arXiv subjects

Rafael Hernández-Jiménez

Publications and source records attributed to Rafael Hernández-Jiménez.

16 recordsLinked to original sources

arXiv2025

Hamiltonian analysis of an Effective action coupled to the Palatini action in 4 dimensions

We carry out the canonical analysis of the coupling of a $4$-dimensional effective action that arises from a dimensional reduction of a $7$-dimensional BF theory to the Palatini action in $4$-dimensions with cosmological constant, focusing on homogeneity and isotropy in all involved fields. We employ Ostrogradsky's methodology because of the presence of second time derivatives. Through the analysis of consistency conditions, we identify three distinct and consistent possibilities. In all these scenarios, we explore the solution of second-class constraints in terms of pairs of canonical variables. Similarly, Hamiltonian analysis is performed only for the $4$-dimensional effective theory. The second-class constraints are solved in terms of canonical coordinates, revealing that this formulation aligns with one of the viable scenarios explored in the coupling to the $4$-dimensional Palatini action, entailing that the $4$-dimensional effective action nullifies gravity.

gr-qc↗

arXiv2025

Conformal metric perturbations and boundary term as physical source

In the context of the Relativistic Quantum Geometry formalism, where the cosmological constant is promoted to a dynamical variable by attributing it a geometric interpretation as a result of a flux on the boundary of a manifold and establishing a connection between the perturbations of the Ricci tensor and the metric tensor, we propose an approach for the perturbations of the metric tensor. From this, imposing that Einstein's equations must hold for the tensors defined from the perturbed quantities obtained from conformal transformations, we derive a functional form for the cosmological parameter $Λ$ in terms of the cosmological parameter $\barΛ$ of the perturbed manifold. We then use the obtained equations to propose a cosmological model based on the Friedmann-Lemaître-Robertson-Walker metric with no spatial curvature, fitting the free parameters using observational data from Hubble and Type Ia Supernovae. The model is statistically comparable to $Λ$CDM; although, the joint analysis produces a smaller $H_{0}^{\rm Conformal}=69.80\rm\,\, Km \,s^{-1}\,Mpc^{-1}$ in contrast to the flat $Λ$CDM result $H_{0}^{Λ\rm CDM}=70.52\rm\,\, Km \,s^{-1}\,Mpc^{-1}$. An evident singularity occurs when the conformal factor $Ξ^{2}=2$, yields an early universe dominated only by matter $ρ_{m}$, which undoubtedly does not correspond to a viable history of our cosmos. Despite these limitations, a specific scenario remains feasible. This study aims to offer insights into the acceleration of the universe and addresses key questions in contemporary cosmology.

gr-qc↗

arXiv2025

Towards a de Sitter quintom-like cosmology from a reduction of a 7-dimensional $BF$ theory

In this article, we analyze a 7-dimensional $BF$ theory that, upon dimensional reduction, transforms into an effective 4-dimensional action in which a generic metric is involved. A constraint is imposed in such a way that this is the Friedmann-Lemaître-Robertson-Walker metric characterized by a scale factor $a(t)=\mathrm{exp}(H_0 t)$ with a Hubble constant $H_{0}=67.70 \,\rm [km\, s^{-1}\,Mpc^{-1}]$. We also compute the barotropic parameter $ω\equiv p/ρ$ from our solutions. Three different scenarios are explored, in which the model transitions from quintessence to phantom regimes, crossing the theoretical phantom divide line. Consequently, the effective action represents a quintom-like scenario. Moreover, we derive some analytic solutions for the scale factor by treating it as a dynamical variable in the effective action. In this case, different outcomes are obtained, where the model can transit from a cosmological constant to a quintessence regime; however, it cannot cross the theoretical phantom divide line. However, this simplistic model successfully captures distinct phases of cosmic expansion.

gr-qc↗

arXiv2024

Some inflationary models under the light of Planck 2018 results

In this work we study four well-known inflationary scenarios that are reported by the most recent Planck observations: Natural inflation, Hilltop quartic inflation, Starobinsky inflationary model, and Large field power-law potentials $V(ϕ)\sim ϕ^{p}$, considering $p=\sfrac{2}{3}, \sfrac{4}{3}$. The analysis is done using both the slow-roll approximation and the numerical solution to the background and perturbation equations. We show that the numerical solution improved the precision of these models with respect to the contour plot $r$ vs. $n_\sca$, having a lower $r$ in each model compared to the value calculated from the slow-roll approximation.

gr-qc↗

arXiv2023

Post-Newtonian Gravitational Waves with cosmological constant $Λ$ from the Einstein-Hilbert theory

We study the Post-Newtonian approach implemented to the Einstein-Hilbert action adding the cosmological constant $Λ$ at 1PN order. We consider very small values of $Λ$ to derive the Lagrangian of a two body compact system at the center of mass frame at 1PN. Furthermore, the phase function $ϕ(t)$ is obtained from the balance equation and the two polarizations $h_{+}$ and $h_{\times}$ are also calculated. We observe changes due to $Λ$ only at very low frequencies and we notice that it plays the role of "stretch" the spacetime such that both amplitudes become smaller; however, given its nearly negligible value, $Λ$ has no relevance at higher frequencies whatsoever.

gr-qc↗

arXiv2023

Geometrical scalar back-reaction effects in inflation

Starting with the Lagrangian formulation of General Relativity, we will conduct an investigation into the production of spacetime waves, due to a geometric boundary term of a closed extended manifold, within the tensor and scalar sectors. This scheme will be studied in an inflationary universe. We explore two distinct scenarios: Cold Inflation and Warm Inflation. The scalar modes $Z_{k}^{\mathbb{R}}$ and $Z_{k}^{\mathbb{I}}$ oscillate within the horizon, and they become constant at (or right after) horizon crossing $k\simeq aH$ and they remain so when radiation starts to dominate. The larger $k/k_{0}$ the $Z_{k}$'s amplitudes increase too. In general we can notice that radiation reduces the size of the $Z_{k}$'s amplitudes, hence yielding smaller signals of such modes. The tensor sector shows an irregular journey due to their abruptly growth just as they cross the horizon. This upshot hinders any probable observational hint or signal. However, we expect this novel mechanism of spacetime waves production brings new cosmological sources, for which no astrophysical source has been identified.

gr-qc↗

arXiv2023

Quintom fields from chiral anisotropic cosmology

In this paper we present an analysis of a chiral anisotropic cosmological scenario from the perspective of quintom fields. In this setup quintessence and phantom fields interact in a non-standard (chiral) way within an anisotropic Bianchi type I background. We present our examination from two fronts: classical and quantum approaches. In the classical program we find analytical solutions given by a particular choice of the emerged relevant parameters. Remarkably, we present an explanation of the ''big-bang'' singularity by means of a ''big-bounce''. Moreover, isotropization is in fact reached as the time evolves. On the quantum counterpart the Wheeler-DeWitt equation is analytically solved for various instances given by the same parameter space from the classical study, and we also include the factor ordering $\rm Q$. Having solutions in this scheme we compute the probability density, which is in effect damped as the volume function and the scalar fields evolve; and it also tends towards a flat FLRW framework when the factor ordering constant $\rm Q \ll 0$. This result might indicate that for a fixed set of parameters, the anisotropies quantum-mechanically vanish for very small values of the parameter $\rm Q$. Finally, classical and quantum solutions reduce to their flat FLRW counterparts when the anisotropies vanish.

gr-qc↗

arXiv2023

A search for distinctive footprints of compact binary coalescence within alternatives theories of gravity

In this review we examine the amplitude intensity associated to tensorial and non-tensorial polarization modes generated by binary systems at their inspiral stage, within the alternative theories of gravity of Brans Dicke, Rosen, and Lightman Lee. This study is performed without making an explicit use of the Transverse Traceless gauge of the General Relativity approach, and at the Newtonian limit. Consequently such additional polarization modes appear (non-tensorial) due to additional degrees of freedom in modified theories of gravitation. We model and compare the different polarization modes and strain signals for each scheme varying the sky location. Our analysis allows us to identify the locations where these modes are more intense, and, therefore susceptible to being identified for the future interferometer detector network. This gives rise to a framework in which the amplitude and the intensity of all polarization modes of general relativity and alternative hypotheses can be compared.

gr-qc↗

arXiv2023

Inflation from a chaotic potential with a step

In this work, we study the effects on the relevant observational parameters of an inflationary universe from a chaotic potential with a step. We numerically evolve the perturbation equations within both cold inflation and warm inflation. On the one hand, in a cold inflation scenario we analyse the scalar power spectrum $P_{\mathcal{R}}$ in terms of the number of e-folds $N_{e}$, and in terms of the ratio $k/k_{0}$, where $k_{0}$ is our pivot scale. We show how $P_{\mathcal{R}}$ oscillates around $0.2< k/k_{0} < 20$. Additionally, we present the evolution of two relevant parameters: the scalar spectral index $n_\mathrm{s}$ and the tensor-to-scalar ratio $r$. In fact, more than one region of $(n_\mathrm{s},r)$ lies within the observable window (Planck 2018). On the other hand, in the warm inflationary case, we also examine the evolution of $P_{\mathcal{R}}$ in terms of $N_{e}$ and $k/k_{0}$. Perturbations are amplified in WI; in fact, $P_{\mathcal{R}}$ can be much larger than the CMB value $P_{\mathcal{R}}> 2.22\times 10^{-9}$. This time, the spectral index $n_\mathrm{s}$ is clearly blue-tilted, at smaller scales, and the tensor-to-scalar ratio $r$ becomes too low. However, $n_\mathrm{s}$ can change from blue-tilted towards red-tilted, since $P_{\mathcal{R}}$ starts oscillating around $k/k_{0}\sim 40$. Indeed, the result from the step potential skims the Planck contours. Finally, one key aspect of this research was to contrast the features of an inflationary potential between both paradigms, and, in fact, they show similarities and differences. Due to a featured background and a combined effect of entropy fluctuations (only in warm inflation), in both scenarios certain fluctuation scales are not longer ``freeze in'' on super-horizon scales.

gr-qc↗

arXiv2023

Emission of spacetime waves from the partial collapse of a compact object

In this work we describe the partial collapse of a compact object and the emission of spacetime waves as a result of back-reaction effects. As a source mass term we propose a non-smooth continuous function that describes a mass-loss, and we then obtain the solution of such setting. We present three distinct examples of the evolution of the norm $|R_{nl}(t,r_{*})|$ in terms of $t$, and four different results are shown for the parameter $l=1,2,5,10$; here $r_{*}$ is the fixed radius of an observer outside the compact object. In all cases, the decay behaviour is actually present at $t\gg 1$ and becomes more evident for larger $l$. In addition, for the results that have smaller $l$'s their amplitudes are larger when the asymptotic character of $|R_{nl}(t,r_{*})|$ clearly appears. Finally, the farther away an observer is set, the fewer oscillations are perceived; however, from our particular fixed set of parameters, the best spot to observe the wiggles of the emitted spacetime waves is close to $r_{*}\simeq α$.

gr-qc↗

arXiv2022

Cosmological Boundary Flux Parameter

The {\it{Cosmological Boundary Flux Parameter}} is a novel proposal that attempts to explain the origin of the cosmological parameter $Λ$ purely by geometric nature. Then we implement this new approach to a flat FLRW universe along with a barotropic fluid. We present an ansatz in which $Λ$ is straightforwardly coupled to the matter sector; therefore, only one additional parameter was introduced: $λ$. Also, through a statistical analysis, using late-time data of observational Hubble and type Ia Supernovae, we computed the joint best-fit value of the free parameters by means of the affine-invariant MCMC. We want to emphasise that the joint analysis produces a smaller $H_{0}^{\rm CBFP}=69.80\rm\,\, Km \,s^{-1}\,Mpc^{-1}$ in contrast to the flat $Λ$CDM result $H_{0}^{Λ\rm CDM}=70.53\rm\,\, Km \,s^{-1}\,Mpc^{-1}$. The work presented here seeks to contribute to the discussion of the possible explanation for the cosmos' acceleration, together with tackling other important questions in modern cosmology.

gr-qc↗

arXiv2022

Quintom fields from chiral K-essence cosmology

In this paper, we present an analysis of a chiral cosmological scenario from the perspective of K-essence formalism. In this setup, several scalar fields interact within the kinetic and potential sectors. However, we only consider a flat Friedmann--Robertson--Lama\^ıtre--Walker universe coupled minimally to two quintom fields: one quintessence and one phantom. We examine a classical cosmological framework, where analytical solutions are obtained. Indeed, we present an explanation of the ``big-bang'' singularity by means of a ``big-bounce''. Moreover, having a barotropic fluid description and for a particular set of parameters, the phantom line is in fact crossed. Additionally, for the quantum counterpart, the Wheeler--DeWitt equation is analytically solved for various instances, where the factor-ordering problem has been taken into account (measured by the factor Q). Hence, this approach allows us to compute the probability density of the previous two classical subcases. It turns out that its behavior is in effect damped as the scale factor and the scalar fields evolve. It also tends towards the phantom sector when the factor ordering constant $\rm Q\ll 0$.

gr-qc↗

arXiv2019

Warm inflation within a supersymmetric distributed mass model

We study the dynamics and observational predictions of warm inflation within a supersymmetric distributed mass model. This dissipative mechanism is well described by the interactions between the inflaton and a tower of chiral multiplets with a mass gap, such that different bosonic and fermionic fields become light as the inflaton scans the tower during inflation. We examine inflation for various mass distributions, analyzing in detail the dynamics and observational predictions. We show, in particular, that warm inflation can be consistently realized in this scenario for a broad parametric range and in excellent agreement with the Planck legacy data. Distributed mass models can be viewed as realizations of the landscape property of string theory, with the mass distributions coming from the underlying spectra of the theory, which themselves would be affected by the vacuum of the theory. We discuss the recently proposed swampland criteria for inflation models on the landscape and analyze the conditions under which they can be met within the distributed mass warm inflation scenario. We demonstrate mass distribution models with a range of consistency with the swampland criteria including cases in excellent consistency.

hep-ph↗

arXiv2019

Classical and quantum exact solutions for the anisotropic Bianchi type I in multi-scalar field cosmology with an exponential potential driven inflation

The anisotropic Bianchi type I in multi-scalar field cosmology is studied with a particular potential of the form $\rm V= V_0 e^{-\left[λ_1 ϕ_1 + \cdots + λ_n ϕ_n \right]}\,,$ which emerges as a condition between the time derivatives of their corresponding momenta. Using the Hamiltonian formalism for the inflation epoch with a quintessence framework we find the exact solutions for the Einstein-Klein-Gordon (EKG) system with different scenarios specified by the parameter $\rm λ^2= \sum_{i=1}^n λ_i^2$. For the quantum scheme of this model, the corresponding Wheeler-DeWitt (WDW) equation is solved by applying an appropriate change of variables and suitable ansatz.

gr-qc↗

arXiv2018

Classical and quantum exact solutions for a FRW multi-scalar field cosmology with an exponential potential driven inflation

A flat Fiedmann-Robertson-Walker (FRW) multi-scalar field cosmology is studied with a particular potential of the form $ \rm V(ϕ,σ)=V_0 e^{-λ_1 ϕ-λ_2 σ}$, which emerges as a relation between the time derivatives of the scalars field momenta. Classically, by employing the Hamiltonian formalism of two scalar fields $\rm(ϕ,σ)$ with standard kinetic energy, exact solutions are found for the Einstein-Klein-Gordon (EKG) system for different scenarios specified by the parameter $\rmλ^2=λ_1^2+λ_2^2$, as well as the e-folding function $\rm N_{e}$ which is also computed. For the quantum scheme of this model, the corresponding Wheeler-DeWitt (WDW) equation is solved by applying an appropriate change of variables.

gr-qc↗

arXiv2018

Hamilton's approach in cosmological inflation with an exponential potential and its observational constraints

The Friedmann-Robertson-Walker (FRW) cosmology is analyzed with a general potential $\rm V(ϕ)$ in the scalar field inflation scenario. The Bohmian approach (a WKB-like formalism) was employed in order to constraint a generic form of potential to the most suited to drive inflation, from here a family of potentials emerges; in particular we select an exponential potential as the first non trivial case and remains the object of interest of this work. The solution to the Wheeler-DeWitt (WDW) equation is also obtained for the selected potential in this scheme. Using Hamilton's approach and equations of motion for a scalar field $\rm ϕ$ with standard kinetic energy, we find the exact solutions to the complete set of Einstein-Klein-Gordon (EKG) equations without the need of the slow-roll approximation (SR). In order to contrast this model with observational data (Planck 2018 results), the inflationary observables: the tensor-to-scalar ratio and the scalar spectral index are derived in our proper time, and then evaluated under the proper condition such as the number of e-folding corresponds exactly at 50-60 before inflation ends. The employed method exhibits a remarkable simplicity with rather interesting applications in the near future.

gr-qc↗