Gravitational Corrections Research Articles

Gravitational radiative corrections from effective field theory

In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures "post-Minkowskian" corrections to the multipole expansion due to non-linear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from non-relativistic binaries, including long distance effects up to 3PN ($v^6$) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.

Gravitational corrections to Yukawa systems

We compute the gravitational corrections to the running of couplings in a scalar-fermion system, using the Wilsonian approach. Our discussion is relevant for symmetric as well as for broken scalar phases. We find that the Yukawa and quartic scalar couplings become irrelevant at the Gaussian fixed point.

Gravitational Corrections to Yukawa andφ4Interactions

We consider the lowest order quantum gravitational corrections to Yukawa and phi{4} interactions. Our results show that quantum gravity leads to contributions to the running coupling constants if the particles are massive and therefore alters the scaling behavior of the standard model. Furthermore, we find that the gravitational contributions to the running of the masses vanish.

GRAVITATIONAL CORRECTION TO SU(5) GAUGE COUPLING UNIFICATION

The gravitational corrections to the gauge coupling constants of Abelian and non-Abelian gauge theories have been shown to diverge quadratically. Since this result will have interesting consequences, this has been analyzed by several authors from different approaches. We propose to discuss this issue from a phenomenological approach. We analyze the SU(5) gauge coupling unification and argue that the gravitational corrections to gauge coupling constants may not vanish when higher dimensional non-renormalizable terms are included in the problem.

QUANTUM GRAVITATIONAL CORRECTIONS TO THE HYDROGEN ATOM AND HARMONIC OSCILLATOR

It is shown that the rate of corrections to the hydrogen atom and harmonic oscillator energy levels due to the profound quantum gravitational effect of space–time dimension running/reduction coincides well with those obtained by means of minimum-length-deformed quantum mechanics. The rate of corrections is pretty much the same within the accuracy with which we can judge the quantum gravitational corrections at all. Such a convergence of results makes the concept of space–time dimension running more appreciable. As a remarkable distinction, the energy shift due to dimension reduction has the opposite sign as compared with the correction obtained by means of minimum-length-modified quantum mechanics. Therefore, the sign of total quantum gravitational correction remains somewhat obscure.

QUANTUM-GRAVITATIONAL RUNNING/REDUCTION OF THE SPACE–TIME DIMENSION

Quantum gravity causes the space–time dimension to depend on the size of the region; it monotonically increases with the size of the region and asymptotically approaches 4 for large distances. This effect was discovered in numerical simulations of lattice quantum gravity in the framework of causal dynamical triangulation (arXiv:hep-th/0505113), as well as in the renormalization group approach to quantum gravity (arXiv:hep-th/0508202). However, in these approaches the interpretation and physical meaning of the effective change of dimension at shorter scales is not clear. Without invoking particular models in this paper, we show that the box-counting dimension in the face of finite resolution of space–time (generally implied by quantum gravity) indicates a simple way in which both the qualitative and the quantitative features of this effect can be understood. In this way we derive a simple analytic expression of space–time dimension running, which implies the modification of Newton's inverse square law in perfect agreement with the modification coming from one-loop gravitational radiative corrections.

Nonperturbative one-loop effective action for electrodynamics in curved space-time

In this paper we explicitly evaluate the one-loop effective action in four dimensions for scalar and spinor fields under the influence of a strong, covariantly constant, magnetic field in curved space-time. In the framework of zeta function regularization, we find the one-loop effective action to all orders in the magnetic field up to linear terms in the Riemannian curvature. As a particular case, we also obtain the one-loop effective action for massless scalar and spinor fields. In this setting, we found that the vacuum energy of charged spinors with small mass becomes very large due entirely to the gravitational correction.

Low-energy effective action in nonperturbative electrodynamics in curved space-time

We study the heat kernel for the Laplace-type partial differential operator acting on smooth sections of a complex spin-tensor bundle over a generic n-dimensional Riemannian manifold. Assuming that the curvature of the U(1) connection (that we call the electromagnetic field) is constant, we compute the first two coefficients of the nonperturbative asymptotic expansion of the heat kernel which are of zero and the first order in Riemannian curvature and of arbitrary order in the electromagnetic field. We apply these results to the study of the effective action in nonperturbative electrodynamics in four dimensions and derive a generalization of the Schwinger’s result for the creation of scalar and spinor particles in electromagnetic field induced by the gravitational field. We discover a new infrared divergence in the imaginary part of the effective action due to the gravitational corrections, which seems to be a new physical effect.

Cosmological reconstruction of realistic modified [formula omitted] gravities

The cosmological reconstruction scheme for modified F(R) gravity is developed in terms of e-folding (or, redshift). It is demonstrated how any FRW cosmology may emerge from specific F(R) theory. The specific examples of well-known cosmological evolution are reconstructed, including ΛCDM cosmology, deceleration with transition to phantom superacceleration era which may develop singularity or be transient. The application of this scheme to viable F(R) gravities unifying inflation with dark energy era is proposed. The additional reconstruction of such models leads to non-leading gravitational correction mainly relevant at the early/late universe and helping to pass the cosmological bounds (if necessary). It is also shown how cosmological reconstruction scheme may be generalized in the presence of scalar field.

Random versus holographic fluctuations of the background metric. I. (Cosmological) running of space–time dimension

A profound quantum-gravitational effect of space–time dimension running with respect to the size of space–time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of causal dynamical triangulation [hep-th/0505113] as well as in renormalization group approach to quantum gravity [hep-th/0508202]. Unfortunately, along these approaches the interpretation and the physical meaning of the effective change of dimension at shorter scales is not clear. The aim of this Letter is twofold. First, we find that box-counting dimension in face of finite resolution of space–time (generally implied by quantum gravity) shows a simple way how both the qualitative and the quantitative features of this effect can be understood. Second, considering two most interesting cases of random and holographic fluctuations of the background space, we find that it is random fluctuations that gives running dimension resulting in modification of Newton's inverse square law in a perfect agreement with the modification coming from one-loop gravitational radiative corrections.

Note on Chern-Simons term correction to holographic entanglement entropy

From the perspective of AdS/CFT correspondence, we study the gravitational Chern-Simons term correction to the holographic entanglement entropy of CFT on the conformal boundary of asymptotically AdS$_3$ spacetime using the off-shell Euclidean path integral method. We show that, like the BTZ black hole entropy, the holographic entanglement entropy is indeed modified due to the gravitational Chern-Simons term although the bulk geometry does not change.

Newton’s constant inf(R,RμνRμν,□R)theories of gravity and constraints from BBN

We consider corrections to the Einstein-Hilbert action which contain both higher order and nonlocal terms. We derive an effective Newtonian gravitational constant applicable at the weak field limit and use the primordial nucleosynthesis (BBN) bound and the local gravity constraints on $G_{eff}$ in order to test the viability of several cases of our general Lagrangian. We will also provide a BBN constrain on the $\Box R$ gravitational correction.

Gravitational contributions to pioneer space probe decelerations and the time-delay-doppler “Relativistic Confusion”

Relativistic corrections to the calculations of Pioneer 10 space probe motion (mentioned but not sufficiently detailed by the authors of the observation [1]) are analyzed basing on the assumption that the Solar System gravity is described by the Kerr metric. The geodesic equation for ecliptic-plane motion of the space probe is solved, and all specific gravitational corrections to the probe acceleration are computed up to the 2nd order of the small parameters; values of all general-relativistic corrections are found to be small as compared to the Pioneer anomaly. On the contrary, a study of kinematic effects in the tangent space based on the Quaternion Relativity formalism (the quaternion square root of the Kerr space-time interval) shows that the probe’s signal frequency distorted by relativistic time-scale stretching, when taken for a Doppler portion of the frequency shift, may result in experimental detection of an additional acceleration of the probe. The value of this apparent “correction” (though steadily dropping with distance) is found to be quite close to that of the Pioneer 10 reported acceleration residual.

The effect of gravitational correction on shoulder internal and external rotation strength

Objective: To study the influence of gravitational correction on the internal (IR) and external rotators (ER) shoulder strength. Methods: The IR and ER isokinetic strength, measured in 30 ◦ scapation, was evaluated concentrically at 60 and 240 ◦ /s and eccentrically at 60 ◦ /s in 33 healthy volunteers. Strength scores were expressed either by incorporating gravitational correction (GC) or without it. Results: With GC, IR strength was significantly lower and ER strength significantly higher than without incorporation of this procedure. Conclusion: The GC procedure has a significant influence on IR and ER strength and should be incorporated when strength deficits of the rotator cuff are expected.

Constraining effective quantum gravity with LISA

All modern routes leading to a quantum theory of gravity – i.e., perturbative quantum gravitational one-loop exact correction to the global chiral current in the standard model, string theory, and perhaps even loop quantum gravity – require supplementing the Einstein-Hilbert action with a parity-violating Chern-Simons term. Such a term leads to amplitude-birefringent gravitational wave propagation: i.e., one (circular) polarization state amplified with propagation while the other is attenuated. The proposed Laser Interferometer Space Antenna (LISA) is capable of observing gravitational wave sources at cosmological distances, suggesting the possibility that LISA observations may place a strong bound on this manifestation of quantum gravity. Here we report on a calculation of the effect that spacetime amplitude birefringence has on the signal LISA is capable of observing from inspiraling supermassive black hole binaries at large redshift. We find that the birefringence manifests itself in the observations as an anomalous precession of the binary's orbital angular momentum as it evolves toward coalescence, whose magnitude depends on the integrated history of the Chern-Simons coupling over the worldline of radiation wavefront. We estimate that LISA could place bounds on Chern-Simons modified gravity that are several orders of magnitude stronger than the present Solar System constraints, thus providing a probe of the quantum structure of spacetime.

Where in the string landscape is quintessence?

We argue that quintessence may reside in certain corners of the string landscape. It arises as a linear combination of internal space components of higher-rank forms, which are axionlike at low energies, and may mix with 4-forms after compactification of the Chern-Simons terms to 4D due to internal space fluxes. The mixing induces an effective mass term, with an action which preserves the axion shift symmetry, breaking it spontaneously after the background selection. With several axions, several 4-forms, and a low string scale, as in one of the setups already invoked for dynamically explaining a tiny residual vacuum energy in string theory, the 4D mass matrix generated by random fluxes may have ultralight eigenmodes over the landscape, which are quintessence. We illustrate how this works in the simplest cases, and outline how to get the lightest mass to be comparable to the Hubble scale now, ${H}_{0}\ensuremath{\sim}{10}^{\ensuremath{-}33}\text{ }\text{ }\mathrm{eV}$. The shift symmetry protects the smallest mass from perturbative corrections in field theory. Further, if the ultralight eigenmode does not couple directly to any sector strongly coupled at a high scale, the nonperturbative field theory corrections to its potential will also be suppressed. Finally, if the compactification length is larger than the string length by more than an order of magnitude, the gravitational corrections may remain small too, even when the field value approaches ${M}_{\mathrm{Pl}}$.

Gravitational contributions to the running Yang-Mills coupling in large extra-dimensional brane worlds

We study the question of a modification of the running gauge coupling of Yang-Mills theories due to quantum gravitational effects in a compact large extra dimensional brane world scenario with a low energy quantum gravity scale. The ADD scenario is applied for a D=d+\delta dimensional space-time in which gravitons freely propagate, whereas the non-abelian gauge fields are confined to a d-dimensional brane. The extra dimensions are taken to be toroidal and the transverse fluctuation modes (branons) of the brane are taken into account. On this basis we have calculated the one-loop corrections due to virtual Kaluza-Klein graviton and branon modes for the gluon two- and three-point functions in an effective field theory treatment. Applying momentum cut-off regularization we find that for a d=4 brane the leading gravitational divergencies cancel irrespective of the number of extra dimensions \delta, generalizing previous results in the absence of extra-dimensions. Hence, again the Yang-Mills \beta-function receives no gravitational corrections at one-loop. This is no longer true in a `universal' extra dimensional scenario with a d>4 dimensional brane. Moreover, the subleading power-law gravitational divergencies induce higher-dimensional counterterms, which we establish in our scheme. Interestingly, for d=4 these gravitationally induced counterterms are of the form recently considered in non-abelian Lee-Wick extensions of the standard model -- now with a possible mass scale in the TeV range due to the presence of large extra dimensions.

Secular dynamics of a coplanar, non-resonant planetary system under the general relativity and quadrupole moment perturbations

We construct a secular theory of a coplanar system of N planets not involved in strong mean motion resonances, and which are far from collision zones. Besides the point-to-point Newtonian mutual interactions, we consider the general relativistic corrections to the gravitational potential of the star and the innermost planet, and also a modification of this potential by the quadrupole moment and tidal distortion of the star. We focus on hierarchical planetary systems. After averaging the model Hamiltonian with a simple algorithm making use of very basic properties of the Keplerian motion, we obtain analytical secular theory of high order in the semimajor axes ratio. A great precision of the analytic approximation is demonstrated with the numerical integrations of the equations of motion. A survey regarding model parameters (the masses, semimajor axes, spin rate of the star) reveals a rich and non-trivial dynamics of the secular system. Our study is focused on its equilibria. Such solutions predicted by the classic secular theory, which correspond to aligned (mode I) or anti-aligned (mode II) apsides, may be strongly affected by the gravitational corrections. The so-called true secular resonance, which is a new feature of the classic two-planet problem discovered by Michtchenko & Malhotra, may appear in other, different regions of the phase space of the generalized model. We found bifurcations of mode II from which emerge new, yet unknown in the literature, secularly unstable equilibria and a complex structure of the phase space. These equilibria may imply secularly unstable orbital configurations even for initially moderate eccentricities. The point mass gravity corrections can affect the long-term stability in the secular time-scale, which may directly depend on the age of the host star through its spin rate. We also analyse the secular dynamics of the υ Andromedae system in the realm of the generalized model. Also in this case of the three-planet system, new secular equilibria may appear.

Reducing the gravitational lensing scatter of type Ia supernovae without introducing any extra bias

Magnification and de-magnification due to gravitational lensing will contribute to the brightness scatter of Type Ia supernovae (SNe Ia). The purpose of this paper is to investigate the possibility to decrease this scatter by correcting individual SNe Ia using observations of galaxies in the foreground, without introducing any extra bias. We simulate a large number of SN Ia lines of sight populated by galaxies. For each line of sight the true magnification factor and an estimate thereof are calculated. The estimated magnification factor corresponds to what an observer would infer from a survey like SNLS. Using the simulated data we investigate the possibility to estimate the magnification of individual supernovae with enough precision to be able to correct their brightness for gravitational lensing with negligible bias. Our simulations show that the bias arising from gravitational lensing corrections of individual SNe Ia is negligible for current and next generation surveys and that the scatter from lensing can be reduced by approximately a factor 2. The total scatter in the SN Ia magnitudes could be reduced by 4% for an intrinsic dispersion of 0.13 mag. For an intrinsic dispersion of 0.09 mag, which might not be to unrealistic for future surveys, the total scatter could be reduced by 6%. This will reduce the errors on cosmological parameters derived from supernova data by 4-8%. The prospect of correcting for lensing is thus very good.

Thermodynamics of Born–Infeld black holes

We discuss the horizon structure for Born–Infeld black holes in the context of Einstein–Born–Infeld gravity. We show that the entropy function formalism agrees with a direct calculation of the entropy. With the entropy function formalism we also obtain the entropy when an axion–dilaton system as well as gravitational derivative corrections are included.