scholarly journals New non-perturbative de Sitter vacua in α′-complete cosmology

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Carmen A. Núñez ◽  
Facundo Emanuel Rost
Keyword(s):  
Equations Of Motion ◽  
Generalized Equations ◽  
De Sitter ◽  
Scale Factors ◽  
Spatial Dimensions ◽  
Higher Derivatives ◽  
De Sitter Vacua ◽  
The Stability ◽  
Derivatives Of ◽  
Constant Dilaton

Abstract The α′-complete cosmology developed by Hohm and Zwiebach classifies the O(d, d; ℝ) invariant theories involving metric, b-field and dilaton that only depend on time, to all orders in α′. Some of these theories feature non-perturbative isotropic de Sitter vacua in the string frame, generated by the infinite number of higher-derivatives of O(d, d; ℝ) multiplets. Extending the isotropic ansatz, we construct stable and unstable non-perturbative de Sitter solutions in the string and Einstein frames. The generalized equations of motion admit new solutions, including anisotropic d + 1-dimensional metrics and non-vanishing b-field. In particular, we find dSn+1× Td−n geometries with constant dilaton, and also metrics with bounded scale factors in the spatial dimensions with non-trivial b-field. We discuss the stability and non-perturbative character of the solutions, as well as possible applications.

Determination of Stability Derivatives by Impulse-Response Techniques

1977 ◽  
Vol 14 (02) ◽  
pp. 265-275
Author(s):  
Carl A. Scragg
Keyword(s):  
Memory Effect ◽  
Impulse Response ◽  
Traditional Method ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Regular Motion ◽  
Stability Derivatives ◽  
The Stability ◽  
Derivatives Of

This paper presents a new method of experimentally determining the stability derivatives of a ship. Using a linearized set of the equations of motion which allows for the presence of a memory effect, the response of the ship to impulsive motions is examined. This new technique is compared with the traditional method of regular-motion tests and experimental results are presented for both methods.

scholarly journals INFLATIONARY DILATONIC de SITTER UNIVERSE FROM ${\mathcal N} = 4$ SUPER-YANG–MILLS THEORY PERTURBED BY SCALARS

2003 ◽  
Vol 18 (18) ◽  
pp. 1257-1264
Author(s):  
JOHN QUIROGA HURTADO
Keyword(s):  
Effective Action ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Scale Factor ◽  
Conformal Anomaly ◽  
Inflationary Universe ◽  
De Sitter ◽  
Yang Mills ◽  
The Stability ◽  
Super Yang Mills Theory

In this paper a quantum [Formula: see text] super-Yang–Mills theory perturbed by dilaton-coupled scalars, is considered. The induced effective action for such a theory is calculated on a dilaton-gravitational background using the conformal anomaly found via AdS/CFT correspondence. Considering such an effective action (using the large N method) as a quantum correction to the classical gravity action with cosmological constant we study the effect from dilaton to the scale factor (which corresponds to the inflationary universe without dilaton). It is shown that, depending on the initial conditions for the dilaton, the dilaton may slow down, or accelerate, the inflation process. At late times, the dilaton is decaying exponentially. At the end of this work, we consider the question how the perturbation of the solution for the scale factor affects the stability of the solution for the equations of motion and therefore the stability of the Inflationary Universe, which could be eternal.

scholarly journals Oh, wait, O8 de Sitter may be unstable!

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Iosif Bena ◽  
G. Bruno De Luca ◽  
Mariana Graña ◽  
Gabriele Lo Monaco
Keyword(s):  
String Theory ◽  
De Sitter ◽  
De Sitter Vacua ◽  
The Stability

Abstract We analyze the stability of four-dimensional de Sitter vacua constructed by compactifying massive Type IIA supergravity in the presence of two O8 sources [1]. When embedded in String Theory the first source has a clear interpretation as an O8− plane, but the second one could correspond to either an O8+ plane or to an O8− plane with 16 D8-branes on top. We find that this latter solution has a tachyonic instability, corresponding to the D8 branes moving away from the O8− plane. We comment on the possible ways of distinguishing between these sources.

scholarly journals Cosmology with higher-derivative matter fields

2016 ◽  
Vol 13 (07) ◽  
pp. 1650102 ◽  
Author(s):  
Tiberiu Harko ◽  
Francisco S. N. Lobo ◽  
Emmanuel N. Saridakis
Keyword(s):  
Dark Energy ◽  
Modified Gravity ◽  
State Parameter ◽  
De Sitter ◽  
Field Equations ◽  
Stiff Matter ◽  
Higher Derivative ◽  
Higher Derivatives ◽  
Derivatives Of ◽  
Matter Fields

We investigate the cosmological implications of a new class of modified gravity, where the field equations generically include higher-order derivatives of the matter fields, arising from the introduction of non-dynamical auxiliary fields in the action. Imposing a flat, homogeneous and isotropic geometry, we extract the Friedmann equations, obtaining an effective dark-energy sector containing higher-derivatives of the matter energy density and pressure. For the cases of dust, radiation and stiff matter, we analyze the cosmological behavior, finding accelerating, de Sitter and non-accelerating phases, dominated by matter or dark-energy. Additionally, the effective dark-energy equation-of-state parameter can be quintessence-like, cosmological-constant-like or even phantom-like. The detailed study of these scenarios may provide signatures, that could distinguish them from other candidates of modified gravity.

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.

Dynamics of Flexible Multibody Systems Using Bond Graphs and Lagrange Multipliers

1990 ◽  
Vol 112 (1) ◽  
pp. 30-35 ◽  
Author(s):  
B. Samanta
Keyword(s):  
Rigid Body ◽  
Lagrange Multipliers ◽  
Equations Of Motion ◽  
Constrained Systems ◽  
System Response ◽  
Bond Graphs ◽  
Higher Derivatives ◽  
Model Constraint ◽  
System Equations ◽  
Derivatives Of

A procedure is presented to study the dynamics of interconnected flexible systems using bond graphs. The concept of Lagrange multipliers, which are commonly used in analysis of constrained systems, is introduced in the procedure. The overall motions of each of the component bodies are described in terms of large rigid body motions and small elastic vibrations. Bond graphs are used to represent both rigid body and flexible dynamics of each body in a unified manner. Bond graphs of such sub-systems are coupled to one another satisfying the kinematic constraints at the interfaces to get the overall system model. Constraint reactions are introduced in the form of Lagrange multipliers at the interfaces without disturbing the integral causality in the subsystem models, which leads to easy derivation of system equations. The equations of motion and higher derivatives of the constraint relations are integrated to obtain the constraint reactions and the system response. The procedure is illustrated by an example system and results are in good agreement with those presented earlier.

scholarly journals DE SITTER STABILITY IN QUADRATIC GRAVITY

2007 ◽  
Vol 16 (06) ◽  
pp. 1075-1085 ◽  
Author(s):  
A. V. TOPORENSKY ◽  
P. V. TRETYAKOV
Keyword(s):  
General Relativity ◽  
Simple Form ◽  
Equations Of Motion ◽  
Cosmological Solution ◽  
Stability Conditions ◽  
De Sitter ◽  
Bianchi I ◽  
Quadratic Gravity ◽  
The Stability ◽  
Hilbert Action

Quadratic curvature corrections to the Einstein–Hilbert action lead in general to higher-order equations of motion, which can induce instability of some unperturbed solutions of General Relativity. We study the conditions for the stability of the de Sitter cosmological solution. We argue that the simple form of this condition known for the FRW background in (3+1) dimensions changes seriously if at least one of these two assumptions is violated. In the present paper, the stability conditions for the de Sitter solution are found for the multidimensional FRW background and for Bianchi I metrics in (3 + 1) dimensions.

scholarly journals de Sitter vacua from ten dimensions

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Shamit Kachru ◽  
Manki Kim ◽  
Liam McAllister ◽  
Max Zimet
Keyword(s):  
Equations Of Motion ◽  
Effective Theory ◽  
De Sitter ◽  
Stress Energy ◽  
Exact Agreement ◽  
De Sitter Vacua ◽  
Brane Action

Abstract We analyze the de Sitter construction of [1] using ten-dimensional supergravity, finding exact agreement with the four-dimensional effective theory. Starting from the fermionic couplings in the D7-brane action, we derive the ten-dimensional stress-energy due to gaugino condensation on D7-branes. We demonstrate that upon including this stress-energy, as well as that due to anti-D3-branes, the ten-dimensional equations of motion require the four-dimensional curvature to take precisely the value determined by the four-dimensional effective theory of [1].

Stability of the Vertical Autorotation of a Single-Winged Samara

1992 ◽  
Vol 59 (4) ◽  
pp. 1000-1008 ◽  
Author(s):  
D. Seter ◽  
A. Rosen
Keyword(s):  
Equilibrium State ◽  
Equations Of Motion ◽  
Numerical Differentiation ◽  
Aerodynamic Stability ◽  
Small Perturbations ◽  
Stability Derivatives ◽  
Basic Equilibrium ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Derivatives Of

A numerical model to investigate the stability of the vertical autorotation of a singlewinged samara is presented. This model is obtained after the method of small perturbations about an equilibrium state is applied on the nonlinear equations of motion of the samara. The aerodynamic stability derivatives of the wing are obtained by numerical differentiation. The model is used in order to study the influence of different parameters on the stability. Since the stability is highly dependent on the basic equilibrium state, the influence of the different parameters on the basic state is also presented and discussed. The theoretical model is validated by comparing its results with qualitative experimental results.

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