Imprints of relic gravitational waves on pulsar timing

Relic gravitational waves （RGWs）, a background originating during inflation, would leave imprints on pulsar timing residuals. This makes RGWs an important source for detection of RGWs using the method of pulsar timing. In this paper, we discuss the effects of RGWs on single pulsar timing, and quantitatively analyze the timing residuals caused by RGWs with different model parameters. In principle, if the RGWs are strong enough today, they can be detected by timing a single millisecond pulsar with high precision after the intrinsic red noises in pulsar timing residuals are understood, even though simultaneously observing multiple millisecond pulsars is a more powerful technique for extracting gravitational wave signals. We correct the normalization of RGWs using observations of the cosmic microwave background （CMB）, which leads to the amplitudes of RGWs being reduced by two orders of magnitude or so compared to our previous works. We obtained new constraints on RGWs using recent observations from the Parkes Pulsar Timing Array, employing the tensor-to-scalar ratio r = 0.2 due to the tensor-type polarization observations of CMB by BICEP2 as a reference value, even though its reliability has been brought into question. Moreover, the constraints on RGWs from CMB and Big Bang nucleosynthesis will also be discussed for comparison.

Detecting Very-High-Frequency Relic Gravitational Waves by a Waveguide

The polarization vector （PV） of an electromagnetic wave （EW） will experience a rotation in a region of spacetime perturbed by gravitational waves （GWs）. Based on this consideration, Cruise＇s group has built an annular waveguide to detect GWs. We give detailed calculations of the rotations of polarization vector of an EW caused by incident GWs from various directions and in various polarization states, and then analyze the accumulative effects on the polarization vector when the EW passes n cycles along the annular waveguide. We reexamine the feasibility and limitation of this method to detect GWs of high frequency around 100 MHz, in particular the relic gravitational waves （RGWs）. By comparing the spectrum of RGWs in the accelerating universe with the detector sensitivity of the current waveguide, it is found that the amplitude of the RGWs is too low to be detected by the waveguide detectors currently operating. Possible ways of improvements on detection are suggested.

Gravitational waves from compact objects

Large ground-based laser beam interferometers are presently in operation both in the USA （LIGO） and in Europe （VIRGO） and potential sources that might be detected by these instruments are revisited. The present generation of detectors does not have a sensitivity high enough to probe a significant volume of the universe and, consequently, predicted event rates are very low. The planned advanced generation of interferometers will probably be able to detect, for the first time, a gravitational sig- nal. Advanced LIGO and EGO instruments are expected to detect few （some）： binary coalescences consisting of either two neutron stars, two black holes or a neutron star and a black hole. In space, the sensitivity of the planned LISA spacecraft constellation will allow the detection of the gravitational signals, even within a ＂pessimistic＂ range of possible signals, produced during the capture of compact objects by supermassive black holes, at a rate of a few tens per year.

Optical gravitational wave detectors on the ground and in space:theory and technology

Major predictions of General Relativity, unforeseen at the beginning of the preceding century, are now under investigation. The existence of black holes of any mass from tens to billions of solar masses is now established, and the physics around these objects begins to be studied through direct observations in a wide electromagnetic spectrum from visible light to X-rays. General relativity, however, provides an extra medium which carries more information on the regions of intense gravitational field, namely gravitational waves （GWs）. Due to their extremely weak coupling to matter, GWs are precisely generated in those regions of spacetime undergoing strong curvature, which is very exciting for modern astrophysics. On the other hand, this weak coupling makes it difficult for GWs to cause appreciable effects in human made instruments. This is why technology of GW detectors took such a long time to reach a sensitivity level consistent with GW amplitudes predicted by theoretical models of sources. In the present status, apart from resonant solid detectors, two large interferometric antennas （LIGO in the USA and the French-Italian Virgo） are beginning to produce data, and a joint ESA-NASA space mission, resulting from a wide effort of European and American groups, is reaching a crucial approval phase. The aim of the present review is to give the theoretical bases of GW detectors using light.

Past,present and future of the Resonant-Mass gravitational wave detectors

Resonant-mass gravitational wave detectors are reviewed from the concept of gravitational waves and its mathematical derivation, using Einstein＇s general relativity, to the present status of bars and spherical detectors, and their prospects for the future, which include dual detectors and spheres with non-resonant transducers. The review not only covers technical aspects of detectors and sciences that will be done, but also analyzes the subject in a historical perspective, covering the various detection efforts over four decades, starting from Weber＇s pioneering work.

The astrophysical gravitational wave stochastic background

A stochastic background of gravitational waves with astrophysical origins may have＇resulted from the superposition of a large number of unresolved sources since the beginning of stellar activity. Its detection would put very strong constraints on the physical properties of compact objects, the initial mass function and star for- marion history. On the other hand, it could be a ＇noise＇ that would mask the stochastic background of its cosmological origin. We review the main astrophysical processes which are able to produce a stochastic background and discuss how they may differ from the primordial contribution in terms of statistical properties. Current detection methods are also presented.

Sensitivity function analysis of gravitational wave detection with single-laser and large-momentum-transfer atomic sensors

Recently, a configuration using atomic interferometers （AIs） had been sug- gested for the detection of gravitational waves. A new AI with some additional laser pulses for implementing large momentum transfer was also put forward, in order to reduce the effect of shot noise and laser frequency noise. We use a sensitivity function to analyze all possible configurations of the new AI and to distinguish how many mo- menta are transferred in a specific configuration. By analyzing the new configuration, we further explore a detection scheme for gravitational waves, in particular, that ame- liorates laser frequency noise. We find that the amelioration occurs in such a scheme, but novelly, in some cases, the frequency noise can be canceled completely by using a proper data processing method.

Long-term evolution and gravitational wave radiation of neutron stars with differential rotation induced by r-modes

In a second-order r-mode theory, Sa and Tome found that the r-mode oscillation in neutron stars （NSs） could induce stellar differential rotation, which naturally leads to a saturated state of the oscillation. Based on a consideration of the coupling of the r-modes and the stellar spin and thermal evolution, we carefully investigate the influences of the differential rotation on the long-term evolution of isolated NSs and NSs in low-mass X-ray binaries, where the viscous damping of the r-modes and its resultant effects are taken into account. The numerical results show that, for both kinds of NSs, the differential rotation can significantly prolong the duration of the r-modes. As a result, the stars can keep nearly a constant temperature and constant angular velocity for over a thousand years. Moreover, the persistent radiation of a quasi-monochromatic gravitational wave would also be predicted due to the long-term steady r-mode oscillation and stellar rotation. This increases the detectability of gravitational waves from both young isolated and old accreting NSs.

Pulsar timing residuals due to individual non-evolving gravitational wave sources

The pulsar timing residuals induced by gravitational waves from non- evolving single binary sources are affected by many parameters related to the relative positions of the pulsar and the gravitational wave sources. We will analyze the various effects due to different parameters. The standard deviations of the timing residuals will be calculated with a variable parameter fixing a set of other parameters. The or- bits of the binary sources will be generally assumed to be elliptical. The influences of different eccentricities on the pulsar timing residuals will also be studied in detail. We find that the effects of the related parameters are quite different, and some of them display certain regularities.

A multi-wavelength study of the gravitational lens COSMOS J095930+023427

We present a multi-wavelength study of the gravitational lens COSMOS J095930＋023427 （Zl = 0.892）, together with the associated galaxy group along the line of sight located at z 0.7, and the lensed background galaxy. The source redshift is currently unknown, but estimated to be at zs ~ 2. This analysis is based on publicly available HST, Subaru and Chandra imaging data, as well as VLT spectroscopy. The lensing system is an early-type galaxy showing a strong [OII] emission line, and pro- duces four bright images of the distant background source. It has an Einstein radius of 0.79＂, about four times larger than the effective radius. We perform a lensing anal- ysis using both a singular isothermal ellipsoid and a peudo-isothermal elliptical mass distribution for the lensing galaxy, and find that the final results on the total mass, the dark matter （DM） fraction within the Einstein radius and the external shear due to a foreground galaxy group are robust with respect to the choice of the parametric model and the source redshift （yet unknown）. We measure the luminous mass from the pho- tometric data, and find the DM fraction within the Einstein radius fDM to be between 0.71 ~ 0.13 and 0.79 ~ 0.15, depending on the unknown source redshift. Meanwhile, the non-null external shear found in our lensing models supports the presence and structure of a galaxy group at z ~ 0.7, and an independent measurement of the 0.5- 2 keV X-ray luminosity within 20＂ around the X-ray centroid provides a group mass of M = （3 - 10） x 1013 Mo, in good agreement with the previous estimate derived through weak lensing analysis. Finally, by inverting the HST/ACS/814 image with the lensing equation, we obtain the reconstructed image of the magnified source galaxy, which has a scale of about 3.3 kpc at z~ = 2 （2.7 kpc at zs = 4） and the typical disturbed disk-like appearance observed in low-mass star-forming galaxies at z ~ 3. However, deep, spatially resolved spectroscopic data for similar lensed sources are still required to detect the first stage of galaxy evolution, since the available spectrum shows no clear features due to the background source.

Discovery of four gravitational lensing systems by clusters in the SDSS DR6

We report the discovery of 4 strong gravitational lensing systems by visual inspections of the Sloan Digital Sky Survey images of galaxy clusters in Data Release 6 （SDSS DR6）. Two of the four systems show Einstein rings while the others show tangen- tial giant arcs. These arcs or rings have large angular separations （〉 8″） from the bright central galaxies and show bluer color compared with the red cluster galaxies. In addition, we found 5 probable and 4 possible lenses by galaxy clusters.

Astrophysical applications of gravitational microlensing

Since the first discovery of microlensing events nearly two decades ago, gravitational microlensing has accumulated tens of TBytes of data and developed into a powerful astrophysical technique with diverse applications. The review starts with a theoretical overview of the field and then proceeds to discuss the scientific highlights. （1） Microlensing observations toward the Magellanic Clouds rule out the Milky Way halo being dominated by MAssive Compact Halo Objects （MACHOs）. This confirms most dark matter is non-baryonic, consistent with other observations. （2） Microlensing has discovered about 20 extrasolar planets （16 published）, including the first two Jupiter-Saturn like systems and the only five ＂cold Neptunes＂ yet de- tected. They probe a different part of the parameter space and will likely provide the most stringent test of core accretion theory of planet formation. （3） Microlensing pro- vides a unique way to measure the mass of isolated stars, including brown dwarfs and normal stars. Half a dozen or so stellar mass black hole candidates have also been pro- posed. （4） High-resolution, target-of-opportunity spectra of highly-magnified dwarf stars provide intriguing ＂age＂ determinations which may either hint at enhanced he- lium enrichment or unusual bulge formation theories. （5） Microlensing also measured limb-darkening profiles for close to ten giant stars, which challenges stellar atmo- sphere models. （6） Data from surveys also provide strong constraints on the geometry and kinematics of the Milky Way bar （through proper motions）; the latter indicates predictions from current models appear to be too anisotropic compared with observa- tions. The future of microlensing is bright given the new capabilities of current surveys and forthcoming new telescope networks from the ground and from space. Some open issues in the field are identified and briefly discussed.

Cusp-core problem and strong gravitational lensing

Cosmological numerical simulations of galaxy formation have led to the cuspy density profile of a pure cold dark matter halo toward the center, which is in sharp contradiction with the observations of the rotation curves of cold dark matter-dominated dwarf and low surface brightness disk galaxies, with the latter tending to favor mass profiles with a flat central core. Many efforts have been devoted to resolving this cusp-core problem in recent years, among them, baryon-cold dark matter interactions are considered to be the main physical mechanisms erasing the cold dark matter （CDM） cusp into a flat core in the centers of all CDM halos. Clearly, baryon-cold dark matter interactions are not customized only for CDM-dominated disk galaxies, but for all types, including giant ellipticals. We first fit the most recent high resolution observations of rotation curves with the Burkert profile, then use the constrained core size-halo mass relation to calculate the lensing frequency, and compare the predicted results with strong lensing observations. Unfortunately, it turns out that the core size constrained from rotation curves of disk galaxies cannot be extrapolated to giant ellipticals. We conclude that, in the standard cosmological paradigm, baryon-cold dark matter interactions are not universal mechanisms for galaxy formation, and therefore, they cannot be true solutions to the cusp-core problem.

Preliminary limits of a logarithmic correction to the Newtonian gravitational potential in binary pulsars

We obtain preliminary limits on a logarithmic correction to the Newtonian gravitational potential by using five binary pulsars： PSR J0737-3039, PSR B 1534＋12, PSR J 1756-2251, PSR B 1913＋ 16 and PSR B2127＋ 11C. This kind of correction may originate from fundamental frameworks, like string theories, effective models of grav- ity due to quantum effects and the non-local gravity scheme. We estimate the upper limit of the Tohline-Kuhn-Kruglyak parameter A and the lower limit of the Fabris- Campos parameter α, which parameterize the correction and are connected to each other by αλ = -1. By analyzing the advances of periastron of these binary pulsars, we find that the preliminary upper limit of a is 0.19 ± 0.14 kpc^-1 and the prelimi- nary lower limit of ）, is -5.2 4± 3.8 kpc. They are compatible with the bounds based on dynamics of spiral galaxies but quite different from those given by solar system dynamics. These results indicate that this logarithmic correction might be more ob- servable in current timings of binary pulsars than in motions of the solar system.

Neutron star mass-radius relation with gravitational field shielding by a scalar field

The currently well-developed models for equations of state （EoSs） have been severely impacted by recent measurements of neutron stars with a small radius and/or large mass. To explain these measurements, the theory of gravitational field shielding by a scalar field is applied. This theory was recently developed in accor- dance with the five-dimensional （5D） fully covariant Kaluza-Klein （KK） theory that has successfully unified Einstein＇s general relativity and Maxwell＇s electromagnetic theory. It is shown that a massive, compact neutron star can generate a strong scalar field, which can significantly shield or reduce its gravitational field, thus making it more massive and more compact. The mass-radius relation developed under this type of modified gravity can be consistent with these recent measurements of neutron stars. In addition, the effect of gravitational field shielding helps explain why the supernova explosions of some very massive stars （e.g.9 40 MQ as measured recently） actually formed neutron stars rather than black holes as expected. The EoS models, ruled out by measurements of small radius and/or large mass neutron stars according to the the- ory of general relativity, can still work well in terms of the 5D fully covariant KK theory with a scalar field.

Mass to light ratio of galaxies and gravitational lensing

We investigate the potential of constraining the mass to light ratio of field galaxies using weak lensing shear and flexions. A suite of Monte Carlo simulations are used to generate weak lensing observations with different noise models. Using mock data, we find that the inclusion of flexions can improve the estimate of foreground halo parameters, but the details are strongly dependent on noise in the model. In the intrinsic noise limit, both shear and flexions are promising tools to study the mass to light ratio of galaxies. However, if the noise model of flexions follows the form described by Rowe et al., there is only - 5% improvement in the constraints even with next generation lensing observations.

Gravitational lensing properties of an isothermal universal halo profile

N-body simulations predict that dark matter halos with different mass scales are described by a universal model, the Navarro-Frenk-White （NFW） den- sity profiles. As a consequence of baryonic cooling effects, these halos will become more concentrated, and similar to an isothermal sphere over a large range in radii （～ 300 h-1 kpc）. The singular isothermal sphere （SIS） model however has to be trun- cated artificially at large radii since it extends to infinity. We model a massive galaxy halo as a combination of an isothermal sphere and an NFW density profile. We give an approximation for the mass concentration at different baryon fractions and present exact expressions for the weak lensing shear and flexion for such a halo. We compare the lensing properties with the SIS and NFW profiles. We find that the combined pro- file can generate higher order lensing signals at small radii and is more efficient in generating strong lensing events. In order to distinguish such a halo profile from the SIS or NFW profiles, one needs to combine strong and weak lensing constraints for small and large radii.

Probing the dark side of the Universe with weak gravitational lensing effects

Arising from gravitational deflections of light rays by large-scale struc- tures in the Universe, weak-lensing effects have been recognized as one of the most important probes in cosmological studies. In this paper, we review the main progress in weak-lensing analyses, and discuss the challenges in future investigations aiming to understand the dark side of the Universe with unprecedented precisions.

Mysteries of the geometrization of gravitation

As we now know, there are at least two major difficulties with general rel- ativity （GR）. The first one is related to its incompatibility with quantum mechanics, in the absence of a consistent, widely accepted theory that combines the two theo- ries. The second problem is related to the requirement of the dark sectors-inflaton, dark matter and dark energy by the energy-stress tensor, which are needed to explain a variety of astronomical and cosmological observations. Research has indicated that the dark sectors themselves do not have any non-gravitational or laboratory evidence. Moreover, the dark energy poses, in addition, a serious confrontation between funda- mental physics and cosmology. Guided by theoretical and observational evidences, we are led to an idea that the source of gravitation and its manifestation in GR should be modified. The result is in striking agreement with not only the theory, but also the ob- servations, without requiring the dark sectors of the standard approach. Additionally, it provides natural explanations to some unexplained puzzles.

New upper limits on deviation from the inverse-square law of gravity in the solar system:a Yukawa parameterization

New physics beyond the standard model of particles might cause deviation from the inverse-square law of gravity. In many theoretical models of modified gravity, it is parameterized by the Yukawa correction to the Newtonian gravitational force in terms of two parameters α and λ. Here α is a dimensionless strength parameter and A is a length scale. Using the supplementary advances in perihelia provided by INPOP10a and EPM2011 ephemerides, we obtain new upper limits on the deviation from the inverse-square law when the uncertainty of the Sun＇s quadrupole moment is taken into account. We find that INPOP10a yields the upper limits as α =- 3.1× 10-11 and λ= 0.15 au, and EPM2011 gives α = 5.2 × 10-11 and λ=- 0.21 au. In both of them, α is at least 10 times less than the previous results.