Parametric Resonance in the Early Universe - A Fitting Analysis

Particle production via parametric resonance in the early Universe, is a nonperturbative, non-linear and out-of-equilibrium phenomenon. Although it is a well studied topic, whenever a new scenario exhibits parametric resonance, a full re-analysis is normally required. To avoid this tedious task, many works present often only a simplified linear treatment of the problem. In order to surpass this circumstance in the future, we provide a fitting analysis of parametric resonance through all its relevant stages: initial linear growth, non-linear evolution, and relaxation towards equilibrium. Using lattice simulations in an expanding grid in 3 + 1 dimensions, we parametrize the dynamics outcome scanning over the relevant ingredients: role of the oscillatory field, particle coupling strength, initial conditions, and background expansion rate. We emphasize the inaccuracy of the linear calculation of the decay time of the oscillatory field, and propose a more appropriate definition of this scale based on the subsequent non-linear dynamics. We provide simple fits to the relevant time scales and particle energy fractions at each stage. Our fits can be applied to post-inflationary preheating scenarios, where the oscillatory field is the inflaton, or to spectator-field scenarios, where the oscillatory field can be e.g. a curvaton, or the Standard Model Higgs.Comment: Extended discussion about the late-time dynamics of the system in quadratic models. Minor changes in numerical fits with respect first version. It matches version published in JCAP (30 pages + Appendices + Bibliography, 13 figures

Higgs-curvature coupling and post-inflationary vacuum instability

We study the post-inflationary dynamics of the Standard Model (SM) Higgs field in the presence of a non-minimal coupling $\xi|\Phi|^2R$ to gravity, both with and without the electroweak gauge fields coupled to the Higgs. We assume a minimal scenario in which inflation and reheating are caused by chaotic inflation with a quadratic potential, and no additional new physics is relevant below the Planck scale. By using classical real-time lattice simulations with a renormalisation group improved effective Higgs potential and by demanding the stability of the Higgs vacuum after inflation, we obtain upper bounds for $\xi$, taking into account the experimental uncertainty of the top-Yukawa coupling. We compare the bounds in the absence and presence of the electroweak gauge bosons, and conclude that the addition of gauge interactions has a rather minimal impact. In the unstable cases, we parametrize the time when such instability develops. For a top-quark mass $m_t \approx173.3 {\rm GeV}$, the Higgs vacuum instability is triggered for $\xi \gtrsim 4 -5$, although a slightly lower mass of $m_t \approx 172.1 {\rm GeV}$ pushes up this limit to $\xi \gtrsim 11 - 12$. This, together with the estimation $\xi \gtrsim 0.06$ for stability during inflation, provides tight constraints to the Higgs-curvature coupling within the SM.Comment: 15 pages, 13 figures. Minor changes to match version published in PR

The Decay of the Standard Model Higgs after Inflation

We study the nonperturbative dynamics of the Standard Model (SM) after inflation, in the regime where the SM is decoupled from (or weakly coupled to) the inflationary sector. We use classical lattice simulations in an expanding box in (3+1) dimensions, modeling the SM gauge interactions with both global and Abelian-Higgs analogue scenarios. We consider different post-inflationary expansion rates. During inflation, the Higgs forms a condensate, which starts oscillating soon after inflation ends. Via nonperturbative effects, the oscillations lead to a fast decay of the Higgs into the SM species, transferring most of the energy into $Z$ and $W^{\pm}$ bosons. All species are initially excited far away from equilibrium, but their interactions lead them into a stationary stage, with exact equipartition among the different energy components. From there on the system eventually reaches equilibrium. We have characterized in detail, in the different expansion histories considered, the evolution of the Higgs and of its dominant decay products, until equipartition is established. We provide a useful mapping between simulations with different parameters, from where we derive a master formula for the Higgs decay time, as a function of the coupling constants, Higgs initial amplitude and postinflationary expansion rate.Comment: Minor changes to match the PRD published version. Modulation of the Higgs amplitude removed for $q > 200$ in Sec. V, due to improving the time resolution in the Higgs equation of motion. Results unaffecte

Gravitational wave production from the decay of the Standard Model Higgs field after inflation

During or towards the end of inflation, the Standard Model (SM) Higgs forms a condensate with a large amplitude. Following inflation, the condensate oscillates, decaying non-perturbatively into the rest of the SM species. The resulting out-of-equilibrium dynamics converts a fraction of the energy available into gravitational waves (GW). We study this process using classical lattice simulations in an expanding box, following the energetically dominant electroweak gauge bosons $W^\pm$ and $Z$. We characterize the GW spectrum as a function of the running couplings, Higgs initial amplitude, and post-inflationary expansion rate. As long as the SM is decoupled from the inflationary sector, the generation of this background is universally expected, independently of the nature of inflation. Our study demonstrates the efficiency of GW emission by gauge fields undergoing parametric resonance. The initial energy of the Higgs condensate represents however, only a tiny fraction of the inflationary energy. Consequently, the resulting background is very suppressed, with an amplitude $h^2 \Omega_{\rm GW}^{(o)} \lesssim 10^{-29}$ today. The amplitude can be boosted to $h^2 \Omega_{\rm GW}^{(o)} \lesssim 10^{-16}$, if following inflation the universe undergoes a kination-domination stage; however the background is shifted in this case to high frequencies $f_p \lesssim 10^{11} {\rm Hz}$. In all cases the signal is out of the range of current or planned GW detectors. This background will therefore remain, most likely, as a curiosity of the SM.Comment: 16 pages, 6 figures. Minor changes to match version published in PR

Energy distribution and equation of state of the early Universe: matching the end of inflation and the onset of radiation domination

We study the energy distribution and equation of state of the universe between the end of inflation and the onset of radiation domination (RD), considering observationally consistent single-field inflationary scenarios, with a potential 'flattening' at large field values, and a monomial shape $V(\phi) \propto |\phi|^p$ around the origin. As a proxy for (p)reheating, we include a quadratic interaction $g^2\phi^2X^2$ between the inflaton $\phi$ and a light scalar 'daughter' field $X$, with $g^2>0$. We capture the non-perturbative and non-linear nature of the system dynamics with lattice simulations, obtaining that: $i)$ the final energy transferred to $X$ depends only on $p$, not on $g^2$, ; $ii)$ the final transfer of energy is always negligible for $2 \leq p < 4$, and of order $\sim 50\%$ for $p \geq 4$; $iii)$ the system goes at late times to matter-domination for $p = 2$, and always to RD for $p > 2$. In the latter case we calculate the number of e-folds until RD, significantly reducing the uncertainty in the inflationary observables $n_s$ and $r$.Comment: 7 pages + references, 5 figures. It matches published versio

The continuity and discontinuity of education policy: a study of change in the Chilean debate about higher education

This thesis's main topic is an exploration of the relationship between continuity and discontinuity in terms of the way in which higher education (HE) policies have been developed in Chile between 2003 and 2016. While neo-liberal and privatisation policies in higher education continue deepening worldwide, the Chilean state started conducting a free education policy with the promise of recovering the public and social role of the HE model in the country. This context represents a particular case in the world in that free-of-charge education has risen as a re-distributive principle, which seeks to improve national social justice through a policy that involves separating family purchasing power from access to educational quality by universal educational state funding. This research aims to analyse the public HE debate to understand the continuity and/or discontinuity of arguments providing legitimacy to the Chilean HE model in a context of policy change. Although this study does not address the policy's implementation and practices, the re-organisation of the critiques and justifications in the HE debate presents an excellent and original opportunity to approach the setting of the HE model's relationship with state and society. As this policy entails the hopes of re-defining the understanding of social justice in the country, there was an analysis of editorials and opinion columns published in the most important newspapers and interviews to relevant HE actors for describing the most significant differences and similarities with previous HE policies within a 14-year period. The findings suggest that justifications around the free education policy represent new forms of understanding neoliberal relationships in a context of policy reform. Through an institutional arrangement anchored on free education promising to improve access to tertiary education, policy continuities and discontinuities seem to work together to construct a new legitimate Chilean HE model

Social learning as a requirement for rural development: The connectivity of Salinas, San Luis Potosí

It is postulated that communities using social learning on rural planning will achieve sustainable development. The construction of roads integrates geographic spaces and it is a requirement for competitiveness and development of the communities. In Mexico, the construction of roads and its improvement use existing ways originated by the transfer of cattle or the pathways drawn over past times, without considering any municipal or local development plan. One looked for to define a reference frame on the importance of the ways, first in Mexico, the state of San Luis Potosí and the behavior of investment in the municipality of Salinas de Hidalgo, San Luis Potosí and to outline an intervention method that allows to design criteria for the decision in the road construction using like planning tool the social learning. Any alternative of road selection it is desirable that should include local actors weighting their needs along with the technical criteria as well under an IPMA competence baseline schem

Hamstring autograft size importance in anterior cruciate ligament repair surgery

Graft size in hamstring autograft anterior cruciate ligament (ACL) surgery is an important factor directly related to failure. Most of the evidence in the field suggests that the size of the graft in hamstring autograft ACL reconstruction matters when the surgeon is trying to avoid failures.The exact graft diameter needed to avoid failures is not absolutely clear and could depend on other factors, but newer studies suggest than even increases of 0.5 mm up to a graft size of 10 mm are beneficial for the patient. There is still no evidence to recommend the use of grafts > 10 mm.Several methods - e.g. folding the graft in more strands that are simple and reproducible have been published lately to address the problem of having an insufficient graft size when performing an ACL reconstruction. Due to the evidence presented, we think it is necessary for the surgeon to have them in his or her arsenal before performing an ACL reconstruction.There are obviously other factors that should be considered, especially age. Therefore, a larger graft size should not be taken as the only goal in ACL reconstruction.No benefits in any form have been received or will be received from a commercial party related directly or indirectly to the subject of this article

El proceso de asentamiento de la migración México-Estados Unidos

Existe un proceso de reconfiguración en la migración mexicana a Estados Unidos. En la actualidad la población migrante es de 11 millones de personas y equivale a 11 por ciento del total de la población mexicana. Los centros de expulsión siguen siendo los de origen rural del bajío mexicano, pero se han sumado los de tipo urbano y particularmente del sur sureste del país, con población indígena. En cuanto al género, éste es balanceado, 56 por ciento masculino y 44 por ciento femenino. Respecto a los destinos en Estados Unidos, Texas, California, Arizona, Nuevo México e Indiana siguen siendo importantes, pero ahora los migrantes mexicanos son mayoría en 43 Estados. Los cruces tradicionales han perdido importancia y han surgido otros como Altar Sonora (Sásabe-Sasabe, Sonoyta, Agua Prieta y Cd. Juárez) cuya principal característica es la peligrosidad para la vida del migrante y la utilización de coyotes para atravesar la frontera