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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 an explicit non-compact lattice formulation of the interaction between a shift -symmetric field and some U ( 1 ) gauge sector, a ( x ) F μ ν F ˜ μ ν , reproducing the continuum limit to order O ( d x μ 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 topological number density K = F μ ν F ˜ μ ν that admits a lattice total derivative representation K = Δ μ + K μ , reproducing to order O ( d x μ 2 ) the continuum expression K = ∂ μ K μ ∝ E → ⋅ 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 ( x → , t ) is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an O ( d x μ 2 ) accuracy). We discuss an iterative scheme allowing to overcome this difficulty. [ABSTRACT FROM AUTHOR]

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 ≃ + 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 ξ ≳ 1 , with a reheating temperature of T RH ≳ O ( 10 10 ) ξ 3 / 2 ( H ⁎ / 10 14 GeV ) 2 GeV . [ABSTRACT FROM AUTHOR]

We investigate the anisotropics 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 x coupled to the inflaton s 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. [ABSTRACT FROM AUTHOR]

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 emphasize 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 0(100) times larger than the large N prediction. [ABSTRACT FROM AUTHOR]

We consider quantum diffusion in ultraslow-roll (USR) inflation. Using the ΔN formalism, we present the first stochastic calculation of the probability distribution P(R) of the curvature perturbation during USR. We capture the nonlinearity 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(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 of ~105 compared with the Gaussian approximation. [ABSTRACT FROM AUTHOR]

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 (ϕ) ∝ | ϕ | p around the origin. As a proxy for (p)reheating, we include a quadratic interaction g 2 ϕ 2 X 2 between the inflaton ϕ 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 ; i i) the final transfer of energy is always negligible for 2 ≤ p < 4 , and of order ∼ 50 % for p ≥ 4 ; i i i) 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. [ABSTRACT FROM AUTHOR]

To confront the numerical results of Γdiff with the analytical results from section 2.3, we originally considered the theoretical prediction for the diffusion rate given by eq. (2.17), which we re-wrote in eq. (4.25). [ABSTRACT FROM AUTHOR]

We study fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. We consider the presence of a chemical potential μ for the fermionic charge, and monitor its evolution with real-time classical lattice simula- tions. 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 chemi- cal 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 Γ 5 ≡ d log μ dt . We provide in this way a new determination of the gauge coupling and magnetic field de- pendence of the chiral rate, which exhibits a best fit scaling as Γ 5 ∝ 11 2 B 2 . We confirm numerically the fluctuation-dissipation relation between Γ5 and Γdiff , 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 ∼ 10 times larger than expected in MHD, signaling that we are in reality exploring a dif- ferent regime accounting for short scale fluctuations. This discrepancy calls for a revision of the implications of fermion number and chirality non-conservation in finite tempera- ture Abelian gauge theories, though no definite conclusion can be made at this point until hard-thermal-loops are included in the lattice simulations. [ABSTRACT FROM AUTHOR]

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∝∫d4xFμνF˜μν, 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 ≠ 0, is due to fluctuations of the gauge fields, similarly as in the case of non-Abelian gauge theories. We have determined numerically, with lattice simulations, the rate Γ of chirality non-conservation, extracting it from the diffusion process. We find that it is a factor ∼ 60 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. [ABSTRACT FROM AUTHOR]

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 that 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. [ABSTRACT FROM AUTHOR]

Abstract: 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 -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 to the temperature anisotropies. We show that when going from non-local to local -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 arc-minute scales, may either detect a contribution from topological defects produced after inflation or place stringent limits on them. Already Planck should be able to improve present constraints on defect models by about an order of magnitude, to the level of . A future full-sky experiment like CMBpol, with polarization sensitivities of the order of 1 μK arcmin, will be able to constrain the defect parameter ϵ to less than a few×10−9, depending on the defect model. [Copyright &y& Elsevier]