Vacuum solutions for a twisted scalar field

1978 ◽  
Vol 363 (1715) ◽  
pp. 581-596 ◽  
Keyword(s):  
Scalar Field ◽  
Ground State ◽  
Characteristic Length ◽  
Scalar Fields ◽  
Finite Energy ◽  
Critical Value ◽  
Dimensional Model ◽  
Translational Invariance ◽  
Spontaneous Breakdown ◽  
Vacuum Solutions

The properties of the ground state of a classical self-interacting twisted scalar field on a two-dimensional Einstein cylinder are discussed. In parti­cular there is a spontaneous breakdown of the spatial translational invariance of the twisted ground state as a characteristic length increases across a critical value. Similar properties are shown to hold in a four­-dimensional model. Finally, it is shown that there exist four-dimensional models which do not have any finite-energy twisted scalar fields.

scholarly journals The hidden scalar Lagrangians within Horndeski theory

2020 ◽  
Vol 29 (14) ◽  
pp. 2043004
Author(s):  
Gregory W. Horndeski
Keyword(s):  
Scalar Field ◽  
Generating Function ◽  
Cotangent Bundle ◽  
Tensor Field ◽  
Scalar Fields ◽  
Field Theories ◽  
Metric Tensor ◽  
Cosmological Solutions ◽  
Different Types ◽  
Vacuum Solutions

In this paper, I show that there exists a new way to obtain scalar–tensor field theories by combining a special scalar field on the cotangent bundle with a scalar field on spacetime. These two scalar fields act as a generating function for the metric tensor. When using these two scalar fields in the Horndeski Lagrangians, we discover, while seeking Friedmann–Lemaître–Robertson–Walker-type cosmological solutions, that hidden in the Horndeski Lagrangians are nondegenerate second-order scalar Lagrangians. In accordance with Ostrogradsky’s work, these hidden scalar Lagrangians lead to multiple vacuum solutions, and thereby predict the existence of the multiverse. The multiverse is comprised of numerous different types of individual universes. For example, some begin explosively, and then coast along exponentially forever at an accelerated rate, while others begin in that manner, and then stop expanding and contract.

scholarly journals Quasinormal modes and their anomalous behavior for black holes in f(R) gravity

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Almendra Aragón ◽  
P. A. González ◽  
Eleftherios Papantonopoulos ◽  
Yerko Vásquez
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Critical Mass ◽  
Quasinormal Modes ◽  
Scalar Fields ◽  
Critical Value ◽  
Anomalous Behavior ◽  
Modified Theories Of Gravity ◽  
De Sitter ◽  
Massive Scalar Field

AbstractWe study the propagation of scalar fields in the background of an asymptotically de Sitter black hole solution in f(R) gravity. The aim of this work is to analyze in modified theories of gravity the existence of an anomalous decay rate of the quasinormal modes (QNMs) of a massive scalar field which was recently reported in Schwarzschild black hole backgrounds, in which the longest-lived modes are the ones with higher angular number, for a scalar field mass smaller than a critical value, while that beyond this value the behavior is inverted. We study the QNMs for various overtone numbers and they depend on a parameter $$\beta $$ β which appears in the metric and characterizes the f(R) gravity. For small $$\beta $$ β , i.e. small deviations from the Schwarzschild–dS black hole the anomalous behavior in the QNMs is present for the photon sphere modes, and the critical value of the mass of the scalar field depends on the parameter $$\beta $$ β while for large $$\beta $$ β , i.e. large deviations, the anomalous behavior and the critical mass does not appear. Also, the critical mass of the scalar field increases when the overtone number increases until the f(R) gravity parameter $$\beta $$ β approaches the near extremal limit at which the critical mass of the scalar field does not depend anymore on the overtone number. The imaginary part of the quasinormal frequencies is always negative leading to a stable propagation of the scalar fields in this background.

scholarly journals Weak cosmic censorship with self-interacting scalar and bound on charge to mass ratio

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yan Song ◽  
Tong-Tong Hu ◽  
Yong-Qiang Wang
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Cosmic Censorship ◽  
Mass Ratio ◽  
Quartic Coupling ◽  
Scalar Theory ◽  
Free Scalar ◽  
The One ◽  
Nonzero Scalar ◽  
Large Charge

Abstract We study the model of four-dimensional Einstein-Maxwell-Λ theory minimally coupled to a massive charged self-interacting scalar field, parameterized by the quartic and hexic couplings, labelled by λ and β, respectively. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. Moreover, we investigate the full nonlinear solution with nonzero scalar field included, and argue that these counterexamples can be removed by assuming charged self-interacting scalar field with sufficiently large charge not lower than a certain bound. In particular, this bound on charge required to preserve cosmic censorship is no longer precisely the weak gravity bound for the free scalar theory. For the quartic coupling, for λ < 0 the bound is below the one for the free scalar fields, whereas for λ > 0 it is above. Meanwhile, for the hexic coupling the bound is always above the one for the free scalar fields, irrespective of the sign of β.

scholarly journals FERMIONIC AND SCALAR FIELDS AS SOURCES OF INTERACTING DARK MATTER–DARK ENERGY

2011 ◽  
Vol 20 (13) ◽  
pp. 2543-2558 ◽  
Author(s):  
SAMUEL LEPE ◽  
JAVIER LORCA ◽  
FRANCISCO PEÑA ◽  
YERKO VÁSQUEZ
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Scalar Field ◽  
Analytical Solution ◽  
Scalar Fields ◽  
Nonminimal Coupling ◽  
Field Equations ◽  
Fermionic Field ◽  
Minimal Coupling ◽  
Constant Type

From a variational action with nonminimal coupling with a scalar field and classical scalar and fermionic interaction, cosmological field equations can be obtained. Imposing a Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the equations lead directly to a cosmological model consisting of two interacting fluids, where the scalar field fluid is interpreted as dark energy and the fermionic field fluid is interpreted as dark matter. Several cases were studied analytically and numerically. An important feature of the non-minimal coupling is that it allows crossing the barrier from a quintessence to phantom behavior. The insensitivity of the solutions to one of the parameters of the model permits it to find an almost analytical solution for the cosmological constant type of universe.

TIGHT-BINDING MODEL FOR THE QUANTUM LADDER IN A MAGNETIC FIELD

1996 ◽  
Vol 10 (28) ◽  
pp. 3827-3856 ◽  
Author(s):  
KAZUMOTO IGUCHI
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Tight Binding ◽  
Critical Value ◽  
Tight Binding Model ◽  
Binding Model ◽  
First Case

A tight-binding model is formulated for the calculation of the electronic structure and the ground state energy of the quantum ladder under a magnetic field, where the magnetic flux at the nth plaquette is given by ϕn. First, the theory is applied to obtain the electronic spectra of the quantum ladder models with particular magnetic fluxes such as uniform magnetic fluxes, ϕn=0 and 1/2, and the staggered magnetic flux, ϕn= (−1)n+1ϕ0. From these, it is found that as the effect of electron hopping between two chains—the anisotropy parameter r=ty/tx—is increased, there are a metal-semimetal transition at r=0 and a semimetal–semiconductor transition at r=2 in the first case, and metal-semiconductor transitions at r=0 in the second and third cases. These transitions are thought of as a new category of metal-insulator transition due to the hopping anisotropy of the system. Second, using the spectrum, the ground state energy is calculated in terms of the parameter r. It is found that the ground state energy in the first case diverges as r becomes arbitrarily large, while that in the second and third cases can have the single or double well structure with respect to r, where the system is stable at some critical value of r=rc and the transition between the single and double well structures is associated with whether tx is less than a critical value of txc. The latter cases are very reminiscent of physics in polyacetylene studied by Su, Schrieffer and Heeger.

scholarly journals LINEAR TIME-DEPENDENT INVARIANTS FOR SCALAR FIELDS AND NOETHER’S THEOREM

1994 ◽  
Vol 09 (19) ◽  
pp. 1785-1790 ◽  
Author(s):  
O. CASTAÑOS ◽  
R. LÓPEZ-PEÑA ◽  
V.I. MAN’KO
Keyword(s):  
Scalar Field ◽  
Infinite Number ◽  
Linear Time ◽  
Scalar Fields ◽  
Time Dependent ◽  
Noether’S Theorem ◽  
Noether's Theorem

The infinite number of time-dependent linear in field and conjugated momenta invariants is derived for the scalar field using the Noether’s theorem procedure.

scholarly journals BOUNDARY ONE-POINT FUNCTIONS, SCATTERING, AND BACKGROUND VACUUM SOLUTIONS IN TODA THEORIES

2003 ◽  
Vol 18 (06) ◽  
pp. 879-899 ◽  
Author(s):  
V. A. FATEEV ◽  
E. ONOFRI
Keyword(s):  
Exact Solutions ◽  
Ground State ◽  
S Matrix ◽  
Parametric Families ◽  
Vacuum Solutions ◽  
Ground State Energies

The parametric families of integrable boundary affine Toda theories are considered. We calculate boundary one-point functions and propose boundary S-matrices in these theories. We use boundary one-point functions and S-matrix amplitudes to derive boundary ground state energies and exact solutions describing classical vacuum configurations.

scholarly journals Quantization of Einstein-aether scalar field cosmology

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
N. Dimakis ◽  
T. Pailas ◽  
A. Paliathanasis ◽  
G. Leon ◽  
Petros A. Terzis ◽  
...  
Keyword(s):  
Scalar Field ◽  
Classical Solution ◽  
Potential Function ◽  
Scalar Fields ◽  
Inflationary Model ◽  
Cosmological Theory ◽  
Local Functions ◽  
Arbitrary Potential ◽  
Scalar Field Cosmology ◽  
First Time

AbstractWe present, for the first time, the quantization process for the Einstein-aether scalar field cosmology. We consider a cosmological theory proposed as a Lorentz violating inflationary model, where the aether and scalar fields interact through the assumption that the aether action constants are ultra-local functions of the scalar field. For this specific theory there is a valid minisuperspace description which we use to quantize. For a particular relation between the two free functions entering the reduced Lagrangian the solution to the Wheeler–DeWitt equation as also the generic classical solution are presented for any given arbitrary potential function.

scholarly journals PRE-INFLATION IN THE PRESENCE OF CONFORMAL COUPLING

2004 ◽  
Vol 19 (11) ◽  
pp. 807-816
Author(s):  
APOSTOLOS KUIROUKIDIS ◽  
DEMETRIOS B. PAPADOPOULOS
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Hubble Parameter ◽  
Field Potential ◽  
Critical Value ◽  
Big Bang ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Conformal Parameter ◽  
Flrw Universe

We consider a massless scalar field, conformally coupled to the Ricci scalar curvature, in the pre-inflation era of a closed FLRW Universe. The scalar field potential can be of the form of the Coleman–Weinberg one-loop potential, which is flat at the origin and drives the inflationary evolution. For positive values of the conformal parameter ξ, less than the critical value ξ c =(1/6), the model admits exact solutions with nonzero minimum scale factor and zero initial Hubble parameter. Thus these solutions can be matched smoothly to the so-called Pre-Big-Bang models. At the end of this pre-inflation era one can match inflationary solutions by specifying the form of the potential and the whole solution is of the class C(1).

INTERACTING GENERALIZED DARK ENERGY AND RECONSTRUCTION OF SCALAR FIELD MODELS

2013 ◽  
Vol 28 (38) ◽  
pp. 1350180 ◽  
Author(s):  
M. SHARIF ◽  
ABDUL JAWAD
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Dark Energy Model ◽  
Cold Dark Matter ◽  
Scalar Potential ◽  
Scalar Fields ◽  
Phantom Divide ◽  
Evolution Parameter ◽  
Scalar Field Models ◽  
Phantom Divide Line

In this paper, we consider the interacting generalized dark energy with cold dark matter and analyze the behavior of evolution parameter via dark energy and interacting parameters. It is found that the evolution parameter crosses the phantom divide line in most of the cases of integration constants. We also establish the correspondence of scalar field models (quintessence, k-essence and dilaton) with this dark energy model in which scalar fields show the increasing behavior. The scalar potential corresponds to attractor solutions in quintessence case.

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