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We consider a galileon field coupled to gravity. The standard no-hair theorems do not apply, because of the galileon's peculiar derivative interactions. We prove that, nonetheless, static spherically symmetric black holes cannot sustain non-trivial galileon profiles. Our theorem holds regardless of whether there are non-minimal couplings between the galileon and gravity of the covariant galileon type.
There is an approximately 9% discrepancy, corresponding to 2.4sigma, between two independent constraints on the expansion rate of the universe: one indirectly arising from the cosmic microwave background and baryon acoustic oscillations, and one more directly obtained from local measurements of the relation between redshifts and distances to sources. We argue that by taking into account the local gravitational potential at the position of the observer this tension - strengthened by the recent Planck results - is partially relieved and the concordance of the standard model of cosmology increased. We estimate that measurements of the local Hubble constant are subject to a cosmic variance of about 2.4% (limiting the local sample to redshifts z>0.010) or 1.3% (limiting it to z>0.023), a more significant correction than that taken into account already. Nonetheless, we show that one would need a very rare fluctuation to fully explain the offset in the Hubble rates. If this tension is further strengthened, a cosmology beyond the standard model may prove necessary.
We propose a new probe of the dependence of the fine structure constant, alpha, on a strong gravitational field using metal lines in the spectra of white dwarf stars. Comparison of laboratory spectra with far-UV astronomical spectra from the white dwarf star G191-B2B recorded by the Hubble Space Telescope Imaging Spectrograph gives limits on the fractional variation of alpha of (Delta alpha/alpha)=(4.2 +- 1.6)x10^(-5) and (-6.1 +- 5.8)x10^(-5) from Fe V and Ni V spectra, respectively, at a dimensionless gravitational potential relative to Earth of (Delta phi) ~ 5x10^(-5). With better determinations of the laboratory wavelengths of the lines employed these results could be improved by up to two orders of magnitude.
Our understanding of quantum gravity suggests that at the Planck scale the usual geometry loses its meaning. If so, the quest for grand unification in a large non-abelian group naturally endowed with the property of asymptotic freedom may also lose its motivation. Instead we propose an unification of all fundamental interactions at the Planck scale in the form of a Universal Landau Pole (ULP), at which all gauge couplings diverge. The Higgs quartic coupling also diverges while the Yukawa couplings vanish. The unification is achieved with the addition of fermions with vector gauge couplings coming in multiplets and with hypercharges identical to those of the the Standard Model. The presence of these particles also prevents the Higgs quartic coupling from becoming negative, thus avoiding the instability (or metastability) of the SM vacuum.
We identify a class of condensate states in the group field theory (GFT) approach to quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a non-linear and non-local extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semi-classical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
MOND predicts that the asymptotic gravitational potential of an isolated, bounded (baryonic) mass, M, is phi(r)=(MGa0)^{1/2}ln(r); a0 is the MOND constant. Relativistic MOND theories predict that the lensing effects of M are dictated by phi(r) as general-relativity lensing is dictated by the Newtonian potential. Thus, MOND predicts that the asymptotic Newtonian potential deduced from galaxy-galaxy gravitational lensing will have: (1) a logarithmic r dependence, and (2) a normalization (parametrized standardly as 2s^2) that depends only on M: s=(MGa0/4)^{1/4}. I compare these predictions with recent results of galaxy-galaxy lensing, and find agreement on all counts. For the "blue"-lenses subsample ("spiral" galaxies) MOND reproduces the observations well with an r'-band M/L of 1-3 solar units, and for "red" lenses ("elliptical" galaxies) with M/L of 3-6 solar units, both consistent with baryons only. In contradistinction, Newtonian analysis requires, typically, M/L values of about 130 solar units, bespeaking a mass discrepancy of a factor of about 40. Compared with the staple, rotation-curve tests, MOND is here tested in a wider population of galaxies, through a different phenomenon, using relativistic test objects, and is probed to several-times-lower accelerations--as low as a few percent of a0.
We report a joint test of local Lorentz invariance and the Einstein equivalence principle for electrons, using long-term measurements of the transition frequency between two nearly degenerate states of atomic dysprosium. We present many-body calculations which demonstrate that the energy splitting of these states is particularly sensitive to violations of both special and general relativity. We limit Lorentz violation for electrons at the level of $10^{-17}$, matching or improving the best laboratory and astrophysical limits by up to a factor of 10, and improve bounds on gravitational redshift anomalies for electrons by 2 orders of magnitude, to $10^{-8}$. With some enhancements, our experiment may be sensitive to Lorentz violation at the level of $9\times 10^{-20}$.
The first-order Holst action with negative cosmological constant is rendered finite by requiring functional differentiability on the configuration space of tetrads and connections. The surface terms that arise in the action for ADS gravity are equivalent to the Euler and Pontryagin densities with fixed weight factors; these terms modify the Noether charges that arise from diffeomorphism invariance of the action.
Cosmic Microwave Background (CMB) polarization B-modes induced by Faraday Rotation (FR) can provide a distinctive signature of primordial magnetic fields because of their characteristic frequency dependence and because they are only weakly damped on small scales. FR also leads to mode-coupling correlations between the E and B type polarization, and between the temperature and the B-mode. These additional correlations can further help distinguish magnetic fields from other sources of B-modes. We review the FR induced CMB signatures and present the constraints on primordial magnetism that can be expected from upcoming CMB experiments. Our results suggest that FR of CMB will be a promising probe of primordial magnetic fields.
We compute the proper time Lyapunov exponent for charged Myers Perry black hole spacetime and investigate the instability of the equatorial circular geodesics (both timelike and null) via this exponent. We also show that for more than four spacetime dimensions $(N \geq 3)$, there are \emph{no} Innermost Stable Circular Orbits (ISCOs) in charged Myers Perry black hole spacetime. We further show that among all possible circular orbits, timelike circular orbits have \emph{longer} orbital periods than null circular orbits (photon spheres) as measured by asymptotic observers. Thus, timelike circular orbits provide the \emph{slowest way} to orbit around the charged Myers Perry black hole.
We present a study of the geodesic equations of a black hole space-time which is a solution of the three-dimensional NMG theory and is asymptotically Lifshitz with $z=3$ and $d=1$ as found in [Ayon-Beato E., Garbarz A., Giribet G. and Hassaine M., Phys. Rev. {\bf D} 80, 104029 (2009)]. By means of the corresponding effective potentials for massive particles and photons we find the allowed motions by the energy levels. Exact solutions for radial and non-radial geodesics are given in terms of the Weierstrass elliptic $\wp$, $σ$, and $ζ$ functions.
We show that the special relativistic dynamics when combined with quantum mechanics and the concept of superstatistics can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy scales. This interpretation leads to Feynman amplitudes that are in the Euclidean regime identical to transition probability of a Brownian particle propagating through a granular space. Some kind of spacetime granularity could be held responsible for the emergence at larger scales of various symmetries. For illustration we consider also the dynamics and the propagator of a spinless relativistic particle. Implications for doubly special relativity, quantum field theory, quantum gravity and cosmology are discussed.
We propose to introduce non-minimal couplings of Affleck-Dine (AD) field to gravity by adding the coupling of AD field to the Ricci scalar curvature. As the Jordan frame supergravity always predict $|Φ|^2 {\cal R}/6$ type coupling for scalars with canonical kinetic terms, we propose a way to realize the required $c_0|Φ|^2 {\cal R}$-type couplings with generic $c_0$ for canonical complex scalar fields after SUSY breaking. The impacts of such non-minimal gravitational couplings for AD field is shown, especially on the Q-balls formation and the associated gravitational wave (GW) productions. New form of scalar potential for AD field in the Einstein frame is obtained. By numerical simulations, we find that, with non-minimal gravitational coupling to AD field, Q-balls can successfully form even with the choice of non-negative $K$ parameter for $ξ>0$. The associated GW productions as well as their dependences on the $ξ$ parameter are also discussed.
A viable quantum theory of gravity is one of the biggest challenges facing physicists. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity -- spontaneous dimensional reduction and self-completeness. The former suggests the spacetime background at the Planck scale may be effectively two-dimensional, while the latter implies a condition of maximal compression of matter by the formation of an event horizon for Planckian scattering. We generalize such a result to an arbitrary number of dimensions, and show that gravity in higher than four dimensions remains self-complete, but in lower dimensions it is not. In such a way we established an "exclusive disjunction" or "exclusive or" (XOR) between the occurrence of self-completeness and dimensional reduction, with the goal of actually reducing the unknowns for the scenario of the physics at the Planck scale. Potential phenomenological implications of this result are considered by studying the case of a two-dimensional dilaton gravity model resulting from dimensional reduction of Einstein gravity.
It is well-known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equations from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)_L instantons and SU(2)_R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.
In this paper, we investigate the thermal effect on the Casimir energy associated with a massive scalar quantum field confined between two large parallel plates in a CPT-even, aether-like Lorentz-breaking scalar field theory. In order to do that we consider a nonzero chemical potential for the scalar field assumed to be in thermal equilibrium at some finite temperature. The calculations of the energies are developed by using the Abel-Plana summation formula, and the corresponding results are analyzed in several asymptotic regimes of the parameters of the system, like mass, separations between the plates and temperature.
We review the new theory of modified supergravity, dubbed F(\cal R) supergravity, and some of its recent applications to inflation and reheating in the early universe cosmology. The F(\cal R) supergravity is the N=1 locally supersymmetric extension of the f(R) gravity in four space-time dimensions. A manifestly supersymmetric formulation of the F(\cal R) supergravity exist in terms of N=1 superfields, by using the (old) minimal Poincar'e supergravity in curved superspace. We find the conditions for stability, the absence of ghosts and tachyons. Three models of the F(\cal R) supergravity are studied. The first example is devoted to a recovery of the standard (pure) N=1 supergravity with a negative cosmological constant from the F(\cal R) supergravity. As the second example, a generic {\cal R}^2-type supergravity is investigated, and the existence of the AdS bound on the scalar curvature is found. As the third (and most important) example, a simple viable realization of chaotic inflation in supergravity is found. Our approach is {\it minimalistic} since it does not introduce new exotic fields or new interactions, beyond those already present in (super)gravity. The universal reheating mechanism is automatic. We establish the consistency of our approach and also apply it to preheating and reheating after inflation. The Higgs inflation and its correspondence to the Starobinsky inflation is established in the context of supergravity. We briefly review other relevant issues such as non-Gaussianity, CP-violation, origin of baryonic asymmetry, lepto- and baryo-genesis. The F(\cal R) supergravity has promise for possible solutions to those outstanding problems too.
The time-varying gravitational field produced by a Weber bar is used to explore mathematical features of the linearized Einstein equation. We present a self-contained formal framework for the treatment of the linear field, which is applicable to several situations where the standard quadrupolar formulas are not adequate. The expressions for retarded integrals reveal a singularity associated with boundary conditions. Results from the transverse traceless subgauge are compared with the radiation calculated from retarded integrals. Lienard-Wiechert potentials are used in a treatment of the Weber bar as a collection of point particles and further possible applications are outlined. The Riemann tensor clarifies the transition from near-field geodesic forces to tidal forces in the far field.