Latest Papers in General Relativity
General Relativity And Quantum Cosmology
B. Boisseau, H. Giacomini
2018-09-24
Recently a class of inflationary models satisfying the constant rate of roll constraint, 
, has been studied and compared with the latest cosmological observational data. We consider the broader class of constraints 
and find an exact particular solution, without initial singularity, which is an attractor of the dynamics governed by a positive periodic potential 
. The spectral index 
and the tensor to scalar ratio 
are consistent with the recent observational data. If we ignore reheating and creation of matter after the end of inflation, this solution develops a period of deceleration and a second period of acceleration, consistent with the experimental results. In addition it yields the value of the Hubble parameter 
and the value of the redshift for the beginning of the second phase of accelerated expansion in agreement with current data.
Norbert Bodendorfer, Fabio M. Mele, Johannes Münch
2019-02-11
In effective models of loop quantum gravity, the onset of quantum effects is controlled by a so-called polymerisation scale. It is sometimes necessary to make this scale phase space dependent in order to obtain sensible physics. A particularly interesting choice recently used to study quantum corrected black hole spacetimes takes the generator of time translations itself to set the scale. We review this idea, point out errors in recent treatments, and show how to fix them in principle.
Elmo Benedetto, Fabiano Feleppa, Ignazio Licata, Hooman Moradpour, Christian Corda
2019-02-11
The Sagnac effect is usually considered as being a relativistic effect produced in an interferometer when the device is rotating. General relativistic explanations are known and already widely explained in many papers. Such general relativistic approaches are founded on Einstein's equivalence principle (EEP), which states the equivalence between the gravitational "force" and the pseudo-force experienced by an observer in a non-inertial frame of reference, included a rotating observer. Typically, the authors consider the so-called Langevin-Landau-Lifschitz metric and the path of light is determined by null geodesics. This approach partially hides the physical meaning of the effect. It seems indeed that the light speed varies by c\pm\omega r in one or the other direction around the disk. In this paper, a slightly different general relativistic approach will be used. The different "gravitational field" acting on the beam splitter and on the two rays of light is analyzed. This different approach permits a better understanding of the physical meaning of the Sagnac effect.
V. M. Khatsymovsky
2018-11-17
Faddeev gravity using a 
-dimensional tetrad (normally 
) is classically equivalent to general relativity (GR). The discrete Faddeev gravity on the piecewise flat spacetime normally assumes slowly varying metric and tetrad from vertex to vertex. Meanwhile, Faddeev action is finite (although not unambiguously defined) for discontinuous tetrad fields thus allowing, in particular, to consider a surface as consisting of virtually independent elementary triangles, and its area spectrum as the sum of elementary area spectra. In the discrete connection form, area tensors are canonically conjugate to SO(10) connection matrices, and earlier we have found the elementary area spectrum, which is nonsingular just at large connection or the strongly varying fields constituting a kind of "antiferromagnetic" structure. We appropriately define discrete {\it connection} Faddeev action to unambiguously determine the discrete Faddeev action for the strongly varying fields, but weakly varying metric, equivalent in the continuum limit to the GR action with this metric. Previously, we considered large variations in only one direction, now we use an ansatz in some respects less common, but overall, probably the most common. A unified simplicial connection representation is written out (depending on an auxiliary connection) both for the discrete Faddeev action and for the Regge action.
Debika Chowdhury, Jerome Martin, Christophe Ringeval, Vincent Vennin
2019-02-11
Inflation is considered as the best theory of the early universe by a very large fraction of cosmologists. However, the validity of a scientific model is not decided by counting the number of its supporters and, therefore, this dominance cannot be taken as a proof of its correctness. Throughout its history, many criticisms have been put forward against inflation. The final publication of the Planck Cosmic Microwave Background data represents a benchmark time to study their relevance and to decide whether inflation really deserves its supremacy. In this paper, we categorize the criticisms against inflation, go through all of them in the light of what is now observationally known about the early universe, and try to infer and assess the scientific status of inflation. Although we find that important questions still remain open, we conclude that the inflationary paradigm is not in trouble but, on the contrary, has rather been strengthened by the Planck data.
Lavinia Heisenberg, Matthias Bartelmann, Robert Brandenberger, Alexandre Refregier
2019-02-11
We investigate the implications of string Swampland criteria for alternative theories of gravity. Even though this has not rigorously been proven, there is some evidence that exact de-Sitter solutions with a positive cosmological constant cannot be successfully embedded into string theory, and that the low energy effective field theories containing a scalar field 
with a potential 
in the habitable landscape should satisfy the Swampland criteria 
. As a paradigmatic class of modified gravity theories for inflation and dark energy, we consider the extensively studied family of Horndeski Lagrangians in view of cosmological observations. Apart from a possible potential term, they contain derivative self-interactions as the Galileon and non-minimal couplings to the gravity sector. Hence, our conclusions on the Galileon sector can be also applied to many other alternative theories with scalar helicity modes containing derivative interactions such as massive gravity and generalized Proca. In the presence of such derivative terms, the dynamics of the scalar mode is substantially modified, and imposing the cosmological evolution constrained by observations places tight constraints on 
within the Swampland conjecture.
D. M. Ghilencea
2018-12-20
We consider the (gauged) Weyl gravity action, quadratic in the scalar curvature (
) and in the Weyl tensor (
) of the Weyl conformal geometry. In the absence of matter fields, this action has spontaneous breaking in which the Weyl gauge field 
becomes massive (mass 
Planck scale) after "eating" the dilaton in the 
term, in a Stueckelberg mechanism. As a result, one recovers the Einstein-Hilbert action with a positive cosmological constant and the Proca action for the massive Weyl gauge field . Below 
this field decouples and Weyl geometry becomes Riemannian. The Einstein-Hilbert action is then just a "low-energy" limit of Weyl quadratic gravity which thus avoids its previous, long-held criticisms. In the presence of matter scalar field 
(Higgs-like), with couplings allowed by Weyl gauge symmetry, after its spontaneous breaking one obtains in addition, at low scales, a Higgs potential with spontaneous electroweak symmetry breaking. This is induced by the non-minimal coupling 
to Weyl geometry, with Higgs mass 
(
is the coefficient of the term). In realistic models 
must be classically tuned 
. We comment on the quantum stability of this value.
A. Füzfa
2019-02-11
By using Kinnersley's solution of general relativity, we model relativistic deep space flights and local celestial sphere on board of rockets that are thrusted by anisotropic absorption or emission of radiation. Relativistic kinematics of the photon rocket are obtained through energy-momentum conservation of the pointlike rocket and applied to light sails (beam-powered propulsion or absorption rockets) and blackbody rockets (i.e., emission rockets thrusted by anisotropic radiative cooling). A relativistic description of high-velocity trips toward Proxima Centauri on board of a light sail and an emission rocket in terms of acceleration, mass variation and time dilation shows that the true problem of interstellar travel is not the amount of propellant, nor the duration of the trip but rather its tremendous energy cost: while an energy of 
suffices for a flyby with an ultralight laser sail, about 
times the current world energy production would be required for sending a 
mission. We then study the propagation of light toward observers on board of radiation rockets with the null geodesics of Kinnersley spacetime in the Hamiltonian formulation. We apply this to the deformation of the local celestial sphere of the accelerated traveller under relativistic aberration and Doppler effect. A model of the traveller's local celestial sphere is built to produce striking illustrations of the change of the front and rear panoramas on-board of radiation spaceships heading toward star Alnilam. We also show how our results could interestingly be further applied to extremely luminous events like the large amount of gravitational waves emitted by binary black hole mergers.
Neven Bilic, Dragoljub D. Dimitrijevic, Goran S. Djordjevic, Milan Milosevic, Marko Stojanovic
2018-09-19
A model of tachyon inflation is proposed in the framework of holographic cosmology. The model is based on a holographic braneworld scenario with a D3-brane located at the holographic boundary of an asymptotic ADS
bulk. The tachyon field that drives inflation is represented by a DBI action on the brane. We solve the evolution equations analytically in the slow-roll regime and solve the exact equations numerically. We calculate the inflation parameters and compare the results with Planck 2018 data.
Prerna Rana, A. Mangalam
2019-01-09
We derive alternate and new closed-form analytic solutions for the non-equatorial eccentric bound trajectories, 
, 
, around a Kerr black hole by using the transformation 
. The application of the solutions is straightforward and numerically fast. We obtain and implement translation relations between energy and angular momentum of the particle, (
, 
), and eccentricity and inverse-latus rectum, (
, 
), for a given spin, 
, and Carter's constant, 
, to write the trajectory completely in the (, , , ) parameter space. The bound orbit conditions are obtained and implemented to select the allowed combination of parameters (, , , ). We also derive specialized formulae for spherical and separatrix orbits. A study of the non-equatorial analog of the previously studied equatorial separatrix orbits is carried out where a homoclinic orbit asymptotes to an energetically bound spherical orbit. Such orbits simultaneously represent an eccentric orbit and an unstable spherical orbit, both of which share the same and values. We present exact expressions for and as functions of the radius of the corresponding unstable spherical orbit, 
, , and , and their trajectories, for (
) separatrix orbits; they are shown to reduce to the equatorial case. These formulae have applications to study the gravitational waveforms from EMRIs besides relativistic precession and phase space explorations. We obtain closed-form expressions of the fundamental frequencies of non-equatorial eccentric trajectories that are equivalent to the previously obtained quadrature forms and also numerically match with the equivalent formulae previously derived. We sketch several orbits and discuss their astrophysical applications.
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