arXiv subjects

Allan L. Alinea

Publications and source records attributed to Allan L. Alinea.

15 recordsLinked to original sources

arXiv2026

Symmetry of the Klein-Gordon Equation under Disformal Transformations with Higher-Order Derivatives

Scalar-Tensor theories extend General Relativity (GR) by including both a scalar field and a metric tensor in describing gravity. Although the matter sector is minimally coupled to the metric in GR, the scalar field coupling to matter may be adjusted by means of Disformal Transformations. One of the most general of these transformations, formulated by Takahashi, Motohashi, and Minamitsuji, include arbitrarily high-order derivatives of the scalar field and are designed to map between two ghost-free Higher-order Scalar-Tensor theories. We used these transformations to determine the most general conditions for the disformal form-invariance of the Klein-Gordon equation for the scalar field. In the second-order case, we identified a family of disformally-related metrics that result in the same propagation solutions. Additionally, higher-order cases could comply with theoretical and phenomenological constraints alongside KG-invariance. Finally, we investigated the notion of disformal transformations as ``deformations'' of the spacetime manifold.

gr-qc↗

arXiv2025

On the KG-constrained Bekenstein's disformal transformation of the Einstein-Hilbert action

Motivated by an inclination for symmetry and possible extension of the General Theory of Relativity within the framework of Scalar Theory, we investigate the Bekenstein's disformal transformation of the Einstein-Hilbert action. Owing to the complicated combinations of second order metric derivatives encoded in the Ricci scalar of the action, such a transformation yields an unwieldy expression. To ``tame'' the transformed action, we exploit the Klein-Gordon (KG) conformal-disformal constraint previously discovered in the study of the invariance of the massless Klein-Gordon equation under disformal transformation. The result upon its application is a surprisingly much more concise and simple action in four spacetime dimensions containing three out of four sub-Lagrangians in the Horndeski action, and three beyond-Horndeski terms. The latter group of terms may be attributed to the kinetic-{term} dependence of the conformal and disformal factors in the Bekenstein's disformal transformation. Going down to three dimensions, we find a relatively simpler resulting action but the signature of the three ``extraneous'' terms remains. Lastly, in two dimensions, we find an invariant action consistent with its topological nature in these dimensions.

gr-qc↗

arXiv2024

On the KG-constrained general disformal transformation of the Einstein-Hilbert action

Although with great successes in explaining phenomena and natural behaviour involving the Universe or a part thereof, the General Theory of Relativity is far from a complete theory. Focusing on its extension within the framework of scalar tensor theory, we investigate the transformation of the Einstein-Hilbert action under the general disformal transformation coupled with a set of triple KG constraints. The idea is that the general disformal transformation leads to an extremely complicated action necessitating a set of constraints to tame the resulting form. Motivated by previous studies on the invertibility and invariance of the massless Klein-Gordon equation under the general disformal transformation, we identify three constraints that significantly simplifies the transformed Einstein-Hilbert action. In four spacetime dimensions, we find that the transformed action is a sum of the original action and a disformal contribution involving a six-term Lagrangian that includes the Ricci tensor coupled to a sum of derivatives of scalar fields and kinetic terms. In three spacetime dimensions, the disformal contribution becomes a five-term Lagrangian. Lastly, in two spacetime dimensions, the Einstein-Hilbert action is invariant under the constrained disformal transformation.

gr-qc↗

arXiv2023

Percolation of 'Civilisation' in a Homogeneous Isotropic Universe

In this work, we consider the spread of a 'civilisation' in an idealised homogeneous isotropic universe where all the planets of interest are habitable. Following a framework that goes beyond the usual idea of percolation, we investigate the behaviour of the number of colonised planets with time, and the total colonisation time for three types of universes. These include static, dark energy-dominated, and matter-dominated universes. For all these types of universes, we find a remarkable fit with the Logistic Growth Function for the number of colonised planets with time. This is in spite of the fact that for the matter- and dark-energy dominated universes, the space itself is expanding. For the total colonisation time, $T$, the case for a dark energy-dominated universe is marked with divergence beyond the linear regime characterised by small values of the Hubble parameter, $H$. Not all planets in a spherical section of this universe can be 'colonised' due to the presence of a shrinking Hubble sphere. In other words, the recession speeds of other planets go beyond the speed of light making them impossible to reach. On the other hand, for a matter-dominated universe, while there is an apparent horizon, the Hubble sphere is growing instead of shrinking. This leads to a finite total colonisation time that depends on the Hubble parameter characterising the universe; in particular, we find $T\sim H$ for small $H$ and $T\sim H^2$ for large $H$.

physics.pop-ph↗

arXiv2023

Extending the symmetry of the massless Klein-Gordon equation under the general disformal transformation

The Klein-Gordon equation, one of the most fundamental equations in field theory, is known to be not invariant under conformal transformation. However, its massless limit exhibits symmetry under Bekenstein's disformal transformation, subject to some conditions on the disformal part of the metric variation. In this study, we explore the symmetry of the Klein-Gordon equation under the general disformal transformation encompassing that of Bekenstein and a hierarchy of `sub-generalisations' explored in the literature (within the context of inflationary cosmology and scalar-tensor theories). We find that the symmetry in the massless limit can be extended under this generalisation provided that the disformal factors takes a special form in relation to the conformal factor. Upon settling the effective extension of symmetry, we investigate the invertibility of the general disformal transformation to avoid propagating non-physical degrees of freedom upon changing the metric. We derive the inverse transformation and the accompanying restrictions that make this inverse possible.

gr-qc↗

arXiv2022

On the Disformal Transformation of the Einstein-Hilbert Action

Disformal transformation is a generalisation of the well-known conformal transformation commonly elaborated in mainstream graduate texts in gravity (relativity) and modern cosmology. This transformation is one of the most important mathematical operations in scalar tensor theories attempting to address pressing problems involving dark energy and dark matter. With this topic yet to penetrate these texts, we present a pedagogically oriented derivation of the disformal transformation of the Einstein-Hilbert action. Along the way of calculation, we encounter apparently problematic terms that could be construed as leading to equations of motion that go beyond second order in derivatives, signalling instability. We demonstrate that these terms can be eliminated and absorbed through the definition of the Riemann curvature tensor. The transformed Einstein-Hilbert action turns out to be a special case of the Horndeski action and the equations of motion for the scalar field that it describes are all up to second order only in derivatives, implying stability.

gr-qc↗

arXiv2021

Transformation of Primordial Cosmological Perturbations Under the General Extended Disformal Transformation

Primordial cosmological perturbations are the seeds that were cultivated by inflation and the succeeding dynamical processes, eventually leading to the current Universe. In this work, we investigate the behavior of the gauge-invariant scalar and tensor perturbations under the general extended disformal transformation, namely, $g_{μν} \rightarrow A(X,Y,Z)g_{μν} + Φ_μΦ_ν$, where $X \equiv -\tfrac{1}{2}ϕ^{;μ}ϕ_{;μ}, Y \equiv ϕ^{;μ}X_{;μ}, Z \equiv X^{;μ}X_{;μ} $ and $Φ_μ\equiv Cϕ_{;μ} + DX_{;μ}$, with $C$ and $D$ being a general functional of $(ϕ,X,Y,Z)$. We find that the tensor perturbation is invariant under this transformation. On the other hand, the scalar curvature perturbation receives a correction due the conformal term only; it is independent of the disformal term at least up to linear order. Within the framework of the full Horndeski theory, the correction terms turn out to depend linearly on the gauge-invariant comoving density perturbation and the first time-derivative thereof. In the superhorizon limit, all these correction terms vanish, leaving only the original scalar curvature perturbation. In other words, it is invariant under the general extended disformal transformation in the superhorizon limit, in the context of full Horndeski theory. Our work encompasses a chain of research studies on the transformation or invariance of the primordial cosmological perturbations, generalizing their results under our general extended disformal transformation.

gr-qc↗

arXiv2020

Cognitive Reflection Test and the Polarizing Force-Identification Questions in the FCI

The set of polarizing force-identification (PFI) questions in the FCI consists of six items all basically asking only one question: the set of forces acting on a given body. Although it may sound trivial, these questions are among the most challenging in the FCI. In this work involving 163 students, we investigate the correlation between student performance on the set of PFI questions and the Cognitive Reflection Test. We find that for both scores in the FCI as a whole and in the PFI questions, the range of values of the Pearson coefficient at 95\% confidence interval, is suggestive that cognitive reflection may be one of the contributing factors in the student performance in the FCI. This is consistent with the idea that high level of cognitive reflection may help in eliminating seemingly valid choices (misconceptions) in the FCI that are intuitive from everyday experience or "common sense" but otherwise misleading. The ability to activate System 2 in Dual Process Theory, whether from System 1 or right after reading a physics problem, may contribute in narrowing down the set of prospective valid answers in a given physics problem. Complementary to cognitive reflection are other factors associated with deep understanding of physics whose effects are expected to become more evident with the level of difficulty of a set of physics problems. Given two students with the same level of cognitive reflection, the one with deeper understanding of physics is more likely to get the correct answer. In our analysis, the range of correlation coefficient for the set of PFI questions is downshifted with respect to that for the FCI as a whole. This may be attributed to the more challenging nature of the latter compared to a significant fraction of the remaining questions in the former.

physics.ed-ph↗

arXiv2017

Adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation

We perform adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation with varying speed of sound. The subtraction is performed within the framework of earlier study by Urakawa and Starobinsky dealing with the canonical inflation. Inspired by Fakir and Unruh's model on nonminimally coupled chaotic inflation, we find upon imposing near scale-invariant condition, that the subtraction term exponentially decays with the number of $ e $-folds. As in the result for the canonical inflation, the regularized power spectrum tends to the "bare" power spectrum as the Universe expands during (and even after) inflation. This work justifies the use of the "bare" power spectrum in standard calculation in the most general context of slow-roll single-field inflation involving non-minimal coupling and varying speed of sound.

gr-qc↗

arXiv2016

Adiabatic regularisation of power spectra in nonminimally coupled chaotic inflation

We investigate the effect of adiabatic regularization on both the tensor- and scalar-perturbation power spectra in \textit{nonminimally} coupled chaotic inflation. Similar to that of the \textit{minimally} coupled general single-field inflation, we find that the subtraction term is suppressed by an exponentially decaying factor involving the number of $ e $-folds. By following the subtraction term long enough beyond horizon crossing, the regularized power spectrum tends to the "bare" power spectrum. This study justifies the use of the unregularized ("bare") power spectrum in standard calculations.

gr-qc↗

arXiv2016

The double-soft limit in cosmological correlation functions and graviton exchange effects

The graviton exchange effect on cosmological correlation functions is examined by employing the double-soft limit technique. A new relation among correlation functions that contain the effects due to graviton exchange diagrams in addition to those due to scalar-exchange and scalar-contact-interaction, is derived by using the background field method and independently by the method of Ward identities associated with dilatation symmetry. We compare these three terms, putting small values for the slow-roll parameters and $(1-n_{s}) = 0.042$, where $n_{s}$ is the scalar spectral index. It is argued that the graviton exchange effects are more dominant than the other two and could be observed in the trispectrum in the double-soft limit. Our observation strengthens the previous work by Seery, Sloth and Vernizzi, in which it has been argued that the graviton exchange dominates in the counter-collinear limit for single field slow-roll inflation.

hep-th↗

arXiv2016

Gender gap and polarisation of physics on global courses

We extend on previous research on the Force Concept Inventory (FCI) given to first year classical mechanics students (N=66 students, over four years) pre and post score, for students on an international (global) course at Osaka University. In particular, we revisit the notion of "polarisation" in connection with the six polarisation-inducing questions in the FCI and examine its gender aspect. Our data suggest that this phenomenon is not unique to one gender. Furthermore, the extent by which it is exhibited by males may differ from that of females at the beginning (pretest) but the gap closes upon learning more about forces (posttest). These findings are for the most part, complemented by our result for the FCI as a whole. Although the differences in means for males and females suggest a gender gap, statistical analysis shows that there is no gender difference at the 95% confidence level.

physics.ed-ph↗

arXiv2015

Logarithmic divergences in the $k$-inflationary power spectra computed through the uniform approximation

We investigate a calculation method for solving the Mukhanov-Sasaki equation in slow-roll $k$-inflation based on the uniform approximation (UA) in conjunction with an expansion scheme for slow-roll parameters with respect to the number of $e$-folds about the so-called \textit{turning point}. Earlier works on this method has so far gained some promising results derived from the approximating expressions for the power spectra among others, up to second order with respect to the Hubble and sound flow parameters, when compared to other semi-analytical approaches (e.g., Green's function and WKB methods). However, a closer inspection is suggestive that there is a problem when higher-order parts of the power spectra are considered; residual logarithmic divergences may come out that can render the prediction physically inconsistent. Looking at this possibility, we map out up to what order with respect to the mentioned parameters several physical quantities can be calculated before hitting a logarithmically divergent result. It turns out that the power spectra are limited up to second order, the tensor-to-scalar ratio up to third order, and the spectral indices and running converge to all orders. This indicates that the expansion scheme is incompatible with the working equations derived from UA for the power spectra but compatible with that of the spectral indices. For those quantities that involve logarithmically divergent terms in the higher-order parts, existing results in the literature for the convergent lower-order parts calculated in the equivalent fashion should be viewed with some caution; they do not rest on solid mathematical ground.

gr-qc↗

arXiv2015

Adiabatic regularisation of power spectra in $k$-inflation

We look at the question posed by Parker et al. about the effect of UV regularisation on the power spectrum for inflation. Focusing on the slow-roll $k$-inflation, we show that up to second order in the Hubble and sound flow parameters, the adiabatic regularisation of such model leads to no difference in the power spectrum apart from certain cases that violate near scale invariant power spectra. Furthermore, extending to non-minimal $k$-inflation, we establish the equivalence of the subtraction terms in the adiabatic regularisation of the power spectrum in Jordan and Einstein frames.

gr-qc↗

arXiv2014

Polarization of physics on global courses

Since October 2010, the Chemistry-Biology Combined Major Program (CBCMP), an international course taught in English at Osaka University, has been teaching small classes (no more than 20 in size). We present data from the Force Concept Inventory (FCI) given to first year classical mechanics students (N=47 students over three years) pre and post score, for a class that predominantly uses interactive engagement (IE), such as MasteringPhysics. Our findings show a $G$-factor improved score of about $\sim$ 0.18, which is marginally about the average of a traditional based course. Furthermore, we analyse in detail a set of six questions from the FCI, involving the identification of forces acting on a body. We find that student answers tend to cluster about "polarising choices"-a pair of choices containing the correct choice and a wrong choice with the latter corresponding to a superset of forces in the former. Our results are suggestive that students have a good idea of the right set of forces acting on a given system but the inclusion of extra force(s) brings about confusion; something that may be explained by misleading ontological categorisation of forces. In an appendix we also comment on possible correlations between the pre/post score and the level of English ability on entry to the course.

physics.ed-ph↗