scholarly journals Fab Four: When John and George Play Gravitation and Cosmology

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
J.-P. Bruneton ◽  
M. Rinaldi ◽  
A. Kanfon ◽  
A. Hees ◽  
S. Schlögel ◽  
...  
Keyword(s):  
Scalar Field ◽  
Solar System ◽  
Parameter Space ◽  
Ad Hoc ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Inflationary Model ◽  
Einstein Tensor ◽  
Chameleon Mechanism ◽  
Derivatives Of

Scalar-tensor theories of gravitation attract again a great interest since the discovery of the Chameleon mechanism and of the Galileon models. The former allows reconciling the presence of a scalar field with the constraints from Solar System experiments. The latter leads to inflationary models that do not need ad hoc potentials. Further generalizations lead to a tensor-scalar theory, dubbed the “Fab Four,” with only first and second order derivatives of the fields in the equations of motion that self-tune to a vanishing cosmological constant. This model needs to be confronted with experimental data in order to constrain its large parameter space. We present some results regarding a subset of this theory named “John,” which corresponds to a nonminimal derivative coupling between the scalar field and the Einstein tensor in the action. We show that this coupling gives rise to an inflationary model with very unnatural initial conditions. Thus, we include the term named “George,” namely, a nonminimal, but nonderivative, coupling between the scalar field and Ricci scalar. We find a more natural inflationary model, and, by performing a post-Newtonian analysis, we derive the set of equations that constrain the parameter space with data from experiments in the Solar System.

scholarly journals α-Attractors and reheating in a nonminimal inflationary model

2020 ◽  
Vol 29 (10) ◽  
pp. 2050077
Author(s):  
R. Shojaee ◽  
K. Nozari ◽  
F. Darabi
Keyword(s):  
Scalar Field ◽  
Spectral Index ◽  
Parameter Space ◽  
Model Potential ◽  
Index Formula ◽  
Inflationary Model ◽  
Scalar Spectral Index ◽  
Canonical Scalar Field

We study [Formula: see text]-attractor models with both E-model and T-model potential in an extended Nonminimal Derivative (NMD) inflation where a canonical scalar field and its derivatives are nonminimally coupled to gravity. We calculate the evolution of perturbations during this regime. Then by adopting inflation potentials of the model we show that in the large [Formula: see text] and small [Formula: see text] limit, the value of the scalar spectral index [Formula: see text] and tensor-to-scalar ratio [Formula: see text] are universal. Next, we study reheating after inflation in this formalism. We obtain some constraints on the model’s parameter space by adopting the results with Planck 2018.

scholarly journals Constraints on scalar–tensor theory of gravity by solar system tests

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
P. A. González ◽  
Marco Olivares ◽  
Eleftherios Papantonopoulos ◽  
Yerko Vásquez
Keyword(s):  
Time Delay ◽  
Scalar Field ◽  
Solar System ◽  
Gravitational Redshift ◽  
Scalar Tensor Theory ◽  
Einstein Tensor ◽  
Perihelion Precession ◽  
Deflection Of Light ◽  
Tensor Theory ◽  
Theory Of Gravity

AbstractWe study the motion of particles in the background of a scalar–tensor theory of gravity in which the scalar field is kinetically coupled to the Einstein tensor. We constrain the value of the derivative parameter z through solar system tests. By considering the perihelion precession we obtain the constraint $$\sqrt{z}/m_{\mathrm{p}} > 2.6\times 10^{12}$$ z / m p > 2.6 × 10 12  m, the gravitational redshift $$\frac{\sqrt{z}}{m_{\mathrm{p}}}>2.7\times 10^{\,10}$$ z m p > 2.7 × 10 10  m, the deflection of light $$\sqrt{z}/m_{\mathrm{p}} > 1.6 \times 10^{11}$$ z / m p > 1.6 × 10 11  m, and the gravitational time delay $$\sqrt{z}/m_{\mathrm{p}} > 7.9 \times 10^{12}$$ z / m p > 7.9 × 10 12  m; thereby, our results show that it is possible to constrain the value of the z parameter in agreement with the observational tests that have been considered.

Partitioning the Parameter Space According to Different Behaviors During Three-Dimensional Impacts

1995 ◽  
Vol 62 (3) ◽  
pp. 740-746 ◽  
Author(s):  
V. Bhatt ◽  
J. Koechling
Keyword(s):  
Parameter Space ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flow Patterns ◽  
The Body ◽  
Qualitative Behavior ◽  
Sliding Velocity ◽  
Physical Behavior ◽  
Rule Out

The equations of motion that define three-dimensional rigid-body impact with finite friction and restitution cannot be solved in a closed form. Previous work has shown that for general shapes and initial conditions, the direction of sliding velocity keeps changing continuously throughout the duration of impact. The flow patterns defined by the trace of the sliding velocity can be classified into a finite number of qualitatively distinct physical behavior. We identify three dimensionless parameters that completely specify the sliding behavior, and determine regions in this parameter space that correspond to each of the different flow patterns. The qualitative behavior during impact can now be determined based on the region which contains the parameters for a given impact configuration. The analysis is also used to study the sensitivity of the sliding behavior to changes in shape or configuration of the body and to rule out the occurrence of certain ambiguities in the post-sticking behavior during impact.

Primordial quantum perturbations

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Slow Roll ◽  
Inflationary Models

This chapter shows that fluctuations of quantum origin are generated during inflation and that this process supplies initial conditions compatible with the observations. These fluctuations are therefore an important prediction of inflationary models. The chapter thus begins with a study of perturbations during inflation, proceeding in a similar manner to the previous chapter by finding the perturbation of the energy–momentum tensor of the scalar field. Another method of deriving the equations of motion of the perturbations is to start from the action of general relativity coupled to a scalar field, and expand to second order in the metric and scalar field perturbations. The chapter then proceeds with the determination of the initial conditions and the slow-roll inflation.

A note on the Hamiltonian theory of quantization. II

1947 ◽  
Vol 43 (2) ◽  
pp. 196-204 ◽  
Author(s):  
T. S. Chang
Keyword(s):  
Variational Principles ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Field Equations ◽  
Gauge Invariant ◽  
Commutation Relations ◽  
Hamiltonian Theory ◽  
Higher Derivatives ◽  
Missing Momenta ◽  
Derivatives Of

It is pointed out that the equations of motion for any field obtained by varying a Lagrangian subject to auxiliary conditions are exactly equivalent to a certain set of canonical equations and that the commutation relations between the dynamical variables for the latter equations are Lorentz-invariant. By extending the theory to Lagrangians containing higher derivatives of the field quantities, it is shown that any given set of field equations can be put into the canonical form, though it is not derived from variational principles. The question of Lagrangians with missing momenta is also considered. It is shown that if the Lagrangian is ‘gauge-invariant’, some of the p's must be missing and the corresponding Eulerian equations can be replaced by equations containing no q and then can be replaced by initial conditions. The commutation relations between gauge-invariant quantities are Lorentz-invariant. For Lagrangians which are not gauge-invariant but are such as to have missing momenta, the passage to quantum theory will in general give rise to non-Lorentz-invariant commutation relations. In both cases, the equations of motion can be cast in canonical forms.

scholarly journals An interstellar origin for high-inclination Centaurs

2020 ◽  
Vol 494 (2) ◽  
pp. 2191-2199 ◽  
Author(s):  
F Namouni ◽  
M H M Morais
Keyword(s):  
Solar System ◽  
Ad Hoc ◽  
Initial Conditions ◽  
Precise Orbit Determination ◽  
Oort Cloud ◽  
The Past ◽  
Real Objects ◽  
Outward Migration ◽  
Current Orbit ◽  
Relaxation Models

ABSTRACT We investigate the possible origins of real high-inclination Centaurs and trans-neptunian objects using a high-resolution statistical search for stable orbits that simulates their evolution back in time to the epoch when planet formation ended 4.5 billion years in the past. The simulation is a precise orbit determination method that does not involve ad hoc initial conditions or assumptions such as those found in planetesimal disc relaxation models upon which their conclusions depend. It can therefore be used to independently test origin theories based on relaxation models by examining the past orbits of specific real objects. Here, we examined 17 multiple-opposition high-inclination Centaurs and the two polar trans-neptunian objects 2008 KV42 and (471325) 2011 KT19. The statistical distributions show that their orbits were nearly polar 4.5 Gyr in the past, and were located in the scattered disc and inner Oort cloud regions. Early polar inclinations cannot be accounted for by current Solar system formation theory as the early planetesimal system must have been nearly flat in order to explain the low-inclination asteroid and Kuiper belts. Furthermore, the early scattered disc and inner Oort cloud regions are believed to have been devoid of Solar system material as the planetesimal disc could not have extended far beyond Neptune’s current orbit in order to halt the planet’s outward migration. The nearly polar orbits of high-inclination Centaurs 4.5 Gyr in the past therefore indicate their probable early capture from the interstellar medium.

scholarly journals SOLAR SYSTEM TESTS OF f(R) GRAVITY

2014 ◽  
Vol 23 (04) ◽  
pp. 1450036 ◽  
Author(s):  
JUN-QI GUO
Keyword(s):  
Solar System ◽  
Functional Form ◽  
Equations Of Motion ◽  
Jordan Frame ◽  
The Sun ◽  
False Vacuum ◽  
Vacuum Decay ◽  
Effective Potentials ◽  
Chameleon Mechanism ◽  
Numerical Approaches

In this paper, we revisit the solar system tests of f(R) gravity. When the sun sits in a vacuum, the field f′ is light, which leads to a metric different from the observations. We reobtain this result in a simpler way by directly focusing on the equations of motion for f(R) gravity in the Jordan frame (JF). The discrepancy between the metric in the f(R) gravity and the observations can be alleviated by the chameleon mechanism. The implications from the chameleon mechanism on the functional form f(R) are discussed. Considering the analogy of the solar system tests to the false vacuum decay problem, the effective potentials in different cases are also explored. The combination of analytic and numerical approaches enables us to ascertain whether an f(R) model can pass the solar system tests or not.

scholarly journals THE SCALAR ETHER-THEORY OF GRAVITATION AND ITS FIRST TEST IN CELESTIAL MECHANICS

2002 ◽  
Vol 17 (29) ◽  
pp. 4203-4208 ◽  
Author(s):  
MAYEUL ARMINJON
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Solar System ◽  
Celestial Mechanics ◽  
Equations Of Motion ◽  
Alternative Interpretation ◽  
Crucial Point ◽  
Ether Theory ◽  
Theory Of Gravitation ◽  
Basic Equations

The motivations for investigating a theory of gravitation based on a concept of "ether" are discussed — a crucial point is the existence of an alternative interpretation of special relativity, named the Lorentz-Poincaré ether theory. The basic equations of one such theory of gravity, based on just one scalar field, are presented. To check this theory in celestial mechanics, an "asymptotic" scheme of post-Newtonian (PN) approximation is summarized and its difference with the standard PN scheme is emphasized. The derivation of PN equations of motion for the mass centers, based on the asymptotic scheme, is outlined. They are implemented for the major bodies of the solar system and the prediction for Mercury is compared with an ephemeris based on general relativity.

scholarly journals Simulations of Switchback, Fragmentation and Sunspot Pair in δ-Sunspots during Magnetic Flux Emergence

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 586
Author(s):  
Che-Jui Chang ◽  
Jean-Fu Kiang
Keyword(s):  
Magnetic Field ◽  
Solar System ◽  
Field Strength ◽  
Magnetic Flux ◽  
Initial Conditions ◽  
Observation Data ◽  
Flux Emergence ◽  
Polarity Inversion ◽  
Simulation Results ◽  
Spot Type

Strong flares and coronal mass ejections (CMEs), launched from δ-sunspots, are the most catastrophic energy-releasing events in the solar system. The formations of δ-sunspots and relevant polarity inversion lines (PILs) are crucial for the understanding of flare eruptions and CMEs. In this work, the kink-stable, spot-spot-type δ-sunspots induced by flux emergence are simulated, under different subphotospheric initial conditions of magnetic field strength, radius, twist, and depth. The time evolution of various plasma variables of the δ-sunspots are simulated and compared with the observation data, including magnetic bipolar structures, relevant PILs, and temperature. The simulation results show that magnetic polarities display switchbacks at a certain stage and then split into numerous fragments. The simulated fragmentation phenomenon in some δ-sunspots may provide leads for future observations in the field.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

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