Graviton Compton Wavelength Research Articles

Bounds on graviton mass and constraining Yukawa-like gravitational potential from planetary motion in the solar system

In this study we used the observed perihelion precession of planetary orbits in the Solar System in order to constrain theory of Yukawa-type gravity, and to bound mass of graviton. For that purpose we assumed that the precession angles of the planets in Yukawa-type gravity should be equal to their observed values, as well as to the corresponding predictions of General Relativity (GR). Starting from these requests we constrain Yukawa-like gravitational potential. The obtained results showed that our estimates for the range of Yukawa interaction ? at the Solar System scales are in good agreement with recent experimental constrains. Assuming that the estimated value of the range of ? corresponds to the Compton wavelength of graviton ?1, we then estimate the upper bound for its mass m1. We found that these estimates were in agreement with our previous results obtained from the observed stellar orbits around the Galactic Center (GC).

The cosmic microwave background and mass power spectrum profiles for a novel and efficient model of dark energy


 
 
 In a previous work [1] it was shown that by considering the quantum nature of the gravitational field mediator, it is possible to introduce the momentum energy of the graviton into the Einstein equations as an effective cosmological constant. The Compton Mass Dark Energy (CMaDE) model proposes that this momentum can be interpreted as dark energy, with a Compton wavelength given by the size of the observable universe RH, implying that the dark energy varies depending on this size. The main result of this previous work is the existence of an effective cosmological constant Λ = 2π2/λ2 that varies very slowly, being λ = (c/H0)RH the graviton Compton wavelength. In the present work we use that the dark energy density rate is given by ΩΛ = 2π2/3/RH2 , it only has the curvature Ωk as a free constant and depends exclusively on the radiation rate Ωr. Using Ωr = 9.54×10−5, the theoretical prediction for a flat universe of the dark energy rate is ΩΛ = 0.6922. We perform a general study for a non-flat universe, using the Planck data and a modified version of the CLASS code we find an excellent concordance with the Cosmic Microwave Background and Mass Power Spectrum profiles, provided that the Hubble parameter today is H0 = 72.6 km/s/Mpc for an universe with curvature Ωk = −0.003. We conclude that the CMaDE model provides a natural explanation for the accelerated expansion and the coincidence problem of the universe.
 
 

New graviton mass bound from binary pulsars

In Einstein's general relativity, gravity is mediated by a massless metric field. The extension of general relativity to consistently include a mass for the graviton has profound implications for gravitation and cosmology. Salient features of various massive gravity theories can be captured by Galileon models, the simplest of which is the cubic Galileon. The presence of the Galileon field leads to additional gravitational radiation in binary pulsars where the Vainshtein mechanism is less suppressed than its fifth-force counterpart, which deserves a detailed confrontation with observations. We prudently choose fourteen well-timed binary pulsars, and from their intrinsic orbital decay rates we put a new bound on the graviton mass, $m_g \lesssim 2 \times 10^{-28}\,{\rm eV}/c^2$ at the 95% confidence level, assuming a flat prior on $\ln m_g$. It is equivalent to a bound on the graviton Compton wavelength $\lambda_g \gtrsim 7 \times 10^{21}\,{\rm m}$. Furthermore, we extensively simulate times of arrival for pulsars in orbit around stellar-mass black holes and the supermassive black hole at the Galactic center, and investigate their prospects in probing the cubic Galileon theory in the near future.

Bound on the graviton mass from Chandra x-ray cluster sample

We present new limits on the graviton Compton wavelength in a Yukawa potential using a sample of 12 relaxed galaxy clusters, for which the temperature and gas density profiles were derived by Vikhlinin et al (2006 Astrophys. J. 640 691) using Chandra x-ray observations. These limits can be converted to a bound on the graviton mass, assuming a non-zero graviton mass would lead to a Yukawa potential at these scales. For this purpose, we first calculate the total dynamical mass from the hydrostatic equilibrium equation in Yukawa gravity and then compare it with the corresponding mass in Newtonian gravity. We calculate a 90% c.l. lower/upper limit on the graviton Compton wavelength/ mass for each of the 12 clusters in the sample. The best limit is obtained for Abell 2390, corresponding to km or eV. This is the first proof of principles demonstration of setting a limit on the graviton mass using a sample of related galaxy clusters with x-ray measurements and can be easily applied to upcoming x-ray surveys such as eRosita.

Limit on graviton mass from galaxy cluster Abell 1689

To date, the only limit on graviton mass using galaxy clusters was obtained by Goldhaber and Nieto in 1974, using the fact that the orbits of galaxy clusters are bound and closed, and extend up to 580 kpc. From positing that only a Newtonian potential gives rise to such stable bound orbits, a limit on the graviton mass mg<1.1×10−29eV was obtained [1]. Recently, it has been shown that one can obtain closed bound orbits for Yukawa potential [2], thus invalidating the main ansatz used in Ref. [1] to obtain the graviton mass bound. In order to obtain a revised estimate using galaxy clusters, we use dynamical mass models of the Abell 1689 (A1689) galaxy cluster to check their compatibility with a Yukawa gravitational potential. We use the mass models for the gas, dark matter, and galaxies for A1689 from Refs. [3,4], who used this cluster to test various alternate gravity theories, which dispense with the need for dark matter. We quantify the deviations in the acceleration profile using these mass models assuming a Yukawa potential and that obtained assuming a Newtonian potential by calculating the χ2 residuals between the two profiles. Our estimated bound on the graviton mass (mg) is thereby given by, mg<1.37×10−29eV or in terms of the graviton Compton wavelength of, λg>9.1×1019km at 90% confidence level.

Tests of General Relativity with GW150914.

The LIGO detection of GW150914 provides an unprecedented opportunity to study the two-body motion of a compact-object binary in the large-velocity, highly nonlinear regime, and to witness the final merger of the binary and the excitation of uniquely relativistic modes of the gravitational field. We carry out several investigations to determine whether GW150914 is consistent with a binary black-hole merger in general relativity. We find that the final remnant's mass and spin, as determined from the low-frequency (inspiral) and high-frequency (postinspiral) phases of the signal, are mutually consistent with the binary black-hole solution in general relativity. Furthermore, the data following the peak of GW150914 are consistent with the least-damped quasinormal mode inferred from the mass and spin of the remnant black hole. By using waveform models that allow for parametrized general-relativity violations during the inspiral and merger phases, we perform quantitative tests on the gravitational-wave phase in the dynamical regime and we determine the first empirical bounds on several high-order post-Newtonian coefficients. We constrain the graviton Compton wavelength, assuming that gravitons are dispersed in vacuum in the same way as particles with mass, obtaining a 90%-confidence lower bound of 10^{13} km. In conclusion, within our statistical uncertainties, we find no evidence for violations of general relativity in the genuinely strong-field regime of gravity.

Testing general relativity with LISA including spin precession and higher harmonics in the waveform

We compute the accuracy at which a Laser Interferometer Space Antenna-like space-based gravitational wave detector will be able to observe deviations from general relativity in the low frequency approximation. To do so, we introduce six correction parameters that account for modified gravity in the second post-Newtonian gravitational wave phase for inspiralling supermassive black hole binaries with spin precession on quasicircular orbits. Our implementation can be regarded as a subset of the parametrized post-Einsteinian formalism developed by Yunes and Pretorius, being able to investigate also next-to-leading order effects. In order to find error distributions for the alternative theory parameters, we use the Fisher information formalism and carry out Monte Carlo simulations for 17 different binary black hole mass configurations in the range ${10}^{5}{M}_{\ensuremath{\bigodot}}&lt;M&lt;{10}^{8}{M}_{\ensuremath{\bigodot}}$ with ${10}^{3}$ randomly distributed points in the parameter space each, comparing the full (FWF) and restricted (RWF) versions of the gravitational waveform. We find that the binaries can roughly be separated into two groups: one with low ($\ensuremath{\lesssim}{10}^{7}{M}_{\ensuremath{\bigodot}}$) and one with high total masses ($\ensuremath{\gtrsim}{10}^{7}{M}_{\ensuremath{\bigodot}}$). The RWF errors on the alternative theory parameters are 2 orders of magnitude higher than the FWF errors for high-mass binaries while almost comparable for low-mass binaries. Because of dilution of the available information, the accuracy of the binary parameters is reduced by factors of a few, except for the luminosity distance, which is affected more seriously in the high-mass regime. As an application as well as to compare our research with previous work, we compute an optimal lower bound on the graviton Compton wavelength, which is increased by a factor of $\ensuremath{\sim}1.6$ when using the FWF.

Gravitational wave observations of galactic intermediate-mass black hole binaries with DECIGO path finder

DECIGO path finder is a space-borne gravitational wave (GW) detector with sensitivity in the frequency band 0.1–100 Hz. As a first step mission to DECIGO, it is aiming for launching in 2016–2017. Although its main objective is to demonstrate technology for GW observation in space, DPF still has a chance of detecting GW signals and performing astrophysical observations. With an observable range up to 50 kpc, its main targets are GW signals from galactic intermediate-mass black hole (IMBH) binaries. By using inspiral–merger–ringdown phenomenological waveforms, we perform both pattern-averaged analysis and Monte Carlo simulations including the effect of detector motion to find that the masses and (effective) spins of the IMBHs could be determined with errors of a few percent, should the signals be detected. Since GW signals from IMBH binaries with masses above 104M⊙ cannot be detected by ground-based detectors, these objects can be unique sources for DPF. If the inspiral signal of a 103M⊙ IMBH binary is detected with DPF, it can give alert to the ringdown signal for the ground-based detectors 102–103 s before coalescence. We also estimate the possible bound on the graviton Compton wavelength from a possible IMBH binary in ω Centauri. We obtain a slightly weaker constraint than that from the solar system experiment and an about two orders of magnitude stronger constraint than that from binary pulsar tests. Unfortunately, the detection rate of IMBH binaries is rather small.

Graviton mass bounds from space-based gravitational-wave observations of massive black hole populations

We study the bounds that space-based gravitational-wave detectors could realistically place on the graviton Compton wavelength ${\ensuremath{\lambda}}_{g}=h/({m}_{g}c)$ by observing multiple inspiralling black hole binaries. Observations of individual inspirals will yield mean bounds ${\ensuremath{\lambda}}_{g}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{15}$ km, but the combined bound from observing $\ensuremath{\sim}50$ events in a two-year mission is about ten times better: ${\ensuremath{\lambda}}_{g}\ensuremath{\simeq}3\ifmmode\times\else\texttimes\fi{}{10}^{16}$ km (${m}_{g}\ensuremath{\simeq}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}$ eV). The bound improves faster than the square root of the number of observed events, because typically a few sources provide constraints as much as three times better than the mean. This result is only mildly dependent on details of black hole formation and detector characteristics. The bound achievable in practice should be an order of magnitude better than this figure, because our calculations ignore the merger/ringdown portion of the waveform.

Erratum: Constraining alternative theories of gravity by gravitational waves from precessing eccentric compact binaries with LISA [Phys. Rev. DPRVDAQ1550-799881, 064008 (2010)10.1103/PhysRevD.81.064008

We calculate how strongly one can put constraints on alternative theories of gravity such as Brans-Dicke and massive graviton theories with LISA. We consider inspiral gravitational waves from a compact binary composed of a neutron star (NS) and an intermediate mass black hole (IMBH) in Brans-Dicke (BD) theory and that composed of 2 super massive black holes (SMBHs) in massive graviton theories. We use the restricted 2PN waveforms including the effects of spins. We also take both precession and eccentricity of the orbit into account. For simplicity, we set the fiducial value for the spin of one of the binary constituents to zero so that we can apply the approximation called \textit{simple precession}. We perform the Monte Carlo simulations of $10^4$ binaries, estimating the determination accuracy of binary parameters including the BD parameter $\omega_{\mathrm{BD}}$ and the Compton wavelength of graviton $\lambda_g$ for each binary using the Fisher matrix method. We find that including both the spin-spin coupling $\sigma$ and the eccentricity $e$ into the binary parameters reduces the determination accuracy by an order of magnitude for the Brans-Dicke case, whilst it has less influence on massive graviton theories. On the other hand, including precession enhances the constraint on $\omega_{\mathrm{BD}}$ only 20$%$ but it increases the constraint on $\lambda_g$ by an order of magnitude. Using a $(1.4+1000)M_{\odot}$ NS/BH binary of SNR=$\sqrt{200}$, one can put a constraint $\omega_{\mathrm{BD}}>6944$, whilst using a $(10^7+10^6)M_{\odot}$ BH/BH binary at 3Gpc, one can put $\lambda_g>3.06\times10^{21}$cm, on average. The latter is 4 orders of magnitude stronger than the one obtained from the solar system experiment. These results indicate that the effects of precession and eccentricity must be taken carefully in the parameter estimation analysis.

Effect of spin precession on bounding the mass of the graviton using gravitational waves from massive black hole binaries

Observations of gravitational waves from massive binary black hole systems at cosmological distances can be used to search for a dependence of the speed of propagation of the waves on wavelength, and thereby to bound the mass of a hypothetical graviton. We study the effects of precession of the spins of the black holes and of the orbital angular momentum on the process of parameter estimation based on the method of matched filtering of gravitational-wave signals vs. theoretical template waveforms. For the proposed space interferometer LISA, we show that precession, and the accompanying modulations of the gravitational waveforms, are effective in breaking degeneracies among the parameters being estimated, and effectively restore the achievable graviton-mass bounds to levels obtainable from binary inspirals without spin. For spinning, precessing binary black hole systems of equal masses 106 M⊙ at 3 Gpc, the lower bounds on the graviton Compton wavelength achievable are of the order of 5 × 1016 km.

Constraining alternative theories of gravity by gravitational waves from precessing eccentric compact binaries with LISA

We calculate how strongly one can put constraints on alternative theories of gravity such as Brans-Dicke and massive graviton theories with LISA. We consider inspiral gravitational waves from a compact binary composed of a neutron star and an intermediate mass black hole in Brans-Dicke (BD) theory and that composed of a super massive black hole in massive graviton theories. We use the restricted second post-Newtonian waveforms including the effects of spins. We also take both precession and eccentricity of the orbit into account. For simplicity, we set the fiducial value for the spin of one of the binary constituents to zero so that we can apply the approximation called simple precession. We perform the Monte Carlo simulations of ${10}^{4}$ binaries, estimating the determination accuracy of binary parameters including the BD parameter ${\ensuremath{\omega}}_{\mathrm{BD}}$ and the Compton wavelength of graviton ${\ensuremath{\lambda}}_{g}$ for each binary using the Fisher matrix method. We find that including both the spin-spin coupling $\ensuremath{\sigma}$ and the eccentricity $e$ into the binary parameters reduces the determination accuracy by an order of magnitude for the Brans-Dicke case, while it has less influence on massive graviton theories. On the other hand, including precession enhances the constraint on ${\ensuremath{\omega}}_{\mathrm{BD}}$ only 20% but it increases the constraint on ${\ensuremath{\lambda}}_{g}$ by several factors. Using a $(1.4+1000){M}_{\ensuremath{\bigodot}}$ neutron star/black hole binary of $\mathrm{SNR}=\sqrt{200}$, one can put a constraint ${\ensuremath{\omega}}_{\mathrm{BD}}&gt;6944$, while using a $({10}^{7}+{10}^{6}){M}_{\ensuremath{\bigodot}}$ black hole/black hole binary at 3 Gpc, one can put ${\ensuremath{\lambda}}_{g}&gt;3.10\ifmmode\times\else\texttimes\fi{}{10}^{21}\text{ }\text{ }\mathrm{cm}$, on average. The latter is 4 orders of magnitude stronger than the one obtained from the solar system experiment. These results are consistent with previous results within uncontrolled errors and indicate that the effects of precession and eccentricity must be taken carefully in the parameter estimation analysis.

Bounding the mass of the graviton with gravitational waves: Effect of spin precessions in massive black hole binaries

Observations of gravitational waves from massive binary black-hole systems at cosmological distances can be used to search for a dependence of the speed of propagation of the waves on wavelength, and thereby to bound the mass of a hypothetical graviton. We study the effects of precessions of the spins of the black holes and of the orbital angular momentum on the process of parameter estimation based on the method of matched filtering of gravitational-wave signals vs theoretical template waveforms. For the proposed Laser Interferometer Space Antenna, we show that precessions, and the accompanying modulations of the gravitational waveforms, are effective in breaking degeneracies among the parameters being estimated, and effectively restore the achievable graviton-mass bounds to levels obtainable from binary inspirals without spin. For spinning, precessing binary black-hole systems of equal masses ${10}^{6}{M}_{\ensuremath{\bigodot}}$ at 3 Gpc, the lower bounds on the graviton Compton wavelength achievable are of the order of $5\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{ }\text{ }\mathrm{km}$.

Do observations offer evidence for cosmological-scale extra dimensions?

We present a case that current observations may already indicate new gravitational physicson cosmological scales. The excess of power seen in the Lyman-α forest and small-scale CMB experiments, the anomalously largebulk flows seen both in peculiar velocity surveys and in kinetic SZ, and the higher ISW cross-correlation all indicate thatstructure may be more evolved than expected from ΛCDM. While these anomalies may constitute a statistical fluke or may eventually disappear as systematic effects are better understood, we argue that they can be explained in models with infinite-volume (or, at least, cosmological-size) extra dimensions, where the graviton is a resonance with a tiny width.The longitudinal mode of the graviton mediates an extra scalar force which speeds up structure formation at late times,thereby accounting for the above anomalies. The required graviton Compton wavelength is relatively small compared to the present Hubble radius,of order 300-600 Mpc. Moreover, with certain assumptions about the behavior of the longitudinal mode on super-Hubble scales, our modified gravity framework canalso alleviate the tension with the low quadrupole and the peculiar vanishing of the CMB correlation function on large angular scales, seen both in COBE and WMAP. This relies on a novel mechanism that cancels a late-time ISW contribution against the primordial Sachs-Wolfe amplitude.

Bounding the mass of the graviton with gravitational waves: effect of higher harmonics in gravitational waveform templates

Observations by laser interferometric detectors of gravitational waves from inspiraling compact binary systems can be used to search for a dependence of the waves' propagation speed on wavelength, and thereby to bound the mass or Compton wavelength of a putative graviton. We study the effect of including higher harmonics, as well as their post-Newtonian amplitude corrections, in the template gravitational waveforms employed in the process of parameter estimation using matched filtering. We consider the bounds that could be achieved using advanced LIGO, a proposed third generation instrument called an Einstein telescope and the proposed space interferometer LISA. We find that in all cases, the bounds on the graviton Compton wavelength are improved by almost an order of magnitude for higher masses when amplitude corrections are included.

Testing alternative theories of gravity using LISA

We investigate the possible bounds which could be placed on alternative theories of gravity using gravitational wave detection from inspiralling compact binaries with the proposed LISA space interferometer. Specifically, we estimate lower bounds on the coupling parameter ω of scalar–tensor theories of the Brans–Dicke type and on the Compton wavelength of the graviton λg in hypothetical massive graviton theories. In these theories, modifications of the gravitational radiation damping formulae or of the propagation of the waves translate into a change in the phase evolution of the observed gravitational waveform. We obtain the bounds through the technique of matched filtering, employing the LISA sensitivity curve generator (SCG), available online. For a non-spinning neutron star on a quasi-circular inspiral into a non-spinning 103M⊙ black hole in the Virgo Cluster, in a two-year integration, we find a lower bound ω > 3 × 105. For lower-mass black holes, the bound could be as large as 2 × 106. The bound is independent of LISA arm length, but is inversely proportional to the LISA position noise error, under the assumption that position error noise dominates laser shot noise. Lower bounds on the graviton Compton wavelength ranging from 1015 km to 5 × 1016 km can be obtained from one-year observations of massive binary black-hole inspirals at cosmological distances (3 Gpc) for masses ranging from 104 to 107M⊙. For the highest-mass systems (107M⊙), the bound is proportional to (LISA arm length)1/2 and to (LISA acceleration noise)−1/2. For the others, the bound is independent of these parameters because of the dominance of white-dwarf confusion noise in the relevant part of the frequency spectrum. These bounds improve and extend earlier work which used analytic formulae for the noise curves.

Bounding the mass of the graviton using gravitational-wave observations of inspiralling compact binaries

If gravitation is propagated by a massive field, then the velocity of gravitational waves (gravitons) will depend upon their frequency and the effective Newtonian potential will have a Yukawa form. In the case of inspiralling compact binaries, gravitational waves emitted at low frequency early in the inspiral will travel slightly slower than those emitted at high frequency later, modifying the phase evolution of the observed inspiral gravitational waveform, similar to that caused by post-Newtonian corrections to quadrupole phasing. Matched filtering of the waveforms can bound such frequency-dependent variations in propagation speed, and thereby bound the graviton mass. The bound depends on the mass of the source and on noise characteristics of the detector, but is independent of the distance to the source, except for weak cosmological redshift effects. For observations of stellar-mass compact inspiral using ground-based interferometers of the LIGO/VIRGO type, the bound on the graviton Compton wavelength is of the order of $6 \times 10^{12}$ km, about double that from solar-system tests of Yukawa modifications of Newtonian gravity. For observations of super-massive black hole binary inspiral at cosmological distances using the proposed laser interferometer space antenna (LISA), the bound can be as large as $6 \times 10^{16}$ km. This is three orders of magnitude weaker than model-dependent bounds from galactic cluster dynamics.