Evolution equation for the expectation value of a scalar field in spatially flat RW universes

1987 ◽  
Vol 177 (1) ◽  
pp. 129-166 ◽  
Author(s):  
A. Ringwald
Keyword(s):  
Scalar Field ◽  
Evolution Equation ◽  
Expectation Value

Effective masses in a dense fermion background — Applied to neutrinos, dark matter and dark energy

2014 ◽  
Vol 29 (21) ◽  
pp. 1444010
Author(s):  
Bruce H. J. McKellar ◽  
T. J. Goldman ◽  
G. J. Stephenson
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Scalar Field ◽  
Effective Mass ◽  
Negative Pressure ◽  
Expectation Value ◽  
Effective Masses ◽  
Neutrino Astrophysics

If fermions interact with a scalar field, and there are many fermions present the scalar field may develop an expectation value and generate an effective mass for the fermions. This can lead to the formation of fermion clusters, which could be relevant for neutrino astrophysics and for dark matter astrophysics. Because this system may exhibit negative pressure, it also leads to a model of dark energy.

scholarly journals Weak scale from Planck scale: Mass scale generation in a classically conformal two-scalar system

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Junichi Haruna ◽  
Hikaru Kawai
Keyword(s):  
Scalar Field ◽  
Standard Model ◽  
Planck Scale ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
The Other ◽  
Expectation Value ◽  
Weak Scale ◽  
The Standard Model ◽  
The One

Abstract In the standard model, the weak scale is the only parameter with mass dimensions. This means that the standard model itself cannot explain the origin of the weak scale. On the other hand, from the results of recent accelerator experiments, except for some small corrections, the standard model has increased the possibility of being an effective theory up to the Planck scale. From these facts, it is naturally inferred that the weak scale is determined by some dynamics from the Planck scale. In order to answer this question, we rely on the multiple point criticality principle as a clue and consider the classically conformal $\mathbb{Z}_2\times \mathbb{Z}_2$ invariant two-scalar model as a minimal model in which the weak scale is generated dynamically from the Planck scale. This model contains only two real scalar fields and does not contain any fermions or gauge fields. In this model, due to a Coleman–Weinberg-like mechanism, the one-scalar field spontaneously breaks the $ \mathbb{Z}_2$ symmetry with a vacuum expectation value connected with the cutoff momentum. We investigate this using the one-loop effective potential, renormalization group and large-$N$ limit. We also investigate whether it is possible to reproduce the mass term and vacuum expectation value of the Higgs field by coupling this model with the standard model in the Higgs portal framework. In this case, the one-scalar field that does not break $\mathbb{Z}_2$ can be a candidate for dark matter and have a mass of about several TeV in appropriate parameters. On the other hand, the other scalar field breaks $\mathbb{Z}_2$ and has a mass of several tens of GeV. These results will be verifiable in near-future experiments.

scholarly journals AdS backgrounds and induced gravity

2019 ◽  
Vol 34 (38) ◽  
pp. 2050057
Author(s):  
Hai Lin ◽  
Gaurav Narain
Keyword(s):  
Scalar Field ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Equation Of Motion ◽  
Induced Gravity ◽  
Expectation Value ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Fluctuation Fields ◽  
Ads Geometry

In this paper, we look for AdS solutions to generalized gravity theories in the bulk in various spacetime dimensions. The bulk gravity action includes the action of a non-minimally coupled scalar field with gravity, and a higher-derivative action of gravity. The usual Einstein–Hilbert gravity is induced when the scalar acquires a nonzero vacuum expectation value. The equation of motion in the bulk shows scenarios where AdS geometry emerges on-shell. We further obtain the action of the fluctuation fields on the background at quadratic and cubic orders.

scholarly journals Assessment of an Evolution Equation for the Displacement Speed of a Constant-Density Reactive Scalar Field

2020 ◽  
Author(s):  
Rixin Yu ◽  
Thommie Nilsson ◽  
Geert Brethouwer ◽  
Nilanjan Chakraborty ◽  
Andrei Lipatnikov
Keyword(s):  
Scalar Field ◽  
Evolution Equation ◽  
Constant Density ◽  
Displacement Speed ◽  
Reactive Scalar

scholarly journals Vacuum Expectation Value Profiles of the Bulk Scalar Field in the Generalized Randall-Sundrum Model

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
A. Tofighi ◽  
M. Moazzen ◽  
A. Farokhtabar
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Cosmological Constant ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Brane World ◽  
Dirichlet Boundary Conditions ◽  
World Model ◽  
Expectation Value ◽  
Bulk Scalar Field

In the generalized Randall-Sundrum warped brane-world model the cosmological constant induced on the visible brane can be positive or negative. In this paper we investigate profiles of vacuum expectation value of the bulk scalar field under general Dirichlet and Neumann boundary conditions in the generalized warped brane-world model. We show that the VEV profiles generally depend on the value of the brane cosmological constant. We find that the VEV profiles of the bulk scalar field for a visible brane with negative cosmological constant and positive tension are quite distinct from those of Randall-Sundrum model. In addition we show that the VEV profiles for a visible brane with large positive cosmological constant are also different from those of the Randall-Sundrum model. We also verify that Goldberger and Wise mechanism can work under nonzero Dirichlet boundary conditions in the generalized Randall-Sundrum model.

scholarly journals A Riccati equation based approach to isotropic scalar field cosmologies

2014 ◽  
Vol 23 (07) ◽  
pp. 1450063 ◽  
Author(s):  
Tiberiu Harko ◽  
Francisco S. N. Lobo ◽  
M. K. Mak
Keyword(s):  
Scalar Field ◽  
Evolution Equation ◽  
Interaction Potential ◽  
Arbitrary Function ◽  
Field Potential ◽  
Type Equation ◽  
Scalar Fields ◽  
Cosmological Models ◽  
Late Time ◽  
Field Equations

Gravitationally coupled scalar fields ϕ, distinguished by the choice of an effective self-interaction potential V(ϕ), simulating a temporarily nonvanishing cosmological term, can generate both inflation and late time acceleration. In scalar field cosmological models the evolution of the Hubble function is determined, in terms of the interaction potential, by a Riccati type equation. In the present work, we investigate scalar field cosmological models that can be obtained as solutions of the Riccati evolution equation for the Hubble function. Four exact integrability cases of the field equations are presented, representing classes of general solutions of the Riccati evolution equation. The solutions correspond to cosmological models in which the Hubble function is proportional to the scalar field potential plus a linearly decreasing function of time, models with the time variation of the scalar field potential proportional to the potential minus its square, models in which the potential is the sum of an arbitrary function and the square of the function integral, and models in which the potential is the sum of an arbitrary function and the derivative of its square root, respectively. The cosmological properties of all models are investigated in detail, and it is shown that they can describe the inflationary or the late accelerating phase in the evolution of the universe.

scholarly journals Local zeta regularization and the scalar Casimir effect III. The case with a background harmonic potential

2015 ◽  
Vol 30 (35) ◽  
pp. 1550213 ◽  
Author(s):  
Davide Fermi ◽  
Livio Pizzocchero
Keyword(s):  
Scalar Field ◽  
General Framework ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Harmonic Potential ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Expectation Value ◽  
Stress Energy

Applying the general framework for local zeta regularization proposed in Part I of this series of papers, we renormalize the vacuum expectation value of the stress-energy tensor (and of the total energy) for a scalar field in presence of an external harmonic potential.

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