experiments, electron cooling, a well-established method at low energies (<500 MeV/nucleon), was carried out in a new region of beam parameters, requiring a multi-MeV dc electron beam and an unusual beam transport line. In this Letter, we present the results of the longitudinal cooling force measurements and compare them with theoretical predictions.     

Equilibrium and stability of relativistic stars in extended theories of gravity

We study static, spherically symmetric equilibrium configurations in extended theories of gravity (ETG) following the notation introduced by Capozziello et al. We calculate the differential equations for the stellar structure in such theories in a very generic form i.e., the Tolman–Oppenheimer–Volkoff generalization for any ETG is introduced. Stability analysis is also investigated with special focus on the particular example of scalar–tensor gravity.     

Atom-interferometry tests of the isotropy of post-Newtonian gravity

We present a test of the local Lorentz invariance of post-Newtonian gravity by monitoring Earth's gravity with a Mach-Zehnder atom interferometer that features a resolution of up to 8 x 10{-9}g/sqrt[Hz], the highest reported thus far. Expressed within the standard model extension (SME) or Nordtvedt's anisotropic universe model, the analysis limits four coefficients describing anisotropic gravity at the ppb level and three others, for the first time, at the 10 ppm level. Using the SME we explicitly demonstrate how the experiment actually compares the isotropy of gravity and electromagnetism.     

Experimental tests of distributivity

The Cirel'son bound for the EPR experimental set-up provides a test of the distributivity of the observable algebra and is thus satisfied by Jordan algebras and distributive Segal algebras. By means of nondistributive algebras, the Cirel'son bound may be violated and the Rastall limit attained. It is also shown that Sherman's nondistributive Segal algebras are unsuitable as algebraic models of physical systems.     

Constraining extended theories of gravity using Solar System tests

Solar System tests give nowadays constraints on the estimated value of the cosmological constant, which can be accurately derived from different experiments regarding gravitational redshift, light deflection, gravitational time-delay and geodesic precession. Assuming that each reasonable theory of gravitation should satisfy Solar System tests, we use these limits on the estimated value of the cosmological constant to constrain extended theories of Gravity, which are nowadays studied as possible theories for cosmological models and provide viable solutions to the cosmological constant problem and the explanation of the present acceleration of the Universe. We obtain that the estimated values, from Solar System tests, for the parameters appearing in the extended theories of Gravity are orders of magnitude bigger than the values obtained in the framework of cosmologically relevant theories.     

Issue of the spherically symmetric static vacuum metric in the relativistic theory of gravity

The spherically symmetric vacuum metric in the relativistic theory of gravity is analyzed numerically. It is found that there is no deviation of the numerical solution from that of general relativity except in the near-horizon range. The solution obtained has the well-established analytical asymptotics for both the near-and far-horizon limits. It satisfies the causality principle and does not impose a lower limit on the graviton mass.      

Experimental tests of extra dimensions

Spherically symmetric solutions of general relativity in higher dimensions are tested. We find that the existence of extra dimensions is compatible with the classical tests of general relativity, which place almost no restrictions on the parameters involved. The models studied fail to explain the geological data concerning the apparent variability of the gravitational constant with the distance.