Violation Of Weak Equivalence Principle Research Articles

Weak equivalence principle violation for mixed scalar particles

We investigate the non-relativistic limit of the Klein–Gordon equation for mixed scalar particles and show that, in this regime, one unavoidably arrives at redefining the particle’s inertial mass. This happens because, in contrast to the case when mixing is absent, the antiparticle sector contribution cannot be neglected for particles with definite flavor. To clearly demonstrate this feature, we adopt the Feshbach–Villars formalism for Klein–Gordon particles. Furthermore, within the same framework, we also demonstrate that, in the presence of a weak gravitational field, the mass parameter that couples to gravity (gravitational mass) does not match the effective inertial mass. This, in turn, implies a violation of the weak equivalence principle. Finally, we prove that the Bargmann’s superselection rule, which prohibits oscillating particles on the basis of the Galilean transformation, is incompatible with the non-relativistic limit of the Lorentz transformation and hence does not collide with the results obtained.

Consistent constraints on the equivalence principle from localized fast radio bursts

ABSTRACT Fast radio bursts (FRBs) are short astrophysical transients of extragalactic origin. Their burst signal is dispersed by the free electrons in the large-scale-structure (LSS), leading to delayed arrival times at different frequencies. Another potential source of time delay is the well known Shapiro delay, which measures the space–space and time–time metric perturbations along the line-of-sight. If photons of different frequencies follow different trajectories, i.e. if the universality of free fall guaranteed by the weak equivalence principle (WEP) is violated, they would experience an additional relative delay. This quantity, however, is not observable at the background level as it is not gauge independent, which has led to confusion in previous papers. Instead, an imprint can be seen in the correlation between the time delays of different pulses. In this paper, we derive robust and consistent constraints from twelve localized FRBs on the violation of the WEP in the energy range between 4.6 and 6 meV. In contrast to a number of previous studies, we consider our signal to be not in the model, but in the covariance matrix of the likelihood. To do so, we calculate the covariance of the time delays induced by the free electrons in the LSS, the WEP breaking terms, the Milky Way and host galaxy. By marginalizing both host galaxy contribution and the contribution from the free electrons, we find that the parametrized post-Newtonian parameter γ characterizing the WEP violation must be constant in this energy range to 1 in 1013 at 68 per cent confidence. These are the tightest constraints to-date on Δγ in this low-energy range.

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.

MICROSCOPE. mission analysis, requirements and expected performance

The MICROSCOPE mission aimed to test the weak equivalence principle (WEP) to a precision of 10−15. The WEP states that two bodies fall at the same rate on a gravitational field independently of their mass or composition. In MICROSCOPE, two masses of different compositions (titanium and platinum alloys) are placed on a quasi-circular trajectory around the Earth. They are the test-masses of a double accelerometer. The measurement of their accelerations is used to extract a potential WEP violation that would occur at a frequency defined by the motion and attitude of the satellite around the Earth. This paper details the major drivers of the mission leading to the specification of the major subsystems (satellite, ground segment, instrument, orbit…). Building upon the measurement equation, we derive the objective of the test in statistical and systematic error allocation and provide the mission’s expected error budget.

Investigating the environmental dependence of ultralight scalar dark matter with atom interferometers

We study the environmental dependence of ultralight scalar dark matter (DM) with linear interactions to the standard model particles. The solution to the DM field turns out to be a sum of the cosmic harmonic oscillation term and the local exponential fluctuation term. The amplitude of the first term depends on the local DM density and the mass of the DM field. The second term is induced by the local distribution of matter, such as the Earth. And it depends not only on the mass of the Earth, but also the density of the Earth. Then, we compute the phase shift induced by the DM field in atom interferometers (AIs), through solving the trajectories of atoms. Especially, the AI signal for the violation of weak equivalence principle (WEP) caused by the DM field is calculated. Depending on the values of the DM coupling parameters, contributions to the WEP violation from the first and second terms of the DM field can be either comparable or one larger than the other. Finally, we give some constraints to DM coupling parameters using results from the terrestrial atomic WEP tests.

Upper limits on Einstein’s weak equivalence principle placed by uncertainties of dispersion measures of fast radio bursts

Fast radio bursts (FRBs) are astronomical transients with millisecond timescales occurring at cosmological distances. The observed time lag between different energies of each FRB is well described by the inverse-square law of the observed frequency, i.e., dispersion measure. Therefore, FRBs provide one of the ideal laboratories to test Einstein's weak equivalence principle (WEP): the hypothetical time lag between photons with different energies under a gravitational potential. If WEP is violated, such evidence should be exposed within the observational uncertainties of dispersion measures, unless the WEP violation also depends on the inverse-square of the observed frequency. In this work, we constrain the difference of gamma parameters ($\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}$) between photons with different energies using the observational uncertainties of FRB dispersion measures, where $\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}=0$ for Einstein's general relativity. Adopting the averaged `Shapiro time delay' for cosmological sources, FRB 121002 at $z=1.6\ifmmode\pm\else\textpm\fi{}0.3$ and FRB $180817.\mathrm{J}1533+42$ at $z=1.0\ifmmode\pm\else\textpm\fi{}0.2$ place the most stringent constraints of $\mathrm{log}\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}<\ensuremath{-}20.8\ifmmode\pm\else\textpm\fi{}0.1$ and $\mathrm{log}(\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}/{r}_{E})<\phantom{\rule{0ex}{0ex}}\ensuremath{-}20.9\ifmmode\pm\else\textpm\fi{}0.2$, respectively, where ${r}_{E}$ is the energy ratio between the photons. The former is about three orders of magnitude lower than those of other astrophysical sources in previous works under the same formalization of the Shapiro time delay while the latter is comparable to the tightest constraint so far.

Fisher information and the weak equivalence principle of a quantum particle in a gravitational wave

We show that the weak equivalence principle (WEP) is violated for a quantum particle in a gravitational wave (GW) background, in the sense that extra mass information can be extracted in the presence of the GW. We quantify the degree of violation with the Fisher information of mass. This provides a precise characterisation of WEP violation by quantum systems in a GW, that should be useful in formalising other works that have argued for such violations heuristically.

Systematic error suppression scheme of the weak equivalence principle test by dual atom interferometers in space based on spectral correlation* *Project supported by the National Natural Science Foundation of China (Grants No. 11947057), the Foundation for Distinguished Young Scientist of Jiangxi Province, China (Grant No. 2016BCB23009), and the Postdoctoral Applied Research Program of Qingdao City, Shandong Province, China (Grant No.

Systematic error suppression and test data processing are very important in improving the accuracy and sensitivity of the atom interferometer (AI)-based weak-equivalence-principle (WEP) test in space. Here we present a spectrum correlation method to investigate the test data of the AI-based WEP test in space by analyzing the characteristics of systematic errors and noises. The power spectrum of the Eötvös coefficient η, systematic errors, and noises in AI-based WEP test in space are analyzed and calculated in detail. By using the method, the WEP violation signal is modulated from direct current (DC) frequency band to alternating current (AC) frequency band. We find that the signal can be effectively extracted and the influence of systematic errors can be greatly suppressed by analyzing the power spectrum of the test data when the spacecraft is in an inertial pointing mode. Furthermore, the relation between the Eötvös coefficient η and the number of measurements is obtained under certain simulated parameters. This method will be useful for both isotopic and nonisotopic AI-based WEP tests in space.

Constraints on neutrino speed, weak equivalence principle violation, Lorentz invariance violation, and dual lensing from the first high-energy astrophysical neutrino source TXS 0506+056

We derive stringent constraints on neutrino speed, weak equivalence principle violation, Lorentz invariance violation, and dual lensing from the first high-energy astrophysical neutrino source: TXS 0506+056. Observation of neutrino (IceCube-170922A) and photons in a similar time frame and from the same direction is used to derive these limits. We describe ways in which these constraints can be further improved by orders of magnitude.

Precision test of the weak equivalence principle from gamma-ray burst polarization

If the weak equivalence principle (WEP) is broken, the measured values of the parametrized post-Newtonian parameter $\gamma$ from photons with left- and right-handed circular polarizations should differ slightly, leading to the arrival-time difference of these two circular components. Thus, the polarization vector of a linearly polarized light may rotate during the propagation. The rotation angle of the polarization vector depends on both the photon energy and the distance of the source. It is believed that if the rotation angle differs by more than $\pi/2$ over an energy range, then the net polarization of the signal would be significantly suppressed and could not be as high as the observed level. Thus, the detection of highly polarized photons implies that the relative rotation angle ($\Delta\Theta$) should not be too large. In this paper, we give a detailed calculation on the evolution of gamma-ray burst (GRB) polarization arising from a possible violation of the WEP, and we find that more than $60\%$ of the initial polarization degree can be conserved even if $\Delta\Theta$ is larger than $\pi/2$. In addition, to tightly constrain the WEP violation, GRBs with harder spectra and polarization observations in a wider energy range seem to be favored. Applying our formulas to the measurements of linear polarization from GRB 110721A and GRB 061122, we obtain strict limits on the differences of the $\gamma$ values as low as $\Delta\gamma<1.3\times10^{-33}$ and $\Delta\gamma<0.8\times10^{-33}$. These provide the most stringent limits to date on a deviation from the WEP, improving at least 6 orders of magnitude over previous bounds.

Constraints on differential Shapiro delay between neutrinos and photons from IceCube-170922A

On 22nd September 2017, the IceCube Collaboration detected a neutrino with energy of about 290 TeV from the direction of the gamma-ray blazar TXS 0506+056, located at a distance of about 1.75 Gpc. During the same time, enhanced gamma-ray flaring was also simultaneously observed from multiple telescopes, giving rise to only the second coincident astrophysical neutrino/photon observation after SN 1987A. We point out that for this event, both neutrinos and photons encountered a Shapiro delay of about 6300 days along the way from the source. From this delay and the relative time difference between the neutrino and photon arrival times, one can constrain violations of Einstein’s Weak Equivalence Principle (WEP) for TeV neutrinos. We constrain such violations of WEP using the Parameterized Post-Newtonian (PPN) parameter gamma , which is given by |gamma _mathrm{{nu }}-gamma _{mathrm{EM}}|<5.5 times 10^{-2}, after assuming time difference of 175 days between neutrino and photon arrival times.

Fine-structure constant constraints on late-time dark energy transitions

We use recent astrophysical and local tests of the stability of the fine-structure constant, α, to constrain a particular phenomenological but physically motivated class of models in which the dark energy equation of state can undergo a rapid transition at low redshifts, perhaps associated with the onset of the acceleration phase. We set constraints on the phenomenological parameters describing such possible transitions, in particular improving previous constraints (which used only cosmological data) on the present-day value of the dark energy equation of state in these models. We specifically quantify how these constraints are improved by the addition of the α measurements. We find no evidence for a transition associated with the onset of acceleration. In this model the α measurements lead to a bound on Weak Equivalence Principle violations of η<4×10−15 (at 68.3% confidence level), improving on the recent MICROSCOPE bound by about a factor of three.

Astrometric test of the weak equivalence principle

Weak equivalence principle (WEP) is, for the first time, tested by astrometry on quasars in the sky measured in two wavelengths. Compared to previous WEP tests based on the Shapiro time delay of massless particles, this one has profound superiority that nearly 1,700 quasars with best measured positions commonly in the optical and radio bands are available. It ensures that, among the tests with photons, this one can give the most significantly robust bound on possible violation of WEP.

A New Method to Test the Einstein’s Weak Equivalence Principle

Abstract The Einstein’s weak equivalence principle (WEP) is one of the foundational assumptions of general relativity and some other gravity theories. In the theory of parametrized post-Newtonian (PPN), the difference between the PPN parameters γ of different particles or the same type of particle with different energies, Δγ, represents the violation of WEP. Current constraints on Δγ are derived from the observed time delay between correlated particles of astronomical sources. However, the observed time delay is contaminated by other effects, such as the time delays due to different particle emission times, the potential Lorentz invariance violation, and none-zero photon rest mass. Therefore, current constraints are only upper limits. Here, we propose a new method to test WEP based on the fact that the gravitational time delay is direction-dependent while others are not. This is the first method that can naturally correct other time-delay effects. Using the time-delay measurements of BASTE gamma-ray burst sample and the gravitational potential of local super galaxy cluster Laniakea, we find that the constraint on Δγ of different energy photons can be as low as 10−14. In the future, if more gravitational wave events and fast radio bursts with much more precise time-delay measurements are observed, this method can give a reliable and tight constraint on WEP.

GW170817 falsifies dark matter emulators

On August 17, 2017 the LIGO interferometers detected the gravitational wave (GW) signal (GW170817) from the coalescence of binary neutron stars. This signal was also simultaneously seen throughout the electromagnetic (EM) spectrum from radio waves to gamma-rays. We point out that this simultaneous detection of GW and EM signals rules out a class of modified gravity theories, termed ``dark matter emulators,'' which dispense with the need for dark matter by making ordinary matter couple to a different metric from that of GW. We discuss other kinds of modified gravity theories which dispense with the need for dark matter and are still viable. This simultaneous observation also provides the first observational test of Einstein's Weak Equivalence Principle (WEP) between gravitons and photons. We estimate the Shapiro time delay due to the gravitational potential of the total dark matter distribution along the line of sight (complementary to the calculation in arXiv:1710.05834) to be about 400 days. Using this estimate for the Shapiro delay and from the time difference of 1.7 seconds between the GW signal and gamma-rays, we can constrain violations of WEP using the parameterized post-Newtonian (PPN) parameter $\gamma$, and is given by $|\gamma_{\rm {GW}}-\gamma_{\rm{EM}}|<9.8 \times 10^{-8}$.

Fisher matrix forecasts for astrophysical tests of the stability of the fine-structure constant

We use Fisher Matrix analysis techniques to forecast the cosmological impact of astrophysical tests of the stability of the fine-structure constant to be carried out by the forthcoming ESPRESSO spectrograph at the VLT (due for commissioning in late 2017), as well by the planned high-resolution spectrograph (currently in Phase A) for the European Extremely Large Telescope. Assuming a fiducial model without α variations, we show that ESPRESSO can improve current bounds on the Eötvös parameter—which quantifies Weak Equivalence Principle violations—by up to two orders of magnitude, leading to stronger bounds than those expected from the ongoing tests with the MICROSCOPE satellite, while constraints from the E-ELT should be competitive with those of the proposed STEP satellite. Should an α variation be detected, these measurements will further constrain cosmological parameters, being particularly sensitive to the dynamics of dark energy.

Dealing with missing data in the MICROSCOPE space mission: An adaptation of inpainting to handle colored-noise data

The MICROSCOPE space mission, launched on April 25, 2016, aims to test the weak equivalence principle (WEP) with a 10^-15 precision. To reach this performance requires an accurate and robust data analysis method, especially since the possible WEP violation signal will be dominated by a strongly colored noise. An important complication is brought by the fact that some values will be missing -therefore, the measured time series will not be strictly regularly sampled. Those missing values induce a spectral leakage that significantly increases the noise in Fourier space, where the WEP violation signal is looked for, thereby complicating scientific returns. Recently, we developed an inpainting algorithm to correct the MICROSCOPE data for missing values. This code has been integrated in the official MICROSCOPE data processing pipeline because it enables us to significantly measure an equivalence principle violation (EPV) signal in a model-independent way, in the inertial satellite configuration. In this work, we present several improvements to the method that may allow us now to reach the MICROSCOPE requirements for both inertial and spin satellite configurations. The main improvement has been obtained using a prior on the power spectrum of the colored-noise that can be directly derived from the incomplete data. We show that after reconstructing missing values with this new algorithm, a least-squares fit may allow us to significantly measure an EPV signal with a 0.96x10^-15 precision in the inertial mode and 1.2x10^-15 precision in the spin mode. Although, the inpainting method presented in this paper has been optimized to the MICROSCOPE data, it remains sufficiently general to be used in the general context of missing data in time series dominated by an unknown colored-noise. The improved inpainting software, called ICON, is freely available at http://www.cosmostat.org/software/icon.

Weak-Equivalence Principle Violation and Mass Change of Charged Matter Due to Vacuum Polarization

Weak-Equivalence Principle Violation and Mass Change of Charged Matter Due to Vacuum Polarization

Status of MICROSCOPE, a mission to test the Equivalence Principle in space

MICROSCOPE is a French Space Agency mission that aims to test the Weak Equivalence Principle in space down to an accuracy of 10-15. This is two orders of magnitude better than the current constraints, which will allow us to test General Relativity as well as theories beyond General Relativity which predict a possible Weak Equivalence Principle violation below 10-13. In this communication, we describe the MICROSCOPE mission, its measurement principle and instrument, and we give an update on its status. After a successful instrument's commissioning, MICROSCOPE is on track for on-schedule launch, expected in 2016.

Regression analysis with missing data and unknown colored noise: Application to the MICROSCOPE space mission

The analysis of physical measurements often copes with highly correlated noises and interruptions caused by outliers, saturation events, or transmission losses. We assess the impact of missing data on the performance of linear regression analysis involving the fit of modeled or measured time series. We show that data gaps can significantly alter the precision of the regression parameter estimation in the presence of colored noise, due to the frequency leakage of the noise power. We present a regression method that cancels this effect and estimates the parameters of interest with a precision comparable to the complete data case, even if the noise power spectral density (PSD) is not known a priori. The method is based on an autoregressive fit of the noise, which allows us to build an approximate generalized least squares estimator approaching the minimal variance bound. The method, which can be applied to any similar data processing, is tested on simulated measurements of the MICROSCOPE space mission, whose goal is to test the weak equivalence principle (WEP) with a precision of $1{0}^{\ensuremath{-}15}$. In this particular context the signal of interest is the WEP violation signal expected to be found around a well defined frequency. We test our method with different gap patterns and noise of known PSD and find that the results agree with the mission requirements, decreasing the uncertainty by a factor of 60 with respect to ordinary least squares methods. We show that it also provides a test of significance to assess the uncertainty of the measurement.