Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Λ-term (cosmological constant). In this paper we review both observational and theoretical aspects of a small cosmological Λ-term. We discuss the current observational situation focusing on cosmological tests of Λ including the age of the universe, high redshift supernovae, gravitational lensing, galaxy clustering and the cosmic microwave background. We also review the theoretical debate surrounding Λ: the generation of Λ in models with spontaneous symmetry breaking and through quantum vacuum polarization effects — mechanisms which are known to give rise to a large value of Λ hence leading to the "cosmological constant problem." More recent attempts to generate a small cosmological constant at the present epoch using either field theoretic techniques, or by modelling a dynamical Λ-term by scalar fields are also extensively discussed. Anthropic arguments favouring a small Λ-term are briefly reviewed. A comprehensive bibliography of recent work on Λ is provided.

http://cds.cern.ch/record/385991/files/9904398.pdf

The Case for a Positive Cosmological Λ-Term

This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion of the role of fundamental constants, their definition and link with metrology, it reviews the various constraints on the variation of the fine-structure constant, the gravitational, weak- and strong-interaction couplings and the electron-to-proton mass ratio. The review aims (1) to provide the basics of each measurement, (2) to show as clearly as possible why it constrains a given constant, and (3) to point out the underlying hypotheses. Such an investigation is of importance in comparing the different results and in understanding the recent claims of the detection of a variation of the fine-structure constant and of the electron-to-proton mass ratio in quasar absorption spectra. The theoretical models leading to the prediction of such variation are also reviewed, including Kaluza-Klein theories, string theories, and other alternative theories. Cosmological implications of these results are also discussed. The links with the tests of general relativity are emphasized.

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The fundamental constants and their variation: observational and theoretical status

TianQin is a proposal for a space-borne detector of gravitational waves in the millihertz frequencies. The experiment relies on a constellation of three dragfree spacecraft orbiting the Earth. Inter-spacecraft laser interferometry is used to monitor the distances between the test masses. The experiment is designed to be capable of detecting a signal with high confidence from a single source of gravitational waves within a few months of observing time. We describe the preliminary mission concept for TianQin, including the candidate source and experimental designs. We present estimates for the major constituents of the experiment's error budget and discuss the project's overall feasibility. Given the current level of technological readiness, we expect TianQin to be flown in the second half of the next decade.

https://iopscience.iop.org/article/10.1088/0264-9381/33/3/035010/pdf

TianQin: a space-borne gravitational wave detector

Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. Thus, it is of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We detail the relations between the constants, the tests of the local position invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, solar system observations, meteorite dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of different constants. To finish, we discuss the more speculative possibility of understanding their numerical values and the apparent fine-tuning that they confront us with.

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Varying Constants, Gravitation and Cosmology

On 21 July 1969, during the first manned lunar mission, Apollo 11, the first retroreflector array was placed on the moon, enabling highly accurate measurements of the Earthmoon separation by means of laser ranging. Lunar laser ranging (LLR) turns the Earthmoon system into a laboratory for a broad range of investigations, including astronomy, lunar science, gravitational physics, geodesy, and geodynamics. Contributions from LLR include the three-orders-of-magnitude improvement in accuracy in the lunar ephemeris, a several-orders-of-magnitude improvement in the measurement of the variations in the moon's rotation, and the verification of the principle of equivalence for massive bodies with unprecedented accuracy. Lunar laser ranging analysis has provided measurements of the Earth's precession, the moon's tidal acceleration, and lunar rotational dissipation. These scientific results, current technological developments, and prospects for the future are discussed here.

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Lunar Laser Ranging: A Continuing Legacy of the Apollo Program

Results are presented from the analysis of solar-system astrometric data, notably the range data to the Viking landers on Mars. A least-squares fit of the parameters of the solar system model to these data limits a simple time variation in the effective Newtonian gravitational constant to (2 + or - 4) x 10 to the -12th/yr and a rate of drift of atomic clocks relative to the implicit clock of relativistic dynamics to (1 + or - 8) x 10 to the -12th/yr. The error limits quoted are the result of uncertainties in the masses of the asteroids.

Experimental test of the variability of G using Viking lander ranging data

To determine whether particular sources of gravitational radiation will be detectable by a specific gravitational wave detector, it is necessary to know the sensitivity limits of the instrument. These instrumental sensitivities are often depicted ~after averaging over source position and polarization! by graphing the minimal values of the gravitational wave amplitude detectable by the instrument versus the frequency of the gravitational wave. This paper describes in detail how to compute such a sensitivity curve given a set of specifications for a spaceborne laser interferometer gravitational wave observatory. Minor errors in the prior literature are corrected, and the first ~mostly! analytic calculation of the gravitational wave transfer function is presented. Example sensitivity curve calculations are presented for the proposed LISA interferometer. PACS number~s!: 04.80.Nn, 95.55.Ym Advances in modern technology have ushered in an era of large laser interferometers designed to be used in the detection of gravitational radiation, both on the ground and in space. Such projects include the Laser Interferometric Gravitational Wave Observatory ~LIGO! and VIRGO @1,2# ground-based interferometers, and the proposed Laser Interferometer Space Antenna ~LISA! and OMEGA @3,4# spacebased interferometers. As these detectors come on-line, a new branch of astronomy will be created and a radically new view of the Universe is expected to be revealed. With the era of gravitational wave astronomy on the horizon, much effort has been devoted to the problem of categorizing sources of gravitational radiation, and extensive studies are underway to determine what sources will be visible to the various detectors. Typically, the sensitivity of detectors to sources of gravitational radiation has been illustrated using graphs which compare source strengths ~dimensionless strain! to instrument noise as functions of the gravitational wave frequency. Many different types of plots have appeared in the literature, ranging from single plots of spectral density to separate am

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Sensitivity curves for spaceborne gravitational wave interferometers

In an effort to eliminate laser phase noise in laser interferometer spaceborne gravitational wave detectors, several combinations of signals have been found that allow the laser noise to be cancelled out while gravitational wave signals remain. This process is called time delay interferometry (TDI). In the papers that defined the TDI variables, their performance was evaluated in the limit that the gravitational wave detector is fixed in space. However, the performance depends on certain symmetries in the armlengths that are available if the detector is fixed in space, but that will be broken in the actual rotating and flexing configuration produced by the LISA orbits. In this paper we investigate the performance of these TDI variables for the real LISA orbits. First, addressing the effects of rotation, we verify Daniel Shaddock's result that the Sagnac variables α(t), β(t) and γ(t) will not cancel out the laser phase noise, and we also find the same result for the symmetric Sagnac variable ζ(t). The loss of the latter variable would be particularly unfortunate since this variable also cancels out gravitational wave signal, allowing instrument noise in the detector to be isolated and measured. Fortunately, we have found a set of more complicated TDI variables, which we call Δ-Sagnac variables, one of which accomplishes the same goal as ζ(t) to good accuracy. Finally, however, as we investigate the effects of the flexing of the detector arms due to non-circular orbital motion, we show that all variables, including the interferometer variables, X(t), Y(t) and Z(t), which survive the rotation-induced loss of direction symmetry, will not completely cancel laser phase noise when the armlengths are changing with time. This unavoidable problem will place a stringent requirement on laser stability of ~5 Hz Hz−1/2.

https://iopscience.iop.org/article/10.1088/0264-9381/20/22/009/pdf

The Effects of orbital motion on LISA time delay interferometry

A determination of the masses of Ceres, Pallas, and Vesta from their perturbations upon the orbit of Mars

Currently proposed space-based gravitational wave detectors consist of satellite arrays deployed in an equilateral triangle either in the ecliptic plane or in a precessing plane tilted at 60° with respect to the ecliptic. This paper summarizes recent calculations of how well these two types of detectors can resolve the angular positions of two kinds of sources: low-mass compact binary sources and massive-black-hole binaries just before coalescence. Our results show that including higher-order post-Newtonian terms in the gravitational wavefunctions is important when predicting the angular resolution of ecliptic-plane detectors.

Ronald W. Hellings

Papers

Experimental test of the variability of G using Viking lander ranging data

Sensitivity curves for spaceborne gravitational wave interferometers

The Effects of orbital motion on LISA time delay interferometry

A determination of the masses of Ceres, Pallas, and Vesta from their perturbations upon the orbit of Mars

The angular resolution of space-based gravitational wave detectors