Scalar Field Action Research Articles

Solving higher curvature gravity theories

Solving field equations in the context of higher curvature gravity theories is a formidable task. However in many situations, e.g., in the context of $f(R)$ theories the higher curvature gravity action can be written as Einstein-Hilbert action plus a scalar field action. We show that not only the action but the field equations derived from the action are also equivalent provided the spacetime is regular. We also demonstrate that such equivalence continues to hold even when gravitational field equations are projected on a lower dimensional hypersurface. We have further depicted explicit examples in which the solutions for Einstein-Hilbert and a scalar field system lead to solutions of the equivalent higher curvature theory. The same, but on the lower dimensional hypersurface, has been illustrated in the reverse order as well. We conclude with a brief discussion on this technique of solving higher curvature field equations.

Conformal symmetry and nonlinear extensions of nonlocal gravity

We study two nonlinear extensions of the nonlocal $R\,\Box^{-2}R$ gravity theory. We extend this theory in two different ways suggested by conformal symmetry, either replacing $\Box^{-2}$ with $(-\Box + R/6)^{-2}$, which is the operator that enters the action for a conformally-coupled scalar field, or replacing $\Box^{-2}$ with the inverse of the Paneitz operator, which is a four-derivative operator that enters in the effective action induced by the conformal anomaly. We show that the former modification gives an interesting and viable cosmological model, with a dark energy equation of state today $w_{\rm DE}\simeq -1.01$, which very closely mimics $\Lambda$CDM and evolves asymptotically into a de Sitter solution. The model based on the Paneitz operator seems instead excluded by the comparison with observations. We also review some issues about the causality of nonlocal theories, and we point out that these nonlocal models can be modified so to nicely interpolate between Starobinski inflation in the primordial universe and accelerated expansion in the recent epoch.

Effective action for a quantum scalar field in warped spaces

We investigate the one-loop corrections at zero, as well as finite temperature, of a scalar field taking place in a braneworld motived warped background. After to reach a well defined problem, we calculate the effective action with the corresponding quantum corrections to each case.

Dark energy and dark matter from hidden symmetry of gravity model with a non-Riemannian volume form

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by $$\sqrt{-g}$$ (square root of the determinant of the pertinent Riemannian metric) and another non-Riemannian volume form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless “dust” fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from the above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding an appropriate perturbation, which breaks the above hidden symmetry and along with this couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.

Effective action for a free scalar field in the presence of spacetime foam

We model spacetime foam by a gas of virtual wormholes. For a free scalar field we derive the effective Lagrangian which accounts for the interaction with spacetime foam and contains two additional non-local terms. One term describes the scattering of scalar particles on virtual wormholes and explicitly reproduces the Pauli-Villars regularization procedure. The second term describes the back reaction of particles on the number density of wormholes and introduces a self-interaction between particles.

Effective action for cosmological scalar fields at finite temperature

Scalar fields appear in many theories beyond the Standard Model of particle physics. In the early universe, they are exposed to extreme conditions, including high temperature and rapid cosmic expansion. Understanding their behavior in this environment is crucial to understand the implications for cosmology. We calculate the finite temperature effective action for the field expectation value in two particularly important cases, for damped oscillations near the ground state and for scalar fields with a flat potential. We find that the behavior in both cases can in good approximation be described by a complex valued effective potential that yields Markovian equations of motion. Near the potential minimum, we recover the solution to the well-known Langevin equation. For large field values we find a very different behavior, and our result for the damping coefficient differs from the expressions frequently used in the literature. We illustrate our results in a simple scalar model, for which we give analytic approximations for the effective potential and damping coefficient. We also provide various expressions for loop integrals at finite temperature that are useful for future calculations in other models.

Field theory on Newton-Cartan backgrounds and symmetries of the Lifshitz vacuum

Holography for Lifshitz space-times corresponds to dual field theories on a fixed torsional Newton-Cartan (TNC) background. We examine the coupling of non-relativistic field theories to TNC backgrounds and uncover a novel mechanism by which a global U(1) can become local. This involves the TNC vector $M_\mu$ which sources a particle number current, and which for flat NC space-time satisfies $M_{\mu}=\partial_{\mu}M$ with a Schroedinger symmetry realized on $M$. We discuss various toy model field theories on flat NC space-time for which the new mechanism leads to extra global space-time symmetries beyond the generic Lifshitz symmetry, allowing for an enhancement to Schroedinger symmetry. On the holographic side, the source $M$ also appears in the Lifshitz vacuum with exactly the same properties as for flat NC space-time. In particular, the bulk diffeomorphisms that preserve the boundary conditions realize a Schroedinger algebra on $M$, allowing for a conserved particle number current. Finally, we present a probe action for a complex scalar field on the Lifshitz vacuum, which exhibits Schroedinger invariance in the same manner as seen in the field theory models.

Power spectrum and non-Gaussianities in anisotropic inflation

We study the planar regime of curvature perturbations for single field inflationary models in an axially symmetric Bianchi I background. In a theory with standard scalar field action, the power spectrum for such modes has a pole as the planarity parameter goes to zero. We show that constraints from back reaction lead to a strong lower bound on the planarity parameter for high-momentum planar modes and use this bound to calculate the signal-to-noise ratio of the anisotropic power spectrum in the CMB, which in turn places an upper bound on the Hubble scale during inflation allowed in our model. We find that non-Gaussianities for these planar modes are enhanced for the flattened triangle and the squeezed triangle configurations, but show that the estimated values of the fNL parameters remain well below the experimental bounds from the CMB for generic planar modes (other, more promising signatures are also discussed). For a standard action, fNL from the squeezed configuration turns out to be larger compared to that from the flattened triangle configuration in the planar regime. However, in a theory with higher derivative operators, non-Gaussianities from the flattened triangle can become larger than the squeezed configuration in a certain limit of the planarity parameter.

Self-quartic interaction for a scalar field in an extended DFR noncommutative space–time

The framework of Doplicher–Fredenhagen–Roberts (DFR) for a noncommutative (NC) space–time is considered as an alternative approach to study the NC space–time of the early Universe. Concerning this formalism, the NC constant parameter, θμν, is promoted to coordinate of the space–time and consequently we can describe a field theory in a space–time with extra-dimensions. We will see that there is a canonical momentum associated with this new coordinate in which the effects of a new physics can emerge in the propagation of the fields along the extra-dimensions. The Fourier space of this framework is automatically extended by the addition of the new momenta components. The main concept that we would like to emphasize from the outset is that the formalism demonstrated here will not be constructed by introducing a NC parameter in the system, as usual. It will be generated naturally from an already NC space. We will review that when the components of the new momentum are zero, the (extended) DFR approach is reduced to the usual (canonical) NC case, in which θμν is an antisymmetric constant matrix. In this work we will study a scalar field action with self-quartic interaction ϕ4⋆ defined in the DFR NC space–time. We will obtain the Feynman rules in the Fourier space for the scalar propagator and vertex of the model. With these rules we are able to build the radiative corrections to one loop order of the model propagator. The consequences of the NC scale, as well as the propagation of the field in extra-dimensions, will be analyzed in the ultraviolet divergences scenario. We will investigate about the actual possibility that this kμν conjugate momentum has the property of healing the combination of IR/UV divergences that emerges in this recently new NC spacetime quantum field theory.

Cosmological black holes from self-gravitating fields

Both cosmological expansion and black holes are ubiquitous features of our observable Universe, yet exact solutions connecting the two have remained elusive. To this end, we study self-gravitating classical fields within dynamical spherically symmetric solutions that can describe black holes in an expanding universe. After attempting a perturbative approach of a known black-hole solution with scalar hair, we show by exact methods that the unique scalar field action with first-order derivatives that can source shear-free expansion around a black hole requires noncanonical kinetic terms. The resulting action is an incompressible limit of $k$-essence, otherwise known as the cuscuton theory, and the spacetime it describes is the McVittie metric. We further show that this solution is an exact solution to the vacuum Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity with anisotropic Weyl symmetry.

Scalar-tensor gravity cosmology: Noether symmetries and analytical solutions

In this paper, we present a complete Noether Symmetry analysis in the framework of scalar-tensor cosmology. Specifically, we consider a non-minimally coupled scalar field action embedded in the FLRW spacetime and provide a full set of Noether symmetries for related minisuperspaces. The presence of symmetries implies that the dynamical system becomes integrable and then we can compute cosmological analytical solutions for specific functional forms of coupling and potential functions selected by the Noether Approach.

Effective gravitational interactions of dark matter axions

We investigate the structure of gravitational self-interactions of coherently oscillating axions in the general relativistic framework. A generic action for a massive scalar field in the Friedmann-Robertson-Walker background is first introduced based on the effective field theory approach to cosmological perturbations. Using the obtained setup, we evaluate the effective gravitational interaction of the massive scalar field, i.e. scalar quartic interactions mediated by metric perturbations. Applying the results to the system of dark matter axions, we estimate their self-interaction rate and discuss its implications for the axion Bose-Einstein condensate dark matter scenario. Leading contributions for the gravitational interactions of axions are given by the process mediated by the dynamical graviton field, which is essentially the Newtonian potential induced by fluctuations of the background fluids. We find that it leads to the same order of magnitude for the interaction rate of dark matter axions in the condensed regime, compared with the results of previous studies using the Newtonian approximation.

Axion-induced birefringence effects in laser driven nonlinear vacuum interaction

The propagation of a probe electromagnetic field through a counterpropagating strong plane wave is investigated. The effects of the electromagnetic field-(pseudo)scalar axion field interaction and of the self-interaction of the electromagnetic field mediated by virtual electron-positron pairs in the effective Lagrangian approach are included. First, we show that if the strong field is circularly polarized, contrary to the leading-order nonlinear QED effects, the axion-photon interaction induces a chiral-like birefringence and a dichroism in the vacuum. The latter effect is explained by evoking the conservation of the total angular momentum along the common propagation direction of probe and the strong wave, which allows for real axion production only for probe and strong fields with the same helicity. Moreover, in the case of ultra-short strong pulses, it is shown that the absorption coefficients of probe photons depend on the form of the pulse and, in particular, on the carrier-envelope phase of the strong beam. The present results can be exploited experimentally to isolate nonlinear vacuum effects stemming from light-axion interaction, especially at upcoming ultra-strong laser facilities, where stringent constraints on the axion-photon coupling constant are in principle provided.

Scalar domain wall as the universe

We develop a formulation where, for an arbitrarily given warp factor, we construct a scalar field action which reproduces the warp factor as a solution of the Einstein equation and field equation corresponding to the action. This formulation could be called the reconstruction. By using the formulation of the reconstruction, we construct models which have an exact solution describing the domain wall. The shape of the domain wall can be flat, de Sitter space-time, or anti-de Sitter space-time. In the constructed domain wall solutions, there often appears a ghost with negative kinetic energy. We give, however, an example of the de Sitter domain wall solution without a ghost, which could be a toy model of inflation. We also investigate the localization of gravity as in the Randall-Sundrum model. It is demonstrated that the four-dimensional Newton law could be reproduced even in the de Sitter space-time domain wall solution. We show that we can construct a space-time, where the domain wall is the general Friedmann-Robertson-Walker universe and the warp factor can be arbitrary. For such a construction, we use two scalar fields. It is also illustrated that the scalar field equations are equivalent to the Bianchi identities: ${\ensuremath{\nabla}}^{\ensuremath{\mu}}({R}_{\ensuremath{\mu}\ensuremath{\nu}}\ensuremath{-}\frac{1}{2}R{g}_{\ensuremath{\mu}\ensuremath{\nu}})=0$.

Instant-Form and Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an <i>U</i>(1) Gauge Field

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world-sheet time σ0=τ=constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time σ+= (τ+σ) =constant. The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field Bαβ(σ,τ) or in the presence of U(1) gauge field Aα(σ,τ) and the constant scalar axion field C(σ,τ), then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino or Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

Hawking radiation for non-asymptotically flat dilatonic black holes using gravitational anomaly

The $d$-dimensional scalar field action may be reduced, in the background geometry of a black hole, to a 2-dimensional effective action. In the near horizon region, it appears a gravitational anomaly: the energy-momentum tensor of the scalar field is not conserved anymore. This anomaly is removed by introducing a term related to the Hawking temperature of the black hole. Even if the temperature term introduced is not covariant, a gauge transformation may restore the covariance. We apply this method to compute the temperature of the black hole of the dilatonic non asymptotically flat black holes. We compare the results with those obtained through other methods.

Scalar and spinor field actions on fuzzy S 4: fuzzy $\mathbb{C}{{\text{P}}^3}$ as a $S_F^2$ bundle over $S_F^4$

We present a manifestly Spin(5) invariant construction of squashed fuzzy $CP^3$ as a fuzzy $S^2$ bundle over fuzzy $S^4$. We develop the necessary projectors and exhibit the squashing in terms of the radii of the $S^2$ and $S^4$. Our analysis allows us give both scalar and spinor fuzzy action functionals whose low lying modes are truncated versions of those of a commutative $S^4$.

String Gauge Symmetries in the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of Background Gauge Fields

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world- sheet time σ0 = τ = constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time . The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field or in the presence of gauge field and the constant scalar axion field , then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino/Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

Light-Front Quantization of Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an U(1) Gauge Field

Light-front quantization of the conformally gauge-fixed Polyakov D1 brane action in the presence of a constant background scalar axion field C(τ, σ) and an U(1) gauge field Aα(τ, σ) is studied. The axion field C and the U(1) gauge field Aα, are seen to behave like the Wess–Zumino (WZ) fields and the term involving these fields is seen to behave like a WZ term for this action.

On the Hurwitz zeta function of imaginary second argument

In this work, we exploit Jonquière's formula relating the Hurwitz zeta function to a linear combination of polylogarithmic functions in order to evaluate the real and imaginary part of ζH(s, ia) and its first derivative with respect to the first argument s. In particular, we obtain expressions for the real and imaginary party of ζH(s, ia) and its derivative for s = m with \documentclass[12pt]{minimal}\begin{document}$m\in \mathbb {Z}\backslash \lbrace 1\rbrace$\end{document}m∈Z∖{1} involving simpler transcendental functions. We apply these results to the computation of the imaginary part of the one-loop effective action for massive scalar fields under the influence of a strong electric field in higher dimensional Minkowski spacetime.