Search

We consider quantum diffusion in ultra-slow-roll (USR) inflation. Using the $\Delta N$ formalism, we present the first stochastic calculation of the probability distribution $P(\mathcal{R})$ of the curvature perturbation during USR. We capture the non-linearity of the system, solving the coupled evolution of the coarse-grained background with random kicks from the short wavelength modes, simultaneously with the mode evolution around the stochastic background. This leads to a non-Markovian process from which we determine the highly non-Gaussian tail of $P(\mathcal{R})$. Studying the production of primordial black holes in a viable model, we find that stochastic effects during USR increase their abundance by a factor $\sim 10^5$ compared to the Gaussian approximation., Comment: 6 pages, 2 figures. v2: 5+3 pages, 2 figures. Improved analysis and text, gathered 400 times more data. Small change in results. Published version

It is commonly assumed that the energy density of the Universe was dominated by radiation between reheating after inflation and the onset of matter domination 54,000 years later. While the abundance of light elements indicates that the Universe was radiation dominated during Big Bang Nucleosynthesis (BBN), there is scant evidence that the Universe was radiation dominated prior to BBN. It is therefore possible that the cosmological history was more complicated, with deviations from the standard radiation domination during the earliest epochs. Indeed, several interesting proposals regarding various topics such as the generation of dark matter, matter-antimatter asymmetry, gravitational waves, primordial black holes, or microhalos during a nonstandard expansion phase have been recently made. In this paper, we review various possible causes and consequences of deviations from radiation domination in the early Universe - taking place either before or after BBN - and the constraints on them, as they have been discussed in the literature during the recent years., 67 pages, 18 figures. v2: Discussion and references added. Accepted for publication in The Open Journal of Astrophysics

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 $V(��) \propto |��|^p$ around the origin. As a proxy for (p)reheating, we include a quadratic interaction $g^2��^2X^2$ between the inflaton $��$ 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 $r$., 7 pages + references, 5 figures. It matches published version

The first direct measurement of gravitational waves by the LIGO and Virgo collaborations has opened up new avenues to explore our Universe. This white paper outlines the challenges and gains expected in gravitational wave searches at frequencies above the LIGO/Virgo band, with a particular focus on Ultra High-Frequency Gravitational Waves (UHF-GWs), covering the MHz to GHz range. The absence of known astrophysical sources in this frequency range provides a unique opportunity to discover physics beyond the Standard Model operating both in the early and late Universe, and we highlight some of the most promising gravitational sources. We review several detector concepts which have been proposed to take up this challenge, and compare their expected sensitivity with the signal strength predicted in various models. This report is the summary of the workshop "Challenges and opportunities of high-frequency gravitational wave detection" held at ICTP Trieste, Italy in October 2019, that set up the stage for the recently launched Ultra-High-Frequency Gravitational Wave (UHF-GW) initiative., Published in Living Reviews in Relativity

Cosmological phase transitions in the early Universe may produce relics in the form of a network of cosmic defects. Independently of the order of a phase transition, topology of the defects, and their global or gauge nature, the defects are expected to emit gravitational waves (GWs) as the network energy-momentum tensor adapts itself to maintaining {scaling}. We show that the evolution of any defect network (and for that matter any scaling source) emits a GW background with spectrum $\Omega_{\rm GW} \propto f^3$ for $f \ll f_0$, $\Omega_{\rm GW} \propto 1/f^2$ for $f_0 \lesssim f \lesssim f_{\rm eq}$, and $\Omega_{\rm GW} \propto~const$ (i.e.~exactly scale-invariant) for $f \gg f_{\rm eq}$, where $f_0$ and $ f_{\rm eq}$ denote respectively the frequencies corresponding to the present and matter-radiation equality horizons. This background represents an irreducible emission of GWs from any scaling network of cosmic defects, with its amplitude characterized only by the symmetry breaking scale and the nature of the defects. Using classical lattice simulations we calculate the GW signal emitted by defects created after the breaking of a global symmetry $O(N) \rightarrow O(N-1)$. We obtain the GW spectrum for $N$ between 2 and 20 with two different techniques: integrating over unequal time correlators of the energy momentum tensor, updating our previous work on smaller lattices, and for the first time, comparing the result with the real time evolution of the tensor perturbations sourced by the same defects. Our results validate the equivalence of the two techniques. Using CMB upper bounds on the defects' energy scale, we discuss the difficulty of detecting this GW background in the case of global defects., Comment: 24 pages, 8 figures

Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present a lattice formulation of the interaction between a $shift$-symmetric field and some $U(1)$ gauge sector, $a(x)\tilde{F}_{\mu\nu}F^{\mu\nu}$, reproducing the continuum limit to order $\mathcal{O}(dx_\mu^2)$ and obeying the following properties: (i) the system is gauge invariant and (ii) shift symmetry is exact on the lattice. For this end we construct a definition of the {\it topological number density} $Q = \tilde{F}_{\mu\nu}F^{\mu\nu}$ that admits a lattice total derivative representation $Q = \Delta_\mu^+ K^\mu$, reproducing to order $\mathcal{O}(dx_\mu^2)$ the continuum expression $Q = \partial_\mu K^\mu \propto \vec E \cdot \vec B$. If we consider a homogeneous field $a(x) = a(t)$, the system can be mapped into an Abelian gauge theory with Hamiltonian containing a Chern-Simons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. When $a(x) = a(\vec x,t)$ is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an $\mathcal{O}(dx_\mu^2)$ accuracy). We discuss an iterative scheme allowing to overcome this difficulty., Comment: 30 pages

If the Standard Model (SM) Higgs is weakly coupled to the inflationary sector, the Higgs is expected to be universally in the form of a condensate towards the end of inflation. The Higgs decays rapidly after inflation - via non-perturbative effects - into an out-of-equilibrium distribution of SM species, which thermalize soon afterwards. If the post-inflationary equation of state of the universe is stiff, $w \simeq +1$, the SM species eventually dominate the total energy budget. This provides a natural origin for the relativistic thermal plasma of SM species, required for the onset of the `hot Big Bang' era. The viability of this scenario requires the inflationary Hubble scale $H_*$ to be lower than the instability scale for Higgs vacuum decay, the Higgs not to generate too large curvature perturbations at cosmological scales, and the SM dominance to occur before Big Bang Nucleosynthesis. We show that successful reheating into the SM can only be obtained in the presence of a non-minimal coupling to gravity $\xi \gtrsim 1$, with a reheating temperature of $T_{\rm RH} \gtrsim \mathcal{O}(10^{10})\xi^{3/2}(H_*/10^{14}{\rm GeV})^2~{\rm GeV}$., Comment: 6 pages, 2 figures, minor changes with new figures to match published version in PLB

We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce the basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of 𝒪(δ t2) accuracy like staggered leapfrog and Verlet integration, to Runge-Kutta methods up to 𝒪(δ t4) accuracy, and the Yoshida and Gauss-Legendre higher-order integrators, accurate up to 𝒪(δ t10). We adapt these methods for their use in classical lattice simulations of the non-linear dynamics of scalar and gauge fields in an expanding grid in 3+1 dimensions, including the case of `self-consistent' expansion sourced by the volume average of the fields' energy and pressure densities. We present lattice formulations of canonical cases of: i) Interacting scalar fields, ii) Abelian (1) gauge theories, and iii) Non-Abelian (2) gauge theories. In all three cases we provide symplectic integrators, with accuracy ranging from 𝒪(δ t2) up to 𝒪(δ t10). For each algorithm we provide the form of relevant observables, such as energy density components, field spectra and the Hubble constraint. We note that all our algorithms for gauge theories always respect the Gauss constraint to machine precision, including when `self-consistent' expansion is considered. As a numerical example we analyze the post-inflationary dynamics of an oscillating inflaton charged under (2)×(1). We note that the present manuscript is meant to be part of the theoretical basis for the code 𝒞osmoℒattice, a multi-purpose MPI-based package for simulating the non-linear evolution of field theories in an expanding universe, publicly available at http://www.cosmolattice.net.

Cosmic string networks offer one of the best prospects for detection of cosmological gravitational waves (GWs). The combined incoherent GW emission of a large number of string loops leads to a stochastic GW background (SGWB), which encodes the properties of the string network. In this paper we analyze the ability of the Laser Interferometer Space Antenna (LISA) to measure this background, considering leading models of the string networks. We find that LISA will be able to probe cosmic strings with tensions $G\mu \gtrsim \mathcal{O}(10^{-17})$, improving by about $6$ orders of magnitude current pulsar timing arrays (PTA) constraints, and potentially $3$ orders of magnitude with respect to expected constraints from next generation PTA observatories. We include in our analysis possible modifications of the SGWB spectrum due to different hypotheses regarding cosmic history and the underlying physics of the string network. These include possible modifications in the SGWB spectrum due to changes in the number of relativistic degrees of freedom in the early Universe, the presence of a non-standard equation of state before the onset of radiation domination, or changes to the network dynamics due to a string inter-commutation probability less than unity. In the event of a detection, LISA's frequency band is well-positioned to probe such cosmic events. Our results constitute a thorough exploration of the cosmic string science that will be accessible to LISA., Comment: 40 pages, 12 figures, 1 appendix

We present a set of tools to assess the capabilities of LISA to detect and reconstruct the spectral shape and amplitude of a stochastic gravitational wave background (SGWB). We first provide the LISA power-law sensitivity curve and binned power-law sensitivity curves, based on the latest updates on the LISA design. These curves are useful to make a qualitative assessment of the detection and reconstruction prospects of a SGWB. For a quantitative reconstruction of a SGWB with arbitrary power spectrum shape, we propose a novel data analysis technique: by means of an automatized adaptive procedure, we conveniently split the LISA sensitivity band into frequency bins, and fit the data inside each bin with a power law signal plus a model of the instrumental noise. We apply the procedure to SGWB signals with a variety of representative frequency profiles, and prove that LISA can reconstruct their spectral shape. Our procedure, implemented in the code SGWBinner, is suitable for homogeneous and isotropic SGWBs detectable at LISA, and it is also expected to work for other gravitational wave observatories., 40 pages, 22 figures

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 PRD

We forecast the prospective of detection for a stochastic gravitational wave background sourced by cosmological first-order phase transitions. We focus on first-order phase transitions with negligible plasma effects, and consider the experimental infrastructures built by the end of the LISA mission. We make manifest the synergy among LISA, pulsar time array experiments, and ground-based interferometers. For phase transitions above the TeV scale or below the electroweak scale, LISA can detect the corresponding gravitational wave signal together with Einstein Telescope, SKA or even aLIGO-aVIRGO-KAGRA. For phase transitions at the electroweak scale, instead, LISA can be the only experiment observing the gravitational wave signal. In case of detection, by using a parameter reconstruction method that we anticipate in this work, we show that LISA on its own has the potential to determine when the phase transition occurs and, consequently, the energy scale above which the standard model of particle physics needs to be modified. The result may likely guide the collider community in the post-LHC era., Comment: 7 pages, 6 figures; v3: some clarifications, extra references, matches published version

Gravitational waves (GWs) have a great potential to probe cosmology. We review early universe sources that can lead to cosmological backgrounds of GWs. We begin by presenting definitions of GWs in flat space-time and in a cosmological setting, and discussing the reasons why GW backgrounds from the early universe are of a stochastic nature. We recap current observational constraints on stochastic backgrounds, and discuss some of the characteristics of present and future GW detectors including advanced LIGO, advanced Virgo, the Einstein Telescope, KAGRA, LISA. We then review in detail early universe GW generation mechanisms proposed in the literature, as well as the properties of the GW backgrounds they give rise to. We classify the backgrounds in five categories: GWs from quantum vacuum fluctuations during standard slow-roll inflation, GWs from processes that operate within extensions of the standard inflationary paradigm, GWs from post-inflationary preheating and related non-perturbative phenomena, GWs from first order phase transitions (related or not to the electroweak symmetry breaking), and GWs from topological defects, in particular from cosmic strings. The phenomenology of early universe processes that can generate a stochastic background of GWs is extremely rich, and some backgrounds are within the reach of near-future GW detectors. A future detection of any of these backgrounds will provide crucial information on the underlying high energy theory describing the early universe, probing energy scales well beyond the reach of particle accelerators., third version, corrected typos and the section about the transfer function, acknowledgements added

Parametric resonance is among the most efficient phenomena generating gravitational waves (GWs) in the early Universe. The dynamics of parametric resonance, and hence of the GWs, depend exclusively on the resonance parameter $q$. The latter is determined by the properties of each scenario: the initial amplitude and potential curvature of the oscillating field, and its coupling to other species. Previous works have only studied the GW production for fixed value(s) of $q$. We present an analytical derivation of the GW amplitude dependence on $q$, valid for any scenario, which we confront against numerical results. By running lattice simulations in an expanding grid, we study for a wide range of $q$ values, the production of GWs in post-inflationary preheating scenarios driven by parametric resonance. We present simple fits for the final amplitude and position of the local maxima in the GW spectrum. Our parametrization allows to predict the location and amplitude of the GW background today, for an arbitrary $q$. The GW signal can be rather large, as $h^2\Omega_{\rm GW}(f_p) \lesssim 10^{-11}$, but it is always peaked at high frequencies $f_p \gtrsim 10^{7}$ Hz. We also discuss the case of spectator-field scenarios, where the oscillatory field can be e.g.~a curvaton, or the Standard Model Higgs., Comment: Corrected typos, matches version published in JCAP (39 pages + appendix, 11 figures)

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., 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)

Journal of cosmology and astroparticle physics 1811(11), 034 (2018). doi:10.1088/1475-7516/2018/11/034, The stochastic gravitational wave background (SGWB) contains a wealth of information on astrophysical and cosmological processes. A major challenge of upcoming years will be to extract the information contained in this background and to disentangle the contributions of different sources. In this paper we provide the formalism to extract, from the correlation of three signals in the Laser Interferometer Space Antenna (LISA), information about the tensor three-point function, which characterizes the non-Gaussian properties of the SGWB. Compared to the two-point function, the SGWB three-point function has a richer dependence on the gravitational wave momenta and chiralities, and a larger number of signal channels. It can be used therefore as a powerful discriminator between different models. We provide LISA's response functions to a general SGWB three-point function. As examples, we study in full detail the cases of an equilateral and squeezed SGWB bispectra, and provide the explicit form of the response functions, ready to be convoluted with any theoretical prediction of the bispectrum to obtain the observable signal. We further derive the optimal estimator to compute the signal-to-noise ratio. Our formalism covers general shapes of non-Gaussianity, and can be extended straightaway to other detector geometries. Finally, we provide a short overview of models of the early universe that can give rise to non-Gaussian SGWB., Published by IOP, London

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 PRD

We investigate the potential for the LISA space-based interferometer to detect the stochastic gravitational wave background produced from different mechanisms during inflation. Focusing on well-motivated scenarios, we study the resulting contributions from particle production during inflation, inflationary spectator fields with varying speed of sound, effective field theories of inflation with specific patterns of symmetry breaking and models leading to the formation of primordial black holes. The projected sensitivities of LISA are used in a model-independent way for various detector designs and configurations. We demonstrate that LISA is able to probe these well-motivated inflationary scenarios beyond the irreducible vacuum tensor modes expected from any inflationary background., Comment: 53 pages, 18 figures; v2: minor changes to match published version

We show that self-ordering scalar fields (SOSF), i.e. non-topological cosmic defects arising after a global phase transition, cannot explain the B-mode signal recently announced by BICEP2. We compute the full $C_\ell^{B}$ angular power spectrum of B-modes due to the vector and tensor perturbations of SOSF, modeled in the large-N limit of a spontaneous broken global O(N) symmetry. We conclude that the low-$\ell$ multipoles detected by BICEP2 cannot be due mainly to SOSF, since they have the wrong spectrum at low multipoles. As a byproduct we derive the first cosmological constraints on this model, showing that the BICEP2 B-mode polarization data admits at most a 2-3% contribution from SOSF in the temperature anisotropies, similar to (but somewhat tighter than) the recently studied case of cosmic strings., 14 pages, 5 figures

We investigate the anisotropies in the gravitational wave (GW) background produced at preheating after inflation. Using lattice field theory simulations of a massless preheating model, we show that the GW amplitude depends sensitively on the value of the decay product field chi coupled to the inflaton phi, with the only requisite that chi is light during inflation. We find a strong anisotropy in the amplitude of the GW background on large angular scales, the details of which strongly depend on the reheating dynamics. We expect similar conclusions for a wide class of inflationary models with light scalar fields. If future direct detection GW experiments are capable of detecting the GW produced by preheating, they should also be able to detect this effect. This could eventually provide a powerful way to distinguish between different inflationary and preheating scenarios., 5 pages, 3 figures

Preheating and other particle production phenomena in the early Universe can give rise to high- energy out-of-equilibrium fermions with an anisotropic stress. We develop a formalism to calculate the spectrum of gravitational waves due to fermions, and apply it to a variety of scenarios after inflation. We pay particular attention to regularization issues. We show that fermion production sources a stochastic background of gravitational waves with a significant amplitude, but we find that typical frequencies of this new background are not within the presently accessible direct detec- tion range. However, small-coupling scenarios might still produce a signal observable by planned detectors, and thus open a new window into the physics of the very early Universe., Comment: 4 pages, 1 figure, submitted to PRL

We investigate in detail a model where the curvaton is coupled to the Standard Model higgs. Parametric resonance might be expected to cause a fast decay of the curvaton, so that it would not have time to build up the curvature perturbation. However, we show that this is not the case, and that the resonant decay of the curvaton may be delayed even down to electroweak symmetry breaking. This delay is due to the coupling of the higgs to the thermal background, which is formed by the Standard Model degrees of freedom created from the inflaton decay. We establish the occurrence of the delay by considering the curvaton evolution and the structure of the higgs resonances. We then provide analytical expressions for the delay time, and for the subsequent resonant production of the higgs, which ultimately leads to the curvaton effective decay width. Contrary to expectations, it is possible to obtain the observed curvature perturbation for values of the curvaton-higgs coupling as large as 0.1. Our calculations also apply in the general case of curvaton decay into any non Standard Model species coupled to the thermal background., Comment: 39 pages, 2 figures. v2 matches published version (one reference added)

We demonstrate that any scaling source in the radiation era produces a background of gravitational waves with an exact scale-invariant power spectrum. Cosmic defects, created after a phase transition in the early Universe, are such a scaling source. We emphasise that the result is independent of the topology of the cosmic defects, the order of phase transition, and the nature of the symmetry broken, global or gauged. As an example, using large-scale numerical simulations, we calculate the scale invariant gravitational wave power spectrum generated by the dynamics of a global O(N) scalar theory. The result approaches the large N theoretical prediction as N^(-2), albeit with a large coefficient. The signal from global cosmic strings is O(100) times larger than the large N prediction., Comment: 5 pages, 2 figures; minor changes, matches version to be published in PRL

We compute the matter bispectrum in the presence of primordial local non-Gaussianity over a wide range of scales, including the very small nonlinear ones. We use the Halo Model approach, considering non-Gaussian corrections to the halo profiles, the halo mass function and the bias functions. We compare our results in the linear and mildly nonlinear scales to a large ensemble of Gaussian and non-Gaussian numerical simulations. We consider both squeezed and equilateral configurations, at redshift z = 0 and z = 1. For z = 0, the deviations between the Halo Model and the simulations are smaller than 10% in the squeezed limit, both in the Gaussian and non-Gaussian cases. The Halo Model allows to make predictions on scales much smaller than those reached by numerical simulations. For local non-Gaussian initial conditions with a parameter fNL = 100, we find an enhancement of the bispectrum in the squeezed configuration k = k3 = k2 >> k1 \sim 0.01 h^{-1} Mpc, of \sim 15% and \sim 25% on scales k \sim 1 h^{-1} Mpc, at z = 0 and z = 1 respectively. This is mainly due to the non-Gaussian corrections in the linear bias. Finally we provide a very simple expression valid for any scenario, i.e. for any choice of the halo profile, mass and bias functions, which allow for a fast evaluation of the bispectrum on squeezed configurations., 34 pages, 10 figures, Submitted to JCAP

We consider a set of scalar fields, consisting of a single flat direction and one or several non-flat directions. We take our cue from the MSSM, considering separately D-flat and F-flat directions, but our results apply to any supersymmetric scenario containing flat directions. We study the field fluctuations during pure de Sitter Inflation, following the evolution of the infrared modes by numerically solving the appropriate Langevin equations. We demonstrate that for the Standard Model U(1), SU(2) or SU(3) gauge couplings, as well as for large enough Yukawa couplings, the fluctuations along the non-flat directions effectively block the fluctuations along the flat directions. The usual expected behaviour \propto N, with N the number of efolds, may be strongly violated, depending on the coupling strengths. As a consequence, those cosmological considerations, which are derived assuming that during inflation flat directions fluctuate freely, should be revised., Comment: 19 pages, 5 figures, Submitted to JCAP

It has recently been pointed out that the usual procedure employed in order to obtain the transverse-traceless (TT) part of metric perturbations in lattice simulations was inconsistent with the fact that those fields live in the lattice and not in the continuum. It was claimed that this could lead to a larger amplitude and a wrong shape for the gravitational wave (GW) spectra obtained in numerical simulations of (p)reheating. In order to address this issue, we have defined a consistent prescription in the lattice for extracting the TT part of the metric perturbations. We demonstrate explicitly that the GW spectra obtained with the old continuum-based TT projection only differ marginally in amplitude and shape with respect to the new lattice-based ones. We conclude that one can therefore trust the predictions appearing in the literature on the spectra of GW produced during (p)reheating and similar scenarios simulated on a lattice., Comment: 22 pages, 8 figures, Submitted to JCAP

The Universe may harbor relics of the post-inflationary epoch in the form of a network of self-ordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and provide a simple approximation that may be useful for data analysis. The bispectrum is largest for triangles that are aligned (have edges $k_1\simeq 2 k_2 \simeq 2 k_3$) as opposed to the local-model bispectrum, which peaks for squeezed triangles ($k_1\simeq k_2 \gg k_3$), and the equilateral bispectrum, which peaks at $k_1\simeq k_2 \simeq k_3$. We estimate that this non-Gaussianity should be detectable by the Planck satellite if the contribution from self-ordering scalar fields to primordial perturbations is near the current upper limit., 11 pages, 1 figure

We present a new and especially powerful signature of cosmic strings and other topological or non-topological defects in the polarization of the cosmic microwave background (CMB). We show that even if defects contribute 1% or less in the CMB temperature anisotropy spectrum, their signature in the local $\tilde{B}$-polarization correlation function at angular scales of tens of arc minutes is much larger than that due to gravitational waves from inflation, even if the latter contribute with a ratio as big as $r\simeq 0.1$ to the temperature anisotropies. We show that when going from non-local to local $\tilde{B}$-polarization, the ratio of the defect signal-to-noise with respect to the inflationary value increases by about an order of magnitude. Proposed B-polarization experiments, with a good sensitivity on arcminute scales, may either detect a contribution from topological defects produced after inflation or place stringent limits on them. Even Planck should be able to improve present constraints on defect models by at least an order of magnitude, to the level of $\ep, Version Published in Physics Letters B

Primordial gravitational waves provide a very important stochastic background that could be detected soon with interferometric gravitational wave antennas or indirectly via the induced patterns in the polarization anisotropies of the cosmic microwave background. The detection of these waves will open a new window into the early Universe, and therefore it is important to characterize in detail all possible sources of primordial gravitational waves. In this paper we develop theoretical and numerical methods to study the production of gravitational waves from out-of-equilibrium gauge fields at preheating. We then consider models of preheating after hybrid inflation, where the symmetry breaking field is charged under a local U(1) symmetry. We analyze in detail the dynamics of the system in both momentum and configuration space, and show that gauge fields leave specific imprints in the resulting gravitational wave spectra, mainly through the appearence of new peaks at characteristic frequencies that are related to the mass scales in the problem. We also show how these new features in the spectra correlate with string-like spatial configurations in both the Higgs and gauge fields that arise due to the appearance of topological winding numbers of the Higgs around Nielsen-Olesen strings. We study in detail the time evolution of the spectrum of gauge fields and gravitational waves as these strings evolve and decay before entering a turbulent regime where the gravitational wave energy density saturates., This paper is dedicated to the memory of Lev Kofman. Added references and comments in Sec. III.B. Version accepted in PRD

21 pages, 2 figures.-- Full-text version available Open Access at the journal site., Gravitational waves were copiously produced in the early Universe whenever the processes taking place were sufficiently violent. The spectra of several of these gravitational wave backgrounds on subhorizon scales have been extensively studied in the literature. In this paper we analyze the shape and amplitude of the gravitational wave spectrum on scales which are superhorizon at the time of production. Such gravitational waves are expected from the self ordering of randomly oriented scalar fields which can be present during a thermal phase transition or during preheating after hybrid inflation. We find that, if the gravitational wave source acts only during a small fraction of the Hubble time, the gravitational wave spectrum at frequencies lower than the expansion rate at the time of production behaves as Ω(GW)(f) α f^3 with an amplitude much too small to be observable by gravitational wave observatories like LIGO, LISA or BBO. On the other hand, if the source is active for a much longer time, until a given mode which is initially superhorizon (kη* << 1), enters the horizon, for kη >~ 1, we find that the gravitational wave energy density is frequency independent, i.e. scale invariant. Moreover, its amplitude for a GUT scale scenario turns out to be within the range and sensitivity of BBO and marginally detectable by LIGO and LISA. This new gravitational wave background can compete with the one generated during inflation, and distinguishing both may require extra information., DGF also acknowledges support from a FPU-Fellowship from the Spanish M.E.C., with ref. AP-2005-1092. This work is supported by the Swiss National Science Foundation. We also acknowledge financial support from the Madrid Regional Government (CAM) under the program HEP-HACOS P-ESP-00346, and the Spanish Science Research Ministry (MEC) under contract FPA2006-05807. DGF and JGB participate in the Consolider-Ingenio 2010 PAU (CSD2007-00060), as well as in the European Union Marie Curie Network "UniverseNet" under contract MRTN-CT-2006-035863.

We discuss the cosmological degeneracy between the Hubble parameter H(z), the age of the universe and cosmological parameters describing simple variations from the minimal LCDM model. We show that independent determinations of the Hubble parameter H(z) such as those recently provided by Simon et al., Phys. Rev. D 71 (2005) 123001, combined with Cosmic Microwave Background data, can provide stringent constraints on possible deviations from the LCDM model. In particular we find that this data combination constrains at the 68% (95%) confidence level the following parameters: sum of the neutrino masses < 0.5 (1.0) eV, number of relativistic neutrino species N_rel = 4.1^{+0.4}_{-0.9} (^{+1.1}_{-1.5}), dark energy equation of state parameter w = -0.95 +- 0.17 (+- 0.32), and curvature \Omega_k = 0.002 +- 0.006 (+- 0.014), in excellent agreement with dataset combinations involving Cosmic Microwave Background, Supernovae and Baryon Acoustic Oscillations. This offers a valuable consistency check for systematic errors., Comment: 10 pages, 7 figures. Added references. Minor changes added to match accepted version in JCAP

Out-of-equilibrium fermions can be created in the early Universe by non-perturbative parametric effects, both at preheating or during the thermal era. An anisotropic stress is developed in the fermion distribution, acting as a source of a stochastic background of gravitational waves (GW). We derive a general formalism to calculate the spectrum of GW produced by an ensemble of fermions, which we apply to a variety of scenarios after inflation. We discuss in detail the regularization of the source, i.e. of the unequal-time-correlator of the fermions' transverse-traceless anisotropic stress. We discuss how the GW spectrum builds up in time and present a simple parametrization of its final amplitude and peak frequency. We find that fermions may generate a GW background with a significant amplitude at very high frequencies, similarly to the case of preheating with scalar fields. A detection of this GW background would shed light about the physics of the very early Universe, but new technology at high frequencies is required, beyond the range accessible to currently planned detectors., Comment: 62 pages, 7 figures (updated to match published version in JHEP)

We discuss the non-conservation of fermion number (or chirality breaking, depending on the fermionic charge assignment) in Abelian gauge theories at finite temperature. We study different mechanisms of fermionic charge disappearance in the high temperature plasma, using both analytical estimates and real-time classical lattice numerical simulations. We investigate the random walk of the Chern-Simons number $Q \propto \int d^4x F_{\mu\nu}{\tilde F}^{\mu\nu}$, and show that it has a diffusive behaviour in the presence of an external magnetic field $B$. This indicates that the mechanism for fermionic number non-conservation for $B \neq 0$, is due to fluctuations of the gauge fields, similarly as in the case of non-Abelian gauge theories. We determine numerically, with lattice simulations, the rate $\Gamma$ of chirality non-conservation associated with this diffusion. We find the rate to be a factor $\mathcal{O}(10)$ larger compared to previous theoretical estimates, what calls for a revision of the implications of Abelian fermion number and chirality non-conservation for baryogenesis, magnetogenesis and chiral symmetry evolution. An erratum can be found at the end of the manuscript, following the results obtained in JHEP 10 (2019) 142 (1904.11892 [hep-th]), which reduce our original claim in the discrepancy between theory and numerics by a factor $\sim 5-6$., Comment: Version matching publication, former Section V on 'Dynamics of chiral charge' removed, and erratum appended at the end in light of the results obtained in 1904.11892 [hep-th]

We study fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. We consider the presence of a chemical potential $\mu$ for the fermionic charge, and monitor its evolution with real-time classical lattice simulations. This method accounts for short-scale fluctuations not included in the usual effective magneto-hydrodynamics (MHD) treatment. We observe a self-similar decay of the chemical potential, accompanied by an inverse cascade process in the gauge field that leads to a production of long-range helical magnetic fields. We also study the chiral charge dynamics in the presence of an external magnetic field $B$, and extract its decay rate $\Gamma_5 \equiv -{d\log \mu\over dt}$. We provide in this way a new determination of the gauge coupling and magnetic field dependence of the chiral rate, which exhibits a best fit scaling as $\Gamma_5 \propto e^{11/2}B^2$. We confirm numerically the fluctuation-dissipation relation between $\Gamma_5$ and $\Gamma_{\rm diff}$, the Chern-Simons diffusion rate, which was obtained in a previous study. Remarkably, even though we are outside the MHD range of validity, the dynamics observed are in qualitative agreement with MHD predictions. The magnitude of the chiral/diffusion rate is however a factor $\sim 10$ times larger than expected in MHD, signaling that we are in reality exploring a different regime accounting for short scale fluctuations. This discrepancy calls for a revision of the implications of fermion number and chirality non-conservation in finite temperature Abelian gauge theories, though not definite conclusion can be made at this point until hard-thermal-loops (HTL) are included in the lattice simulations., Comment: 32 pages, 11 figures. V2: Improved introduction, added some discussions and references. Corrected typos. Corresponds to published version

We present a lattice formulation of an interaction ${\phi\over\Lambda} F\tilde F$ between an axion and some $U(1)$ gauge sector with the following properties: it reproduces the continuum theory up to $\mathcal{O}(dx_\mu^2)$ corrections, it preserves exact gauge invariance and shift symmetry on the lattice, and it is suitable for self-consistent expansion of the Universe. The lattice equations of motion can no longer be solved by explicit methods, but we propose an implicit method to overcome this difficulty, which preserves the relevant system constraints down to arbitrary (tunable) precision. As a first application we study, in a comoving grid in $(3+1)$ dimensions, the last efolds of axion-inflation with quadratic potential and the preheating stage following afterwards. We fully account for the inhomogeneity and non-linearity of the system, including the gauge field contribution to the expansion rate of the Universe and its backreaction into the axion dynamics. We characterize in detail, as a function of the coupling, the energy transfer from the axion to the gauge field. Two coupling regimes are identified, sub- and super-critical, depending on whether the final energy fraction stored in the gauge field is below or above $\sim 50\%$ of the total energy. The Universe is very efficiently reheated for super-critical couplings, rapidly entering in a radiation dominated stage. Our results on preheating confirm previously published results., Comment: 33 pages, 14 figures

The expansion history of the Universe between the end of inflation and the onset of radiation-domination (RD) is currently unknown. If the equation of state during this period is stiffer than that of radiation, $w > 1/3$, the gravitational wave (GW) background from inflation acquires a blue-tilt ${d\log��_{\rm GW}\over d\log f} = {2(w-1/3)\over (w+1/3)} > 0$ at frequencies $f \gg f_{\rm RD}$ corresponding to modes re-entering the horizon during the stiff-domination (SD), where $f_{\rm RD}$ is the frequency today of the horizon scale at the SD-to-RD transition. We characterized in detail the transfer function of the GW energy density spectrum, considering both 'instant' and smooth modelings of the SD-to-RD transition. The shape of the spectrum is controlled by $w$, $f_{\rm RD}$, and $H_{\rm inf}$ (the Hubble scale of inflation). We determined the parameter space compatible with a detection of this signal by LIGO and LISA, including possible changes in the number of relativistic degrees of freedom, and the presence of a tensor tilt. Consistency with upper bounds on stochastic GW backgrounds, however, rules out a significant fraction of the observable parameter space. We find that this renders the signal unobservable by Advanced LIGO, in all cases. The GW background remains detectable by LISA, though only in a small island of parameter space, corresponding to scenarios with an equation of state in the range $0.46 \lesssim w \lesssim 0.56$ and a high inflationary scale $H_{\rm inf} \gtrsim 10^{13}~{\rm GeV}$, but low reheating temperature $1~{\rm MeV} \lesssim T_{\rm RD} \lesssim 150~{\rm MeV}$ (equivalently, $10^{-11}~{\rm Hz} \lesssim f_{\rm RD} \lesssim 3.6\cdot10^{-9}~{\rm Hz}$). Implications for early Universe scenarios resting upon an SD epoch are briefly discussed., Matching published version in JCAP, 32 pages, 8 figures