Single-field Inflation Research Articles

Inflationary non-Gaussianities in alpha vacua and consistency with conformal symmetries

We study the conformal invariance of inflationary non-Gaussianities associated with scalar fluctuations in a non-Bunch-Davies initial state, known as the α-vacuum, in single-field slow-roll inflation. The α-vacuum is a one-parameter family of states, including the Bunch-Davies one, that preserves the conformal symmetry of inflationary dynamics in a nearly de-Sitter space-time. Working within the leading slow-roll approximation, we compute the four-point scalar correlator (the trispectrum) in α-vacuum using the in-in formalism. We check that the conformal Ward identities are met between the three and four-point scalar α-vacua correlators. Surprisingly, this contrasts the previously reported negative result of the Ward identities being violated between the two and the three-point correlators. We have also extended the wave-functional method, previously used for correlators with Bunch-Davies initial condition, to compute the three and four-point scalar correlators in α-vacua. The results obtained from the wave-function method match the corresponding in-in results, adding further justification to our check of Ward identities with α-vacua correlators.

Inflationary Butterfly Effect: Nonperturbative Dynamics from Small-Scale Features.

For the first time, we investigate the nonperturbative dynamics of single field inflation with a departure from slow roll. Using simulations, we find that oscillatory features in the potential can drastically alter the course of inflation, with major phenomenological implications. In certain cases, the entire Universe gets trapped in a forever inflating de Sitter state. In others, only some regions get stuck in a false vacuum, offering an alternative channel for primordial black hole formation. Analogous to the flap of a butterfly, these results show that small-scale phenomena can have profound consequences on the evolution of the entire Universe. More generally, our work shows the power of simulations in the exploration of the small-scale physics of inflation, particularly in the regime relevant for gravitational-wave astronomy.

Comparing sharp and smooth transitions of the second slow-roll parameter in single-field inflation

In single-field inflation, violation of the slow-roll approximation can lead to growth of curvature perturbation outside the horizon. This violation is characterized by a period with a large negative value of the second slow-roll parameter. At an early time, inflation must satisfy the slow-roll approximation, so the large-scale curvature perturbation can explain the cosmic microwave background fluctuations. At intermediate time, it is viable to have a theory that violates the slow-roll approximation, which implies amplification of the curvature perturbation on small scales. Specifically, we consider ultraslow-roll inflation as the intermediate period. At late time, inflation should go back to the slow roll period so that it can end. This means that there are two transitions of the second slow-roll parameter. In this paper, we compare two different possibilities for the second transition: sharp and smooth transitions. Focusing on effects generated by the relevant cubic self-interaction of the curvature perturbation, we find that the bispectrum and one-loop correction to the power spectrum due to the change of the second slow-roll parameter vanish if and only if theMukhanov-Sasaki equation for perturbation satisfies a specific condition called Wands duality.We also find in the case of sharp transition that, even though this duality is satisfied in the ultraslow-roll and slow-roll phases, it is severely violated at the transition so that the resultant one-loop correction is extremely large inversely proportional to the duration of the transition.

Reconstructing inflationary potential from NANOGrav 15-year Data: A robust study using Non-Bunch Davies initial condition

We discuss the theoretical framework behind reconstruction of a generic class of inflationary potentials for canonical single-field slow-roll inflation in a model-independent fashion. The Non-Bunch Davies (NBD) initial condition is an essential choice to determine the structure of potential and to accommodate the blue-tilted tensor power spectrum feature recently observed in NANOGrav. Using the reconstruction technique we found the favoured parameter space which supports blue tilted tensor power spectrum. The validity of the EFT prescription in inflation is also maintained through the use of a new field excursion formula while keeping the necessary and sufficient conditions on the sub-Planckian field values in check. We find that the reconstructed potential display inflection point behaviour, which has deeper connection with high energy physics.

Vanilla inflation predicts negative running

We show that the simplest, and currently favoured, theoretical realizations of cosmic inflation yield a sharp prediction for the running of the spectral index . Using latest cosmological data, we compute its marginalized posterior probability distribution over the space of nearly 300 models of single-field slow-roll inflation. The most probable value is , lying within the credible interval . Within the landscape of all the proposed slow-roll inflationary models, positive values for the running are therefore disfavoured at more than three-sigma.

Simulating the Universe from the cosmological horizon to halo scales

Ultra-large scales close to the cosmological horizon will be probed by the upcoming observational campaigns. They hold the promise to constrain single-field inflation as well as general relativity, but in order to include them in the forthcoming analyses, their modelling has to be robust. In particular, general relativistic effects may be mistaken for primordial signals, and no consensus has emerged either from analytical modelling nor from the numerical route, obstructed by the large dynamical range to be simulated. In this work, we present a numerical technique to overcome the latter limitation: we compute the general relativistic displacement field with the N-body relativistic code gevolution and combine it with the accurate Newtonian simulation Gadget-4. This combination leads to an effective simulation reproducing the desired behaviour at the level of the matter power spectrum and bispectrum. We then measure, for the first time in a simulation, the relativistic scale-dependent bias in Poisson gauge; at redshift z = 0, we find b 1 GR = -8.1 ± 2.8. Our results at the field level are only valid in the Poisson gauge and need to be complemented with a relativistic ray tracing algorithm to compute the number count observable.

Superhorizon Curvature Perturbations Are Protected against One-Loop Corrections.

We examine one-loop corrections from small-scale curvature perturbations to the superhorizon-limit ones in single-field inflation models, which have recently caused controversy. We consider the case where the Universe experiences transitions of slow-roll (SR)→intermediate period→SR. The intermediate period can be an ultra-slow-roll period or a resonant amplification period, either of which enhances small-scale curvature perturbations. We assume that the superhorizon curvature perturbations are conserved at least during each of the SR periods. Within this framework, we show that the superhorizon curvature perturbations during the first and the second SR periods coincide at one-loop level in the slow-roll limit.

Full-shape analysis with simulation-based priors: Constraints on single field inflation from BOSS

Full-shape analysis with simulation-based priors: Constraints on single field inflation from BOSS

A Goldstone boson equivalence for inflation

The effective field theory of single-field inflation characterizes the inflationary epoch in terms of a pattern of symmetry breaking. An operator acquires a time-dependent vacuum expectation value, defining a preferred spatial slicing. In the absence of dynamical gravity, the fluctuations around the time-dependent background are described by the Goldstone boson associated with this symmetry breaking process. With gravity, the Goldstone is eaten by the metric, becoming the scalar metric fluctuation. In this paper, we will show that in general single-field inflation, the statistics of scalar metric fluctuations are given by the statistics of this Goldstone boson decoupled from gravity up to corrections that are controlled as an expansion in slow-roll parameters. This even holds in the presence of additional parameters, like the speed of sound, that naively enhance the impact of the gravitational terms. In the process, we derive expressions for leading and sub-leading gravitational corrections to all-orders in the Goldstone boson.

No-go for the formation of heavy mass Primordial Black Holes in Single Field Inflation

We examine the possibility of Primordial Black Holes (PBHs) formation in single field models of inflation. Using the adiabatic or wave function renormalization scheme in the short range modes, we show that one-loop correction to the power spectrum is free from quadratic UV divergence. We consider a framework in which PBHs are produced during the transition from Slow Roll (SR) to Ultra Slow Roll (USR) followed by the end of inflation. We demonstrate that the renormalized power spectrum soften the contribution of the logarithmic IR divergence and severely restricts the possible mass range of produced PBHs in the said transition, namely, MPBH∼102g\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_\ extrm{PBH}\\sim 10^{2}\\,\ extrm{g}$$\\end{document}a^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{\ extrm{a}}$$\\end{document}la a no-go theorem. In particular, we find that the produced PBHs are short lived (tPBHevap∼10-20s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t^\ extrm{evap}_\ extrm{PBH}\\sim 10^{-20}\\,\ extrm{s}$$\\end{document}) and the corresponding number of e-folds in the USR region is restricted to ΔNUSR≈2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta {\\mathcal {N}}_\ extrm{USR}\\approx 2$$\\end{document}.

Large fluctuations in the sky

Renormalization of quantum loop effects generated from large fluctuations is a hugely debatable topic of research these days which rules out the Primordial Black Hole (PBH) formation within the framework of single-field inflation. In this paper, we briefly discuss that the correct implementation of regularization, renormalization, and resummation techniques in a setup described by an ultra-slow-roll phase sandwiched between two slow-roll phases in the presence of smooth or sharp transitions can lead to a stringent constraint on the PBH mass (i.e. [Formula: see text]), which we advertise as a new No-go theorem. Finally, we will give some of the possible way-outs using which one can evade this proposed No-go theorem and produce solar/sub-solar mass PBHs.

Minimizing the tensor-to-scalar ratio in single-field inflation models

We revisit a class of simple single-field inflation models and demonstrate that they can readily produce a negligible tensor/scalar ratio r. Motivated by recent work suggesting the need to introduce higher order operators to stabilize unregulated potentials, as well as by work indicating that such terms can have significant effects on observable predictions, we explicitly construct corrected versions of the quadratic hilltop potential that are motivated by an effective field theory expansion. We employ Markov Chain Monte Carlo methods and optimization techniques to sample viable models and minimize r. We find that such potentials can readily lower r values below projected CMB-S4 sensitivity, while still remaining within observable constraints on ns. Furthermore, we find that the minimum r reached for each order of the expansion considered is well described by a power law rmin(q)∝q−B before asymptoting to a value of rmin∼10−11, where q is the order to which the expansion of V(ϕ) is carried out. Published by the American Physical Society 2024

No time to derive: unraveling total time derivatives in in-in perturbation theory

The in-in formalism provides a way to systematically organize the calculation of primordial correlation functions. Although its theoretical foundations are now firmly settled, the treatment of total time derivative interactions, incorrectly trivialized as “boundary terms”, has been the subject of intense discussions and conceptual mistakes. In this work, we demystify the use of total time derivatives — as well as terms proportional to the linear equations of motion — and show that they can lead to artificially large contributions cancelling at different orders of the in-in operator formalism. We discuss the treatment of total time derivative interactions in the Lagrangian path integral formulation of the in-in perturbation theory, and we showcase the importance of interaction terms proportional to linear equations of motion. We then provide a new route to the calculation of primordial correlation functions, which avoids the generation of total time derivatives, by working directly at the level of the full Hamiltonian in terms of phase-space variables. Instead of integrating by parts, we perform canonical transformations to simplify interactions. We explain how to retrieve correlation functions of the initial phase-space variables from the knowledge of the ones after canonical transformations. As an important first application, we find the explicit sizes of Hamiltonian cubic interactions in single-field inflation with canonical kinetic terms and for any background evolution, straight in terms of the primordial curvature perturbation and its canonical conjugate momentum, as well as the corresponding ones in the tensor sector, and the ones mixing scalars and tensors. We also briefly comment on quartic interactions. Our results are important for performing complete calculations of exchange diagrams in inflation, such as the (scalar and tensor) exchange trispectrum and the one-loop power spectrum. Being already written in a form amenable to characterize quantum properties of primordial fluctuations, they also promise to shed light on the non-linear dynamics of quantum states during inflation.

Evading no-go for PBH formation and production of SIGWs using Multiple Sharp Transitions in EFT of single field inflation

Deploying multiple sharp transitions (MSTs) under a unified framework, we investigate the formation of Primordial Black Holes (PBHs) and the production of Scalar Induced Gravitational Waves (SIGWs) by incorporating one-loop corrected renormalized-resummed scalar power spectrum. With effective sound speed parameter, 1⩽cs⩽1.17, the direct consequence is the generation of PBH masses spanning MPBH∼O(10−31M⊙−104M⊙), thus evading well known No-go theorem on PBH mass. Our results align coherently with the extensive NANOGrav 15-year data and the sensitivities outlined by other terrestrial and space-based experiments (e.g.: LISA, HLVK, BBO, HLV(O3), etc.).

Inflationary initial conditions for the cosmological gravitational wave background

The initial conditions on the anisotropies of the stochastic gravitational-wave background of cosmological origin (CGWB) largely depend on the mechanism that generates the gravitational waves. Since the CGWB is expected to be non-thermal, the computation of the initial conditions could be more challenging w.r.t. the Cosmic Microwave Background (CMB), whose interactions with other particles in the early Universe lead to a blackbody spectrum. In this paper, we show that the initial conditions for the cosmological background generated by quantum fluctuations of the metric during inflation deviate from adiabaticity. These primordial gravitational waves are indeed generated by quantum fluctuations of two independent degrees of freedom (the two polarization states of the gravitons). Furthermore, the CGWB plays a negligible role in the Einstein's equations, because its energy density is subdominant w.r.t. ordinary matter. Therefore, the only possible way to compute the initial conditions for inflationary gravitons is to perturb the energy-momentum tensor of the gravitational field defined in term of the small-scale tensor perturbation of the metric. This new and self-consistent approach shows that a large, non-adiabatic initial condition is present even during the single-field inflation. Such a contribution enhances the total angular power spectrum of the CGWB compared to the standard adiabatic case, increasing also the sensitivity of the anisotropies to the presence of relativistic and decoupled particles in the early Universe. In this work we have also proved that our findings are quite general and apply to both single-field inflation and other scenarios in which the CGWB is generated by the quantum fluctuations of the metric, like the curvaton.

Cosmic Inflation at the crossroads

The capability of Cosmic Inflation to explain the latest Cosmic Microwave Background and Baryonic Acoustic Oscillation data is assessed by performing Bayesian model comparison within the landscape of nearly three-hundred models of single-field slow-roll inflation. We present the first Bayesian data analysis based on the third-order slow-roll primordial power spectra. In particular, the fourth Hubble-flow function ε4 remains unbounded while the third function verifies, at two-sigma, ε3 ∈[-0.4,0.5], which is perfectly compatible with the slow-roll predictions for the running of the spectral index. We also observe some residual excess of B-modes within the BICEP/Keck data favoring, at a non-statistically significant level, non-vanishing primordial tensor modes: log(ε1) > -3.9, at 68% confidence level. Then, for 287 models of single-field inflation, we compute the Bayesian evidence, the Bayesian dimensionality and the marginalized posteriors of all the models' parameters, including the ones associated with the reheating era. The average information gain on the reheating parameter R reh reaches 1.3 ± 0.18 bits, which is more than a factor two improvement compared to the first Planck data release. As such, inflationary model predictions cannot meet data accuracy without specifying, or marginalizing over, the reheating kinematics. We also find that more than 40% of the scenarios are now strongly disfavored, which shows that the constraining power of cosmological data is winning against the increase of the number of proposed models. In addition, about 20% of all models have evidences within the most probable region and are all favored according to the Jeffreys' scale of Bayesian evidences.

Realisation of the ultra-slow roll phase in Galileon inflation andPBH overproduction

We demonstrate the explicit realisation of the ultra-slow roll phase in the framework of the effective field theory of single-field Galileon inflation. The pulsar timing array (PTA) collaboration hints at the scalar-induced gravity waves (SIGW) from the early universe as an explanation for the origin of the observed signal, which, however, leads to an enhancement in the amplitude of the scalar power spectrum giving rise to the overproduction of primordial black holes (PBHs). In the setup under consideration, we examine the generation of SIGW consistent with PTA (NANOGrav15 and EPTA) data, in addition to which we also consider the impact from QCD crossover at the nHz frequencies and address the PBH overproduction issue assuming linear approximations for the over-density without incorporating non-Gaussian effects from the comoving curvature perturbation. The framework is shown to give rise to SIGWs well consistent with the PTA signal with comfortable PBH abundance, 10-3 ≲ fPBH < 1, of near solar-mass black holes.

Improving constraints on inflation with CMB delensing

The delensing of cosmic microwave background (CMB) maps will be increasingly valuable for extracting as much information as possible from future CMB surveys. Delensing provides many general benefits, including sharpening of the acoustic peaks, more accurate recovery of the damping tail, and reduction of lensing-induced B-mode power. In this paper we present several applications of delensing focused on testing theories of early-universe inflation with observations of the CMB. We find that delensing the CMB results in improved parameter constraints for reconstructing the spectrum of primordial curvature fluctuations, probing oscillatory features in the primordial curvature spectrum, measuring the spatial curvature of the universe, and constraining several different models of isocurvature perturbations. In some cases we find that delensing can recover almost all of the constraining power contained in unlensed spectra, and it will be a particularly valuable analysis technique to achieve further improvements in constraints for model parameters whose measurements are not expected to improve significantly when utilizing only lensed CMB maps from next-generation CMB surveys. We also quantify the prospects of testing the single-field inflation tensor consistency condition using delensed CMB data; we find it to be out of reach of current and proposed experimental technology and advocate for alternative detection methods.

Constraining Primordial Black Hole Formation from Single-Field Inflation.

The most widely studied formation mechanism of a primordial black hole is collapse of large-amplitude perturbation on small scales generated in single-field inflation. In this Letter, we calculate one-loop correction to the large-scale power spectrum in a model with sharp transition of the second slow-roll parameter. We find that models producing an appreciable amount of primordial black holes induce nonperturbative coupling on a large scale probed by cosmic microwave background radiation. Our result implies that a small-scale power spectrum can be constrained by large-scale cosmological observations.

Note on the bispectrum and one-loop corrections in single-field inflation with primordial black hole formation

Primordial black holes can be formed from the collapse of large-amplitude perturbation on small scales in the early Universe. Such an enhanced spectrum can be realized by introducing a flat region in the potential of single-field inflation, which makes the inflaton go into a temporary ultraslow-roll period. In this paper, we calculate the bispectrum of curvature perturbation in such a scenario. We explicitly confirm that bispectrum satisfies Maldacena’s theorem. At the end of the ultraslow-roll period, the bispectrum is generated by bulk interaction and field redefinition. At the end of inflation, bispectrum is generated only by bulk interaction. We also calculate the one-loop correction to the power spectrum from the bispectrum, called the source method. We find it consistent with the calculation of the one-loop correction from the second-order expansion of in-in perturbation theory. Published by the American Physical Society 2024