arXiv subjects

Gabriel German

Publications and source records attributed to Gabriel German.

At least 37 records · Page 2Linked to original sources

arXiv2020

Precise determination of the inflationary epoch and constraints for reheating

We present a simple formula that allows to calculate the value of the inflaton field, denoted by $ϕ$, at the scale with wavenumber mode $k$. In the extreme case of instantaneous reheating $ϕ_k$ is calculated exactly and all inflationary observables and quantities of interest follow. This formula, together with the fact that the scale factor $a_p$ at the pivot scale wavenumber $k_p=0.05/Mpc$ lies in the radiation era, allows the development of a diagrammatic approach to study the evolution of the universe. This scheme is complementary to the usual analytical method and some interesting results, independent of the model of inflation, can be obtained. As a concrete application of the ideas developed here we discuss them with some detail using the Starobinsky model of inflation.

astro-ph.CO↗

arXiv2020

Measuring the expansion of the universe

We draw a figure from where it is possible to measure the number of e-folds of expansion of the universe with a ruler. We find model independent bounds for the number of e-folds during inflation, reheating and radiation. We also give a lower bound to the size of the universe at the beginning of observable inflation. Finally, we show that consistency with a relevant diagram requires the existence of a new form of energy to drive the present expansion of the universe.

astro-ph.CO↗

arXiv2019

Geodesic structure of a rotating regular black hole

We examine the dynamics of particles around a rotating regular black hole. In particular we focus on the effects of the characteristic length parameter of the spinning black hole on the motion of the particles by solving the equation of orbital motion. We have found that there is a fourth constant of motion that determines the dynamics of orbits out the equatorial plane similar as in the Kerr black hole. Through detailed analyses of the corresponding effective potentials for massive particles the possible orbits are numerically simulated. A comparison with the trajectories in a Kerr spacetime shows that the differences appear when the black holes rotate slowly for large values of the characteristic length parameter.

gr-qc↗

arXiv2018

Mixed constraints to inflationary models

We show how to constrain inflationary models and reheating by using mixed constraints. In particular we study the physics of the reheating phase after inflation from observational constraints to the inflationary stage. We show that it is possible to determine $ω$, the equation of state during reheating, by using the reported values of the spectral index and the {\it full} number of $e$-folds $N(n_s,ω)= N_H(n_s)+N_{re}(n_s,w)\approx 60$, which includes the accelerated expansion and the reheating phase. We show that the reheating number of $e$-folds $N_{re}$ is quite sensitive to this equation of state. Requiring $N_{re}>0$ and a sensible value for the thermalization scale $T_{re}$, demands in general a reheating phase with $ω\neq 0$. We exemplify the constraints with two particular examples: We show how the Starobinsky model allows only large values of $T_{re}$ if the reheating phase is dominated by dust ($w =0$), and if Primordial Black Hole production is subdominant. For the case of $N=1$ Supergravity inflation, the extra parameter of the potential provides the necessary freedom to afford lower-scale thermalization in a dust-like reheating phase and yet our method serves to determine the rest of the observable parameters.

astro-ph.CO↗

arXiv2018

Theoretical and observational constraints on Tachyon Inflation

We constrain several models in Tachyonic Inflation derived from the large-$N$ formalism by considering theoretical aspects as well as the latest observational data. On the theoretical side, we assess the field range of our models by means of the excursion of the equivalent canonical field. On the observational side, we employ BK14+PLANCK+BAO data to perform a parameter estimation analysis as well as a Bayesian model selection to distinguish the most favoured models among all four classes here presented. We observe that the original potential $V \propto \textrm{sech}(T)$ is strongly disfavoured by observations with respect to a reference model with flat priors on inflationary observables. This realisation of Tachyon inflation also presents a large field range which may demand further quantum corrections. We also provide examples of potentials derived from the polynomial and the perturbative classes which are both statistically favoured and theoretically acceptable.

astro-ph.CO↗

arXiv2017

General bounds in Hybrid Natural Inflation

Recently we have studied in great detail a model of Hybrid Natural Inflation (HNI) by constructing two simple effective field theories. These two versions of the model allow inflationary energy scales as small as the electroweak scale in one of them or as large as the Grand Unification scale in the other, therefore covering the whole range of possible energy scales. In any case the inflationary sector of the model is of the form $V(ϕ)=V_0 \left(1+a \cos(ϕ/f)\right)$ where $0\leq a<1$ and the end of inflation is triggered by an independent waterfall field. One interesting characteristic of this model is that the slow-roll parameter $ε(ϕ)$ is a non-monotonic function of $ϕ$ presenting a {\it maximum} close to the inflection point of the potential. Because the scalar spectrum $\mathcal{P}_s(k)$ of density fluctuations when written in terms of the potential is inversely proportional to $ε(ϕ)$ we find that $\mathcal{P}_s(k)$ presents a {\it minimum} at $ϕ_{min}$. The origin of the HNI potential can be traced to a symmetry breaking phenomenon occurring at some energy scale $f$ which gives rise to a (massless) Goldstone boson. Non-perturbative physics at some temperature $T<f$ might occur which provides a potential (and a small mass) to the originally massless boson to become the inflaton (a pseudo-Nambu-Goldstone boson). Thus the inflaton energy scale $Δ$ is bounded by the symmetry breaking scale, $Δ\equiv V_H^{1/4} <f.$ To have such a well defined origin and hierarchy of scales in inflationary models is not common. We use this property of HNI to determine bounds for the inflationary energy scale $Δ$ and for the tensor-to-scalar ratio $r$.

astro-ph.CO↗

arXiv2017

Collapse threshold for a cosmological Klein Gordon field

Oscillating scalar fields are useful to model a variety of matter components in the universe. One or more scalar fields participate in the reheating process after inflation, while at much lower energies scalar fields are robust dark matter candidates. Pertaining structure formation in these models, it is well known that inhomogeneities of the Klein-Gordon field are unstable above the characteristic De Broglie wavelength. In this paper we show that such instability implies the existence of a threshold amplitude for the collapse of primordial fluctuations. We use this threshold to correctly predict the cut--off scale of the matter power spectrum in the scalar field dark matter model. Furthermore, for a Klein-Gordon field during reheating we show that this same threshold allows for abundant production of structure (oscillons but not necessarily black holes). Looking at the production of Primordial Black Holes (PBHs) in this scenario we note that the sphericity condition yields a much lower probability of PBH formation at the end of inflation. Remarkably, even after meeting such stringent condition, we find that PBHs may be overproduced during reheating. We finally constrain the epochs at which an oscillating Klein-Gordon field could dominate the early universe.

astro-ph.CO↗

arXiv2017

Bounds for the scale of inflation and the tensor-to-scalar ratio in Hybrid Natural Inflation

Recently we have studied in great detail a model of Hybrid Natural Inflation (HNI) by constructing two simple effective field theories. These two versions of the model allow inflationary energy scales as small as the electroweak scale in one of them or as large as the Grand Unification scale in the other therefore covering the whole range of possible energy scales. The inflationary sector of the model is of the form $V(ϕ)=V_0 \left(1+a \cos(ϕ/f)\right)$ where $0\leq a<1$ and the end of inflation is triggered by an independent waterfall field. One interesting characteristic of this type of models is that the tensor-to-scalar ratio $r$ is a non-monotonic function of $ϕ$ presenting a {\it maximum} close to the inflection point $ϕ_I=π/2$ of the potential. Because the scalar spectrum $\mathcal{P}_s(k)$ of density fluctuations when written in terms of the potential is inversely proportional to $r$ we find that $\mathcal{P}_s(k)$ presents a {\it minimum} at $ϕ_{min}$. We use this property of HNI together with the observation that the spectrum is decreasing during the first 8 e-folds of observable inflation to determine bounds for the inflationary energy scale $Δ$ and for the tensor-to-scalar ratio $r$.

astro-ph.CO↗

arXiv2017

Non-Spherical Szekeres models in the language of Cosmological Perturbations

We study the differences and equivalences between the non-perturbative description of the evolution of cosmic structure furnished by the Szekeres dust models (a non-spherical exact solution of Einstein's equations) and the dynamics of Cosmological Perturbation Theory (CPT) for dust sources in a $Λ$CDM background. We show how the dynamics of Szekeres models can be described by evolution equations given in terms of "exact fluctuations" that identically reduce (at all orders) to evolution equations of CPT in the comoving isochronous gauge. We explicitly show how Szekeres linearised exact fluctuations are specific (deterministic) realisations of standard linear perturbations of CPT given as random fields but, as opposed to the latter perturbations, they can be evolved exactly into the full non-linear regime. We prove two important results: (i) the conservation of the curvature perturbation (at all scales) also holds for the appropriate approximation of the exact Szekeres fluctuations in a $Λ$CDM background, and (ii) the different collapse morphologies of Szekeres models yields, at nonlinear order, different functional forms for the growth factor that follows from the study of redshift space distortions. The metric based potentials used in linear CPT are computed in terms of the parameters of the linearised Szekeres models, thus allowing us to relate our results to linear CPT results in other gauges. We believe that these results provide a solid starting stage to examine the role of non-perturbative General Relativity in current cosmological research.

gr-qc↗

arXiv2016

Hybrid Natural Inflation

We construct two simple effective field theory versions of {\it Hybrid Natural Inflation (HNI)} that illustrate the range of its phenomenological implications. The resulting inflationary sector potential, $V=Δ^4(1+a\cos(ϕ/f))$, arises naturally, with the inflaton field a pseudo-Nambu-Goldstone boson. The end of inflation is triggered by a waterfall field and the conditions for this to happen are determined. Also of interest is the fact that the slow-roll parameter $ε$ (and hence the tensor $r$) is a non-monotonic function of the field with a maximum where observables take universal values that determines the maximum possible tensor to scalar ratio $r$. In one of the models the inflationary scale can be as low as the electroweak scale. We explore in detail the associated HNI phenomenology, taking account of the constraints from Black Hole production, and perform a detailed fit to the Planck 2015 temperature and polarisation data.

astro-ph.CO↗

arXiv2016

Canonical single field slow-roll inflation with a non-monotonic tensor-to-scalar ratio

We take a pragmatic, model independent approach to single field slow-roll canonical inflation by imposing conditions, not on the potential, but on the slow-roll parameter $ε(ϕ)$ and its derivatives $ε^{\prime }(ϕ)$ and $ε^{\prime\prime }(ϕ)$, thereby extracting general conditions on the tensor-to-scalar ratio $r$ and the running $n_{sk}$ at $ϕ_{H}$ where the perturbations are produced, some $50$ $-$ $60$ $e$-folds before the end of inflation. We find quite generally that for models where $ε(ϕ)$ develops a maximum, a relatively large $r$ is most likely accompanied by a positive running while a negligible tensor-to-scalar ratio implies negative running. The definitive answer, however, is given in terms of the slow-roll parameter $ξ_2(ϕ)$. To accommodate a large tensor-to-scalar ratio that meets the limiting values allowed by the Planck data, we study a non-monotonic $ε(ϕ)$ decreasing during most part of inflation. Since at $ϕ_{H}$ the slow-roll parameter $ε(ϕ)$ is increasing, we thus require that $ε(ϕ)$ develops a maximum for $ϕ> ϕ_{H}$ after which $ε(ϕ)$ decrease to small values where most $e$-folds are produced. The end of inflation might occur trough a hybrid mechanism and a small field excursion $Δϕ_e\equiv |ϕ_H-ϕ_e |$ is obtained with a sufficiently thin profile for $ε(ϕ)$ which, however, should not conflict with the second slow-roll parameter $η(ϕ)$. As a consequence of this analysis we find bounds for $Δϕ_e$, $r_H$ and for the scalar spectral index $n_{sH}$. Finally we provide examples where these considerations are explicitly realised.

astro-ph.CO↗

arXiv2016

Stability of a tachyon braneworld

Within the braneworld paradigm the tachyonic scalar field has been used to generate models that attempt to solve some of the open problems that physics faces nowadays, both in cosmology and high energy physics as well. When these field configurations are produced by the interplay of higher dimensional warped gravity with some matter content, braneworld models must prove to be {\it stable} under the whole set of small fluctuations of the gravitational and matter fields background, among other consistency tests. Here we present a complete proof of the stability under scalar perturbations of tachyonic thick braneworlds with an embedded maximally symmetric 4D space-time, revealing its physical consistency. This family of models contains a recently reported tachyonic de Sitter thick braneworld which possesses a series of appealing properties. These features encompass complete regularity, asymptotic flatness (instead of being asymptotically dS or AdS) even when it contains a negative bulk cosmological constant, a relevant 3-brane with dS metric which naturally arises from the full set of field equations of the 5D background (it is not imposed), qualitatively describing the inflationary epochs of our Universe, and a graviton spectrum with a single zero mode bound state that accounts for the 4D graviton localised on the brane and is separated from the continuum of Kaluza-Klein massive graviton excitations by a mass gap. Gauge vector fields with a single massless bound state in its mass spectrum are also localised on this braneworld model a fact that allows us to recover the Coulomb's law of our 4D world. All these properties of the above referred tachyonic braneworld together with the positive stability analysis provided in this work, constitute a firm step towards the construction of realistic cosmological models within the braneworld paradigm.

hep-th↗

arXiv2015

Tachyon inflation in the Large-$N$ formalism

We study tachyon inflation within the large-$N$ formalism, which takes a prescription for the small Hubble flow slow--roll parameter $ε_1$ as a function of the large number of $e$-folds $N$. This leads to a classification of models through their behaviour at large $N$. In addition to the perturbative $N$ class, we introduce the polynomial and exponential classes for the $ε_1$ parameter. With this formalism we reconstruct a large number of potentials used previously in the literature for Tachyon Inflation. We also obtain new families of potentials form the polynomial class. We characterize the realizations of Tachyon Inflation by computing the usual cosmological observables up to second order in the Hubble flow slow--roll parameters. This allows us to look at observable differences between tachyon and canonical single field inflation. The analysis of observables in light of the Planck 2015 data shows the viability of some of these models, mostly for certain realization of the polynomial and exponential classes.

astro-ph.CO↗

arXiv2015

On spherical dust fluctuations: the exact vs. the perturbative approach

We examine the relation between the dynamics of Lema\^ıtre-Tolman-Bondi (LTB) dust models (with and without $Λ$) and the dynamics of dust perturbations in two of the more familiar formalisms used in cosmology: the metric based Cosmological Perturbation Theory (CPT) and the Covariant Gauge Invariant (GIC) perturbations. For this purpose we recast the evolution of LTB models in terms of a covariant and gauge invariant formalism of local and non-local "exact fluctuations " on a Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) background defined by suitable averages of covariant scalars. We examine the properties of these fluctuations, which can be defined for a confined comoving domain or for an asymptotic domain extending to whole time slices. In particular, the non-local density fluctuation provides a covariant and precise definition for the notion of the "density contrast ". We show that in their linear regime these LTB exact fluctuations (local and non-local) are fully equivalent to the conventional cosmological perturbations in the synchronous-comoving gauge of CPT and to GIC perturbations. As an immediate consequence, we show the time-invariance of the spatial curvature perturbation in a simple form. The present work may provide important theoretical connections between the exact and perturbative (linear or no-linear) approach to the dynamics of dust sources in General Relativity.

gr-qc↗

arXiv2015

Constraining Hybrid Natural Inflation with recent CMB data

We study the Hybrid Natural Inflation (HNI) model and some of its realisations in the light of recent CMB observations, mainly Planck temperature and WMAP-9 polarization, and compare with the recent release of BICEP2 dataset. The inflationary sector of HNI is essentially given by the potential $V(ϕ) = V_0(1+a\cos (\fracϕ{f} ) )$, where $a$ is a positive constant smaller or equal to one and $f$ is the scale of (pseudo Nambu-Goldstone) symmetry breaking. We show that to describe the HNI model realisations we only need two observables; the spectral index $n_s$, the tensor-to-scalar ratio, and a free parameter in the amplitude of the cosine function $a$. We find that in order to make the HNI model compatible with the BICEP2 observations, we require a large positive running of the spectra. We find that this could over-produce primordial black holes in the most consistent case of the model. This situation could be aleviated if, as recently argued, the BICEP2 data do not correspond to primordial gravitational waves.

astro-ph.CO↗

arXiv2014

Discrete graviton spectrum from super-exponential cup potentials and their application to braneworld physics

Super-exponential warp factors have been proposed in the context of two-brane models to solve the gauge hierarchy problem of scales by using a compactification scale of the same order of the fundamental Planck scale, completely eliminating the hierarchy between the electroweak and the Planck scales. However, most of the so far studied families of braneworlds with super-exponential warp factors do not localize 4D gravity when one of the branes is sent to infinity. Recently a braneworld model generated by a canonical scalar field $ϕ$ minimally coupled to 5D gravity with a bulk cosmological constant was shown to localize 4D gravity and to be stable under linear tensorial and scalar perturbations. Here we present an explicit new solution for the latter braneworld configuration and study the dynamics of its tensorial perturbations: we find that they obey a Schrödinger-like equation with a well potential which possesses exponentially increasing walls (we call it the {\it cup potential}), yielding a {\it novel discrete spectrum} for the massive Kaluza-Klein (KK) tensorial excitations, despite the non-compact nature of the fifth dimension, and in contrast to the braneworld models proposed so far, where the mass spectrum of the KK modes is continuous, or at most mixed. Finally, the corrections to Newton's law coming from these massive KK modes are computed. Their novelty arises from the fact that these {\it KK excitations possess quantized masses and are bound to the brane}, however, they are all of the Planck mass order, leading to unreachable energy scales from the phenomenological viewpoint.

hep-th↗

arXiv2014

Testing Hybrid Natural Inflation with BICEP2

We analyse Hybrid Natural Inflation in view of the recent results for the tensor index reported by BICEP2. We find that it predicts a large running of the scalar spectrum which is potentially detectable by large scale structure and $21\, \mathrm{cm} $ observations. The running of the running is also relatively large becoming close to $10^{-2}$. Along the way, we find general consistency relations at which observables are subject if the slow-roll approximation is imposed. Failure to satisfy these equations by the values obtained for the observables in surveys would be a failure of the slow-roll approximation itself.

astro-ph.CO↗

arXiv2014

On the Lyth bound and single field slow-roll inflation

We take a pragmatic, model independent approach to single field slow-roll inflation by imposing conditions to the slow-roll parameter $ε$ and its derivative $ε^{\prime }.$ To accommodate the recent (large) values of $r$ reported by the BICEP2 collaboration we advocate for a decreasing $ε$ during most part of inflation. However because at $ϕ_{\mathrm{H}}$, at which the perturbations are produced, some $50$ $-$ $60$ e-folds before the end of inflation, $ε$ is increasing we thus require that $ε$ develops a maximum for $ϕ> ϕ_{\mathrm{H}}$ and then decrease to small values where most e-folds are produced. The end of inflation might occur trough a hybrid field and a small $Δϕ$ is obtained with a sufficiently thin $ε$ which, however, should not conflict with the curvature of the potential measured by the second slow-roll parameter $η$. The conclusion is that under these circumstances $Δϕ$ and the spectral index $n_{\mathrm{s}}$ are restricted to narrow windows of values.

astro-ph.CO↗