The Confrontation between General Relativity and Experiment

Single-Photon Interference over 8.4 km Urban Atmosphere: Toward Testing Quantum Effects in Curved Spacetime with Photons

The emergence of quantum mechanics and general relativity has transformed our understanding of the natural world significantly. However, integrating these two theories presents immense challenges, and their interplay remains untested. Recent theoretical studies suggest that the single-photon interference covering huge space can effectively probe the interface between quantum mechanics and general relativity. We developed an alternative design using unbalanced Michelson interferometers to address this and validated its feasibility over an 8.4 km free-space channel. Using a high-brightness single-photon source based on quantum dots, we demonstrated single-photon interference along this long-distance baseline. We achieved a phase measurement precision of 16.2 mrad, which satisfied the measurement requirements for a gravitational redshift at the geosynchronous orbit by 5 times the standard deviation. Our results confirm the feasibility of the single-photon version of the Colella-Overhauser-Werner experiment for testing the quantum effects in curved spacetime.

Methodological reflections on the MOND/dark matter debate

The paper re-examines the principal methodological questions, arising in the debate over the cosmological standard model's postulate of Dark Matter vs. rivalling proposals that modify standard (Newtonian and general-relativistic) gravitational theory, the so-called Modified Newtonian Dynamics (MOND) and its subsequent extensions. What to make of such seemingly radical challenges of cosmological orthodoxy? In the first part of our paper, we assess MONDian theories through the lens of key ideas of major 20th century philosophers of science (Popper, Kuhn, Lakatos, and Laudan), thereby rectifying widespread misconceptions and misapplications of these ideas common in the pertinent MOND-related literature. None of these classical methodological frameworks, which render precise and systematise the more intuitive judgements prevalent in the scientific community, yields a favourable verdict on MOND and its successors-contrary to claims in the MOND-related literature by some of these theories' advocates; the respective theory appraisals are largely damning. Drawing on these insights, the paper's second part zooms in on the most common complaint about MONDian theories, their ad-hocness. We demonstrate how the recent coherentist model of ad-hocness captures, and fleshes out, the underlying-but too often insufficiently articulated-hunches underlying this critique. MONDian theories indeed come out as severely ad hoc: they do not cohere well with either theoretical or empirical-factual background knowledge. In fact, as our complementary comparison with the cosmological standard model's Dark Matter postulate shows, with respect to ad-hocness, MONDian theories fare worse than the cosmological standard model.

A lab-based test of the gravitational redshift with a miniature clock network

Einstein's theory of general relativity predicts that a clock at a higher gravitational potential will tick faster than an otherwise identical clock at a lower potential, an effect known as the gravitational redshift. Here we perform a laboratory-based, blinded test of the gravitational redshift using differential clock comparisons within an evenly spaced array of 5 atomic ensembles spanning a height difference of 1 cm. We measure a fractional frequency gradient of [ - 12.4 ± 0. 7(stat) ± 2. 5(sys)] × 10-19/cm, consistent with the expected redshift gradient of - 10.9 × 10-19/cm. Our results can also be viewed as relativistic gravitational potential difference measurements with sensitivity to mm scale changes in height on the surface of the Earth. These results highlight the potential of local-oscillator-independent differential clock comparisons for emerging applications of optical atomic clocks including geodesy, searches for new physics, gravitational wave detection, and explorations of the interplay between quantum mechanics and gravity.

Equivalence of Active and Passive Gravitational Mass Tested with Lunar Laser Ranging

Lunar Laser Ranging (LLR) measures the distance between observatories on Earth and retro-reflectors on the Moon since 1969. In this Letter, we study the possible violation of the equivalence of passive and active gravitational mass (m_{a}/m_{p}), for aluminum (Al) and iron (Fe), using LLR data. Our new limit of 3.9×10^{-14} is about 100 times better than that of Bartlett and Van Buren [Equivalence of Active and Passive Gravitational Mass Using the Moon, Phys. Rev. Lett. 57, 21 (1986)PRLTAO0031-900710.1103/PhysRevLett.57.21] reflecting the benefit of the many years of LLR data.

The dominating mode of two competing massive modes of quadratic gravity

Over the last two decades, motivations for modified gravity have emerged from both theoretical and observational levels. f(R) and Chern-Simons gravity have received more attention as they are the simplest generalization. However, f(R) and Chern-Simons gravity contain only an additional scalar (spin-0) degree of freedom and, as a result, do not include other modes of modified theories of gravity. In contrast, quadratic gravity (also referred to as Stelle gravity) is the most general second-order modification to 4-D general relativity and contains a massive spin-2 mode that is not present in f(R) and Chern-Simons gravity. Using two different physical settings-the gravitational wave energy-flux measured by the detectors and the backreaction of the emitted gravitational radiation on the spacetime of the remnant black hole-we demonstrate that massive spin-2 mode carries more energy than the spin-0 mode. Our analysis shows that the effects are pronounced for intermediate-mass black holes, which are prime targets for LISA.

Entanglement Witness for the Weak Equivalence Principle

The Einstein equivalence principle is based on the equality of gravitational and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a great precision. However, all these tests and the corresponding arguments are based on a classical setup where the notion of position and velocity of the mass is associated with a classical value as opposed to the quantum entities.Here, we provide a simple quantum protocol based on creating large spatial superposition states in a laboratory to test the quantum regime of the equivalence principle where both matter and gravity are treated at par as a quantum entity. The two gravitational masses of the two spatial superpositions source the gravitational potential for each other. We argue that such a quantum protocol is unique with regard to testing especially the generalisation of the weak equivalence principle by constraining the equality of gravitational and inertial mass via witnessing quantum entanglement.

Gravitational redshift test using Rb clocks of eccentric GPS satellites

This paper reports a test of gravitational redshift, which is a consequence of the Einstein equivalence principle, using the Rb clocks of GPS Block IIF satellites. The fractional deviation in the gravitational redshift was measured using 6,640 days of data from three Rb clocks onboard GPS Block IIF satellites. The systematic effects related to orbital uncertainty, temperature, and magnetic field were modeled conservatively. The fractional deviation in the gravitational redshift from the general relativity prediction was measured with ( 0.23 ± 1.34 ) × 10 - 3 at one sigma.

Reconstruction of Scalar-Torsion Gravity Theories from the Physical Potential of a Scalar Field

We consider scalar-torsion gravity theories based on the exact solutions of a physical type of potential for cosmological inflationary models based on the non-minimal coupling of a scalar field and torsion. We analyzed the inflationary models with different types of inflationary dynamics and corresponding scalar field parameters. Such an approach allows us to consider different physical potentials and types of scalar-torsion gravity theories in the context of the realization of both stages of accelerated expansion of the universe. We also considered the correspondence surrounding the proposed inflationary models and the observational constraints on the parameters of cosmological perturbations.

Generation of Entanglement from Mechanical Rotation

Many phenomena and fundamental predictions, ranging from Hawking radiation to the early evolution of the Universe rely on the interplay between quantum mechanics and gravity or more generally, quantum mechanics in curved spacetimes. However, our understanding is hindered by the lack of experiments that actually allow us to probe quantum mechanics in curved spacetime in a repeatable and accessible way. Here we propose an experimental scheme for a photon that is prepared in a path superposition state across two rotating Sagnac interferometers that have different diameters and thus represent a superposition of two different spacetimes. We predict the generation of genuine entanglement even at low rotation frequencies and show how these effects could be observed even due to the Earth's rotation. These predictions provide an accessible platform in which to study the role of the underlying spacetime in the generation of entanglement.

The deep space quantum link: prospective fundamental physics experiments using long-baseline quantum optics

The National Aeronautics and Space Administration's Deep Space Quantum Link mission concept enables a unique set of science experiments by establishing robust quantum optical links across extremely long baselines. Potential mission configurations include establishing a quantum link between the Lunar Gateway moon-orbiting space station and nodes on or near the Earth. This publication summarizes the principal experimental goals of the Deep Space Quantum Link. These goals, identified through a multi-year design study conducted by the authors, include long-range teleportation, tests of gravitational coupling to quantum states, and advanced tests of quantum nonlocality.

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.

Gravitational Waves from Accretion-Induced Descalarization in Massive Scalar-Tensor Theory

Many classes of extended scalar-tensor theories predict that dynamical instabilities can take place at high energies, leading to the formation of scalarized neutron stars. Depending on the theory parameters, stars in a scalarized state can form a solution-space branch that shares a lot of similarities with the so-called mass twins in general relativity appearing for equations of state containing first-order phase transitions. Members of this scalarized branch have a lower maximum mass and central energy density compared to Einstein ones. In such cases, a scalarized star could potentially overaccrete beyond the critical mass limit, thus triggering a gravitational phase transition where the star sheds its scalar hair and migrates over to its nonscalarized counterpart. Such an event resembles, but is distinct from, a nuclear or thermodynamic phase transition. We dynamically track a gravitational transition by first constructing hydrostatic, scalarized equilibria for realistic equations of state, and then allowing additional material to fall onto the stellar surface. The resulting bursts of monopolar radiation are dispersively stretched to form a quasicontinuous signal that persists for decades, carrying strains of order ≳10^{-22}  (kpc/L)^{3/2} Hz^{-1/2} at frequencies of ≲300  Hz, detectable with the existing interferometer network out to distances of L≲10  kpc, and out to a few hundred kpc with the inclusion of the Einstein Telescope. Electromagnetic signatures of such events, involving gamma-ray and neutrino bursts, are also considered.

An S-matrix approach to gravitational-wave physics

The detection of gravitational waves emitted by binary systems has opened a new astronomical window into the Universe. We describe recent advances in the field of scattering amplitudes applied to the post-Minkowskian expansion, and the extraction of the effective two-body gravitational potential. The techniques presented here apply to any effective field theory of gravity and are not restricted to four-dimensional Einstein gravity. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.

Binary X-ray Sources in Massive Brans–Dicke Gravity

This study focuses on the X-ray emission of low-mass black hole binaries in massive Brans–Dicke gravity. First, we compute the accretion disk with the well-known Shakura–Sunyaev model for an optically thick, cool, and geometrically thin disk. Moreover, we assume that the gravitational field generated by the stellar-mass black hole is an analogue of the Schwarzschild space-time of Einstein’s theory in massive Brans–Dicke gravity. We compute the most relevant quantities of interest, i.e., (i) the radial velocity, (ii) the energy and surface density, and (iii) the pressure as a function entirely of the radial coordinate. We also compute the soft spectral component of the X-ray emission produced by the disk. Furthermore, we investigate in detail how the mass of the scalar field modifies the properties of the binary as described by the more standard Schwarzschild solution.

Extended Gravity Constraints at Different Scales

We review a set of the possible ways to constrain extended gravity models at Galaxy clusters scales (the regime of dark energy explanations and comparison with ΛCDM), for black hole shadows, gravitational wave astronomy, binary pulsars, the Solar system and a Large Hadron Collider (consequences for high-energy physics at TeV scale). The key idea is that modern experimental and observational precise data provide us with the chance to go beyond general relativity.

Geometrical origins of the universe dark sector: string-inspired torsion and anomalies as seeds for inflation and dark matter

In a modest attempt to present potentially new paradigms in cosmology, including its inflationary epoch, and initiate discussions, I review in this article some novel, string-inspired cosmological models, which entail a purely geometrical origin of the dark sector of the Universe but also of its observed matter-antimatter asymmetry. The models contain gravitational (string-model independent, Kalb-Ramond (KR)) axion fields coupled to primordial gravitational anomalies via CP-violating interactions. The anomaly terms are four-space-time-dimensional remnants of the Green-Schwarz counterterms appearing in the definition of the field strength of the spin-one antisymmetric tensor field of the (bosonic) massless gravitational string multiplet, which also plays the role of a totally antisymmetric component of torsion. I show how in such cosmologies the presence of primordial gravitational waves can lead to anomaly condensates and dynamical inflation of a 'running-vacuum-model' type, without external inflatons, but also to leptogenesis in the radiation era due to anomaly induced Lorentz and CPT violating KR axion backgrounds. I also discuss how the torsion-related KR-axion could acquire a mass during the QCD epoch, thus playing the role of (a component of) dark matter. Phenomenological considerations of the inflationary and post-inflationary (in particular, modern) eras of the model are briefly discussed, including its potential for alleviating the observed tensions in the cosmological data of the current epoch. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.

A gamma-ray pulsar timing array constrains the nanohertz gravitational wave background

After large galaxies merge, their central supermassive black holes are expected to form binary systems. Their orbital motion should generate a gravitational wave background (GWB) at nanohertz frequencies. Searches for this background utilize pulsar timing arrays, which perform long-term monitoring of millisecond pulsars at radio wavelengths. We use 12.5 years of Fermi Large Area Telescope data to form a gamma-ray pulsar timing array. Results from 35 bright gamma-ray pulsars place a 95% credible limit on the GWB characteristic strain of 1.0 × 10^-14 at a frequency of 1 yr^-1. The sensitivity is expected to scale with t _obs, the observing time span, as [Formula: see text]. This direct measurement provides an independent probe of the GWB while offering a check on radio noise models.

No Evidence of Kinetic Screening in Simulations of Merging Binary Neutron Stars beyond General Relativity

We have conducted fully relativistic simulations in a class of scalar-tensor theories with derivative self-interactions and screening of local scales. By using high-resolution shock-capturing methods and a nonvanishing shift vector, we have managed to avoid issues plaguing similar attempts in the past. We have first confirmed recent results by ourselves in spherical symmetry, obtained with an approximate approach and pointing at a partial breakdown of the screening in black-hole collapse. Then, we considered the late inspiral and merger of binary neutron stars. We found that screening tends to suppress the (subdominant) dipole scalar emission, but not the (dominant) quadrupole scalar mode. Our results point at quadrupole scalar signals as large as (or even larger than) in Fierz-Jordan-Brans-Dicke theories with the same conformal coupling, for strong-coupling scales in the MeV range that we can simulate.

The shape of scalar Gauss-Bonnet gravity

We study the consistency of Scalar Gauss-Bonnet Gravity, a generalization of General Relativity where black holes can develop non-trivial hair by the action of a coupling F(Φ)$$ \mathcal{G} $$ G between a function of a scalar field and the Gauss-Bonnet invariant of the space-time. When properly normalized, interactions induced by this term are weighted by a cut-off, and take the form of an Effective Field Theory expansion. By invoking the existence of a Lorentz invariant, causal, local, and unitary UV completion of the theory, we derive positivity bounds for n-to-n scattering amplitudes including exchange of dynamical gravitons. These constrain the value of all even derivatives of the function F(Φ), and are highly restrictive. They require some of the scales of the theory to be of Planckian order, and rule out most of the models used in the literature for black hole scalarization.

Current and Future Tests of General Relativity

General Relativity (GR) holds a special place amongst all fundamental theories of physics: on one hand, it is the theory of all gravitational phenomena; on the other hand, it is also a theory of spacetime [...]

Stochastic Gravitational-Wave Backgrounds: Current Detection Efforts and Future Prospects

The collection of individually resolvable gravitational wave (GW) events makes up a tiny fraction of all GW signals that reach our detectors, while most lie below the confusion limit and are undetected. Similarly to voices in a crowded room, the collection of unresolved signals gives rise to a background that is well-described via stochastic variables and, hence, referred to as the stochastic GW background (SGWB). In this review, we provide an overview of stochastic GW signals and characterise them based on features of interest such as generation processes and observational properties. We then review the current detection strategies for stochastic backgrounds, offering a ready-to-use manual for stochastic GW searches in real data. In the process, we distinguish between interferometric measurements of GWs, either by ground-based or space-based laser interferometers, and timing-residuals analyses with pulsar timing arrays (PTAs). These detection methods have been applied to real data both by large GW collaborations and smaller research groups, and the most recent and instructive results are reported here. We close this review with an outlook on future observations with third generation detectors, space-based interferometers, and potential noninterferometric detection methods proposed in the literature.

Observation of a gravitational Aharonov-Bohm effect

Gravity curves space and time. This can lead to proper time differences between freely falling, nonlocal trajectories. A spatial superposition of a massive particle is predicted to be sensitive to this effect. We measure the gravitational phase shift induced in a matter-wave interferometer by a kilogram-scale source mass close to one of the wave packets. Deflections of each interferometer arm due to the source mass are independently measured. The phase shift deviates from the deflection-induced phase contribution, as predicted by quantum mechanics. In addition, the observed scaling of the phase shift is consistent with Heisenberg’s error-disturbance relation. These results show that gravity creates Aharonov-Bohm phase shifts analogous to those produced by electromagnetic interactions.

Cosmological Tests of Gravity: A Future Perspective

In this review, we outline the expected tests of gravity that will be achieved at cosmological scales in the upcoming decades. We focus mainly on constraints on phenomenologically parameterized deviations from general relativity, which allow to test gravity in a model-independent way, but also review some of the expected constraints obtained with more physically motivated approaches. After reviewing the state-of-the-art for such constraints, we outline the expected improvement that future cosmological surveys will achieve, focusing mainly on future large-scale structures and cosmic microwave background surveys but also looking into novel probes on the nature of gravity. We will also highlight the necessity of overcoming accuracy issues in our theoretical predictions, issues that become relevant due to the expected sensitivity of future experiments.

Testing General Relativity with Gravitational Waves: An Overview

The detections of gravitational-wave (GW) signals from compact binary coalescence by ground-based detectors have opened up the era of GW astronomy. These observations provide opportunities to test Einstein’s general theory of relativity at the strong-field regime. Here we give a brief overview of the various GW-based tests of General Relativity (GR) performed by the LIGO-Virgo collaboration on the detected GW events to date. After providing details for the tests performed in four categories, we discuss the prospects for each test in the context of future GW detectors. The four categories of tests include the consistency tests, parametrized tests for GW generation and propagation, tests for the merger remnant properties, and GW polarization tests.

Torsion in String-Inspired Cosmologies and the Universe Dark Sector

Several aspects of torsion in string-inspired cosmologies are reviewed. In particular, its connection with fundamental, string-model independent, axion fields associated with the massless gravitational multiplet of the string are discussed. It is argued in favour of the role of primordial gravitational anomalies coupled to such axions in inducing inflation of a type encountered in the “Running-Vacuum-Model (RVM)” cosmological framework, without fundamental inflaton fields. The gravitational-anomaly terms owe their existence to the Green–Schwarz mechanism for the (extra-dimensional) anomaly cancellation, and may be non-trivial in such theories in the presence of (primordial) gravitational waves at early stages of the four-dimensional string universe (after compactification). The paper also discusses how the torsion-induced stringy axions can acquire a mass in the post inflationary era, due to non-perturbative effects, thus having the potential to play the role of (a component of) dark matter in such models. Finally, the current-era phenomenology of this model is briefly described with emphasis placed on the possibility of alleviating tensions observed in the current-era cosmological data. A brief phenomenological comparison with other cosmological models in contorted geometries is also made.

Instabilities of Scalar Fields around Oscillating Stars

The behavior of fundamental fields in strong gravity or nontrivial environments is important for our understanding of nature. This problem has interesting applications in the context of dark matter, of dark energy physics, or of quantum field theory. The dynamics of fundamental fields has been studied mainly in static or stationary backgrounds, whereas most of our Universe is dynamic. In this Letter we investigate "blueshift" and parametric instabilities of scalar fields in dynamical backgrounds, which can be triggered (for instance) by oscillating stars in scalar-tensor theories of gravity. We discuss possible implications of our results, which include constraints on an otherwise hard-to-access parameter space of scalar-tensor theories.

Relativistic Fractional-Dimension Gravity

This paper presents a relativistic version of Newtonian Fractional-Dimension Gravity (NFDG), an alternative gravitational model recently introduced and based on the theory of fractional-dimension spaces. This extended version—Relativistic Fractional-Dimension Gravity (RFDG)—is based on other existing theories in the literature and might be useful for astrophysical and cosmological applications. In particular, in this work, we review the mathematical theory for spaces with non-integer dimensions and its connections with the non-relativistic NFDG. The Euler–Lagrange equations for scalar fields can also be extended to spaces with fractional dimensions, by adding an appropriate weight factor, and then can be used to generalize the Laplacian operator for rectangular, spherical, and cylindrical coordinates. In addition, the same weight factor can be added to the standard Hilbert action in order to obtain the field equations, following methods used for scalar-tensor models of gravity, multi-scale spacetimes, and fractional gravity theories. We then apply the field equations to standard cosmology and to the Friedmann-Lemaître-Robertson-Walker metric. Using a suitable weight vtt, depending on the synchronous time t and on a single time-dimension parameter αt, we extend the Friedmann equations to the RFDG case. This allows for the computation of the scale factor at for different values of the fractional time-dimension αt and the comparison with standard cosmology results. Future additional work on the subject, including studies of the cosmological late-time acceleration, type Ia supernovae data, and related dark energy theory will be needed to establish this model as a relativistic alternative theory of gravity.

New Relativistic Theory for Modified Newtonian Dynamics

We propose a relativistic gravitational theory leading to modified Newtonian dynamics, a paradigm that explains the observed universal galactic acceleration scale and related phenomenology. We discuss phenomenological requirements leading to its construction and demonstrate its agreement with the observed cosmic microwave background and matter power spectra on linear cosmological scales. We show that its action expanded to second order is free of ghost instabilities and discuss its possible embedding in a more fundamental theory.

Analysis of Birefringence and Dispersion Effects from Spacetime-Symmetry Breaking in Gravitational Waves

In this work, we review the effective field theory framework to search for Lorentz and CPT symmetry breaking during the propagation of gravitational waves. The article is written so as to bridge the gap between the theory of spacetime-symmetry breaking and the analysis of gravitational-wave signals detected by ground-based interferometers. The primary physical effects beyond General Relativity that we explore here are dispersion and birefringence of gravitational waves. We discuss their implementation in the open-source LIGO-Virgo algorithm library suite, and we discuss the statistical method used to perform a Bayesian inference of the posterior probability of the coefficients for symmetry-breaking. We present preliminary results of this work in the form of simulations of modified gravitational waveforms, together with sensitivity studies of the measurements of the coefficients for Lorentz and CPT violation. The findings show the high potential of gravitational wave sources across the sky to sensitively probe for these signals of new physics.

Metric-Affine Myrzakulov Gravity Theories

In this paper, we review the so-called Myrzakulov Gravity models (MG-N, with N = I, II, …, VIII) and derive their respective metric-affine generalizations (MAMG-N), discussing also their particular sub-cases. The field equations of the theories are obtained by regarding the metric tensor and the general affine connection as independent variables. We then focus on the case in which the function characterizing the aforementioned metric-affine models is linear and consider a Friedmann-Lemaître–Robertson–Walker background to study cosmological aspects and applications. Historical motivation for this research is thoroughly reviewed and specific physical motivations are provided for the aforementioned family of alternative theories of gravity.

Spontaneous Lorentz Violation from Infrared Gravity

In this paper, we investigate a novel implication of the non-negligible spacetime curvature at large distances when its effects are expressed in terms of a suitably modified form of the Heisenberg uncertainty relations. Specifically, we establish a one-to-one correspondence between this modified uncertainty principle and the Standard Model Extension (SME), a string-theoretical effective field theory that accounts for both explicit and spontaneous breaking of Lorentz symmetry. This tight correspondence between string-derived effective field theory and modified quantum mechanics with extended uncertainty relations is validated by comparing the predictions concerning a deformed Hawking temperature derived from the two models. Moreover, starting from the experimental bounds on the gravity sector of the SME, we derive the most stringent constraint achieved so far on the value of the free parameter in the extended Heisenberg uncertainty principle.

Capture of Massless and Massive Particles by Parameterized Black Holes

We study an influence of the leading coefficient of the parameterized line element of the spherically symmetric, static black hole on the capture of massless and massive particles. We have shown that negative (positive) values of ϵ decreases (increases) the radius of characteristic circular orbits and consequently, increases (decreases) the energy and decreases (increases) the angular momentum of the particle moving along these orbits. Moreover, we have calculated and compared the capture cross section of the massive particle in the relativistic and non-relativistic limits. It has been shown that in the case of small deviation from general relativity the capture cross section for the relativistic and nonrelativistic particle has an additional term being linear in the small dimensionless deviation parameter ϵ.

Effects of Quantum Metric Fluctuations on the Cosmological Evolution in Friedmann-Lemaitre-Robertson-Walker Geometries

In this paper, the effects of the quantum metric fluctuations on the background cosmological dynamics of the universe are considered. To describe the quantum effects, the metric is assumed to be given by the sum of a classical component and a fluctuating component of quantum origin . At the classical level, the Einstein gravitational field equations are equivalent to a modified gravity theory, containing a non-minimal coupling between matter and geometry. The gravitational dynamics is determined by the expectation value of the fluctuating quantum correction term, which can be expressed in terms of an arbitrary tensor Kμν. To fix the functional form of the fluctuation tensor, the Newtonian limit of the theory is considered, from which the generalized Poisson equation is derived. The compatibility of the Newtonian limit with the Solar System tests allows us to fix the form of Kμν. Using these observationally consistent forms of Kμν, the generalized Friedmann equations are obtained in the presence of quantum fluctuations of the metric for the case of a flat homogeneous and isotropic geometry. The corresponding cosmological models are analyzed using both analytical and numerical method. One finds that a large variety of cosmological models can be formulated. Depending on the numerical values of the model parameters, both accelerating and decelerating behaviors can be obtained. The obtained results are compared with the standard ΛCDM (Λ Cold Dark Matter) model.