We investigate the observational signatures of many-field inflation and present analytic expressions for the spectral index as a function of the prior. For a given prior we employ the central limit theorem and the horizon crossing approximation to derive universal predictions. These include a specific dependence on the prior choice for initial conditions that has not been seen in previous studies. Our main focus is on quadratic inflation, for which the initial conditions statistics decouple from those of the mass distribution, while other monomials are also briefly discussed. We verify the validity of our calculations by comparing to full numerical simulations with 100 fields using the transport method.
Ideas borrowed from renormalization group are applied to warm inflation to characterize the inflationary epoch in terms of flows away from the de Sitter regime. In this framework different models of inflation fall into universality classes. Furthermore, for warm inflation this approach also helps to characterise when inflation can smoothly end into the radiation dominated regime. Warm inflation has a second functional dependence compared to cold inflation due to dissipation, yet despite this feature, it is shown that the universality classes defined for cold inflation can be consistently exten…
Studies of the initial conditions for inflation have conflicting predictions from exponential suppression to inevitability. At the level of phase space, this conflict arises from the competing intuitions of CPT invariance and thermodynamics. After reviewing this conflict, we enlarge the ensemble beyond phase space to include scalar potential data. We show how this leads to an important contribution from inflection point inflation, enhancing the likelihood of inflation to an inverse cubic power law. In the process, we emphasize the attractor dynamics of the gravity-scalar system and the existen…
The values of, and connection between, the cosmological observables of the primordial power spectrum tilt $n_s$ and the inflationary tensor to scalar ratio $r$ are key guideposts to the physics of inflation. Universality classes can be defined for the tilt from the scale free value proportional to $1/N$, where $N$ is the number of e-folds. We examine the consequences of a $\ln N$ next to leading order correction rather than an expansion in $1/N$, or introducing a new parameter. While nominally this can lower $r$ for some too-high $r$ simple inflation models (e.g. large field models), there is …
It has recently been shown that in single field slow-roll inflation the total volume cannot grow by a factor larger than e^(S_dS/2) without becoming infinite. The bound is saturated exactly at the phase transition to eternal inflation where the probability to produce infinite volume becomes non zero. We show that the bound holds sharply also in any space-time dimensions, when arbitrary higher-dimensional operators are included and in the multi-field inflationary case. The relation with the entropy of de Sitter and the universality of the bound strengthen the case for a deeper holographic inter…
We investigate the inflationary implications of extensions of Poincare symmetry. The simplest constructions with local scale invariance lead to universal predictions: the spectral index is $n_s = 1-2/N$, in excellent agreement with Planck data, while the tensor-to-scalar ratio is determined by a free parameter to $r = 12 α/ N^2$. For the special value $α=1$ one finds symmetry enhancement to the full conformal group. We show that these findings hold both for two-derivative scalar-tensor theories as well as higher-derivative gravity. Therefore scale invariance underlies a promising set of inflat…
We show that the cosmological evolution of a scalar field in a potential can be obtained from a renormalisation group equation. The slow roll regime of inflation models is understood in this context as the slow evolution close to a fixed point, described by the methods of renormalisation group. This explains in part the universality observed in the predictions of a certain number of inflation models. We illustrate this behavior on a certain number of examples and discuss it in the context of the AdS/CFT correspondence.
We study the six-field dynamics of D3-brane inflation for a general scalar potential on the conifold, finding simple, universal behavior. We numerically evolve the equations of motion for an ensemble of more than 7 \times 10^7 realizations, drawing the coefficients in the scalar potential from statistical distributions whose detailed properties have demonstrably small effects on our results. When prolonged inflation occurs, it has a characteristic form: the D3-brane initially moves rapidly in the angular directions, spirals down to an inflection point in the potential, and settles into single-…
We investigate all single-field, slow-roll inflationary models whose slow-roll parameters scale as 1/N in the limit of a large number of e-folds N. We proof that all such models belong to two universality classes, characterised by a single parameter. One class contains small field models like hilltop inflation, while the other class consists of large field models like chaotic inflation. We give the leading expressions for the spectral index and tensor-to-scalar ratio r, which are universal for each class, plus subleading corrections for a number of models. This predicts r either to be unobserv…
In this work we propose a statistical approach to handling sources of theoretical uncertainty in string theory models of inflation. By viewing a model of inflation as a probabilistic graph, we show that there is an inevitable information bottleneck between the ultraviolet input of the theory and observables, as a simple consequence of the data processing theorem. This information bottleneck can result in strong hierarchies in the sensitivity of observables to the parameters of the underlying model and hence universal predictions with respect to at least some microphysical considerations. We al…
We develop a new class of chaotic inflation models with spontaneously broken conformal invariance. Observational consequences of a broad class of such models are stable with respect to strong deformations of the scalar potential. This universality is a critical phenomenon near the point of enhanced symmetry, SO(1,1), in case of conformal inflation. It appears because of the exponential stretching of the moduli space and the resulting exponential flattening of scalar potentials upon switching from the Jordan frame to the Einstein frame in this class of models. This result resembles stretching a…
We develop a numerical statistical method to study linear cosmological fluctuations in inflationary scenarios with multiple fields, and apply it to an ensemble of six-field inflection point models in string theory. The latter are concrete microphysical realizations of quasi-single-field inflation, in which scalar masses are of order the Hubble parameter and an adiabatic limit is reached before the end of inflation. We find that slow-roll violations, bending trajectories and 'many-field' effects are commonplace in realizations yielding more than 60 e-folds of inflation, although models in which…
The review of basic cosmological properties of four-dimensional F(R)-gravity, including FRW equations of motion and its accelerating solutions, generalized fluid and scalar-tensor representation of the theory is done. Cosmological reconstruction equation is written and conditions for stability of cosmological solution are discussed. The overview of realistic F(R)-models unifying inflation with dark energy epoch is made. The avoidance of finite-time future singularities in such theories via the introduction of R^2-term is studied. New realistic non-singular F(R)-gravity unifying early-time infl…
Current bounds from the polarization of the CMB predict the scale-invariant gravitational wave (GW) background of inflation to be out of reach for upcoming GW interferometers. This prospect dramatically changes if the inflaton is a pseudoscalar, in which case its generic coupling to any abelian gauge field provides a new source of GWs, directly related to the dynamics of inflation. This opens up new ways of probing the scalar potential responsible for cosmic inflation. Dividing inflation models into universality classes, we analyze the possible observational signatures. One of the most promisi…
We discuss the cosmological evolution of a scalar field with non standard kinetic term in terms of a Renormalization Group Equation (RGE). In this framework inflation corresponds to the slow evolution in a neighborhood of a fixed point and universality classes for inflationary models naturally arise. Using some examples we show the application of the formalism. The predicted values for the speed of sound $c_s$ and for the amount of non-Gaussianities produced in these models are discussed. In particular, we show that it is possible to introduce models with $c_s^2 \neq 1$ that can be in agreemen…
We prove the universality of predictions for linear perturbations from the entire class of models of inflation driven by a pseudo-scalar field coupled to an SU($N$) gauge boson, where SU($2$) subgroups in the SU($N$) crossed with the background spatial SO($3$) spontaneously break into a single SO($3$). The effect of which SU($2$) subgroup in SU($N$) acquires a VEV through spontaneous symmetry breaking can be quantified by a single parameter $λ$, which always appears in combination with the gauge coupling constant $g$. In the linear perturbations, as well as the background system, the same dyna…
In this PhD thesis, we investigate generic features of inflation which are strictly related to fundamental aspects of UV-physics scenarios, such as string theory or supergravity. After a short introduction to standard and inflationary cosmology, we present our research findings. On the one hand, we show that focusing on universality properties of inflation can yield surprisingly stringent bounds on its dynamics. This approach allows us to identify the regime where the inflationary field range is uniquely determined by both the tensor-to-scalar ratio and the spectral index. Then, we derive a no…
In this contribution we discuss the possibility of generating an observable gravitational wave (GW) background by coupling a pseudo-scalar inflaton to some Abelian gauge fields. This analysis is performed by dividing inflationary models into universality classes. We find that of the most promising scenario is a Starobinsky-like model, which may lead to the generation of observational signatures both in upcoming CMB detectors as well as for direct GW detectors. The signal which can be produced in these models would both be observable in ground-based detectors, such as advanced LIGO, and in spac…
Classifying inflationary scenarios according to their scaling properties is a powerful way to connect theory with observations. A useful tool to make such a classification is the beta-function formalism. By describing inflation in terms of renormalization group equations, within this framework, it is possible to define universality classes, which can be considered as sets of theories that share a common scale invariant limit. In this paper we apply the formalism to define such classes of universality for models of inflation where the inflaton is coupled to gauge fields. We show that the formal…
We provide strong evidence for universality of the inflationary field range: given an accurate measurement of $(n_s,r)$, one can infer $Δϕ$ in a model-independent way in the sub-Planckian regime for a range of universality classes of inflationary models. Both the tensor-to-scalar ratio as well as the spectral tilt are essential for the field range. Given the Planck constraints on $n_s$, the Lyth bound is strengthened by two orders of magnitude: whereas the original bound gives a sub-Planckian field range for $r \lesssim 2 \cdot 10^{-3}$, we find that $n=0.96$ brings this down to $r \lesssim 2 …
Inflationary cosmology proposes that the early Universe undergoes accelerated expansion, driven, in simple scenarios, by a single scalar field, or inflaton. The form of the inflaton potential determines the initial spectra of density perturbations and gravitational waves. We show that constraints on the duration of inflation together with the BICEP3/Keck bounds on the gravitational wave background imply that higher derivatives of the potential are nontrivial with a confidence of 99%. Such terms contribute to the scale-dependence, or running, of the density perturbation spectrum. We clarify the…
Inflection point inflation generically includes a deviation from slow-roll when the inflaton approaches the inflection point. Such deviations are shown to be generated by transitions between singular trajectories. The effects on the power spectrum are studied within the context of universality classes for small-field models. These effects are shown to scale with universality parameters, and can explain the anomalously low power at large scales observed in the CMB. The reduction of power is related to the inflection point's basin of attraction. Implications for the likelihood of inflation are d…
We study a particular version of the theory of cosmological $α$-attractors with $α=1/3$, in which both the dilaton (inflaton) field and the axion field are light during inflation. The kinetic terms in this theory originate from maximal $\mathcal{N}=4$ superconformal symmetry and from maximal $\mathcal{N}=8$ supergravity. We show that because of the underlying hyperbolic geometry of the moduli space in this theory, it exhibits double attractor behavior: their cosmological predictions are stable not only with respect to significant modifications of the dilaton potential, but also with respect to…
A cosmological model dominated at the beginning by a dark radiation followed by a period of inflation is presented. This model is based on a Randall-Sundrum II type brane-world. Current observational data are used to fix the parameters associated to the dark radiation.
The evolutions of the flat FLRW universe and its linear perturbations are studied systematically in the dressed metric approach of LQC. When it is dominated by the kinetic energy of the inflaton at the quantum bounce, the evolution of the background can be divided into three different phases prior to the preheating, {\em bouncing, transition and slow-roll inflation}. During the bouncing phase, the evolution is independent of not only the initial conditions, but also the inflationary potentials. In particular, the expansion factor can be well described by the same exact solution in all the case…
We explore preheating in multi-field models of inflation in which the field-space metric is a highly curved hyperbolic manifold. One broad family of such models is called $α$-attractors, whose single-field regimes have been extensively studied in the context of inflation and supergravity. We focus on a simple two-field generalization of the $T$-model, which has received renewed attention in the literature. Krajewski et al. concluded, using lattice simulations, that multi-field effects can dramatically speed-up preheating. We recover their results and further demonstrate that significant analyt…
We calculate high-precision constraints on Natural Inflation relative to current observational constraints from Planck 2018 + BICEP/Keck(BK15) Polarization + BAO on $r$ and $n_S$, including post-inflationary history of the universe. We find that, for conventional post-inflationary dynamics, Natural Inflation with a cosine potential is disfavored at greater than 95\% confidence out by current data. If we assume protracted reheating characterized by $\overline{w}>1/3,$ Natural Inflation can be brought into agreement with current observational constraints. However, bringing unmodified Natural Inf…
The quantum state of the universe combined with the structure of the landscape potential implies a prior that specifies predictions for observations. We compute the prior for CMB related observables given by the no-boundary wave function (NBWF) in a landscape model that includes a range of inflationary patches representative of relatively simple single-field models. In this landscape the NBWF predicts our classical cosmological background emerges from a region of eternal inflation associated with a plateau-like potential. The spectra of primordial fluctuations on observable scales are characte…
We investigate the initial conditions problem for multifield inflation. In these scenarios the pre-inflationary dynamics can be chaotic, increasing the sensitivity of the onset of inflation to the initial data even in the homogeneous limit. To analyze physically equivalent scenarios we compare initial conditions at fixed energy. This ensures that each trajectory is counted once and only once, since the energy density decreases monotonically. We present a full analysis of hybrid inflation that reveals a greater degree of long range order in the set of "successful" initial conditions than was pr…
We consider inflation driven near a saddle point in a higher dimensional field space, which is the most likely type of slow roll inflation on the string theoretical landscape; anthropic arguments need to be invoked in order to find a sufficiently flat region. To give all inflatons large masses after inflation and yield a small but positive cosmological constant, the trajectory in field space needs to terminate in a hole on the inflationary plateau, introducing a curved end-of-inflation hypersurface. We compute non-Gaussianities (bi- and tri-spectrum) caused by this curved hyper-surface and fin…
How I stop worrying about non-universality and $b_ϕ$: Constraining local $f_{\rm NL}$ with $b_ϕ$ priors from HOD posteriors
Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学）；Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学）；Institute For Interdisciplinary Research in Science and Education, ICISE（理科教育跨学科研究所）
Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters…
In this short note we clarify the role of the boundary terms in the calculation of the leading order tree-level bispectrum in a fairly general minimally coupled single field inflationary model, where the inflaton's Lagrangian is a general function of the scalar field and its first derivatives. This includes k-inflation, DBI-inflation and standard kinetic term inflation as particular cases. These boundary terms appear when simplifying the third order action by using integrations by parts. We perform the calculation in the comoving gauge obtaining explicitly all total time derivative interaction…
Perturbations in cosmic microwave background (CMB) photons and large scale structure of the universe are sourced primarily by the curvature perturbation which is widely believed to be produced during inflation. In this paper we present a 2-field inflationary model in which the inflaton couples bi-quadratically to a spectator field. We show that the spectator induces a rapid growth of the momentum of the curvature perturbation and the associated Gaussian van Neumann entropy during inflation such that the initial conditions at the end of inflation are substantially different from the standard on…
In scalar-tensor theories the scalar fields generically couple nontrivially to gravity. We study the observable properties of inflationary models with non-minimally coupled inflaton and Dirac-Born-Infeld (DBI) kinetic term. Within the assumptions of the priors of our Monte-Carlo simulations we find these models can generate new interesting observable signatures. Our discussion focuses on string theory inspired phenomenological models of relativistic D-brane inflation. While successful string theory constructions of ultra-violet DBI brane inflation remain elusive, we show that in suitable regio…
In scalaron-Higgs inflation the Standard Model Higgs boson is non-minimally coupled to gravity and the Einstein-Hilbert action is supplemented by the quadratic scalar curvature invariant. For the quartic Higgs self-coupling $λ$ fixed at the electroweak scale, we find that the resulting inflationary two-field model effectively reduces to a single field model with the same predictions as in Higgs inflation or Starobinsky inflation, including the limit of a vanishing non-minimal coupling. For the same model, but with the scalar field a priori not identified with the Standard Model Higgs boson, we…
We consider scalar field inflation in the Palatini formulation of general relativity. The covariant derivative of the metric is then non-zero. From the effective theory point of view it should couple to other fields. We write down the most general couplings between it and a scalar field that are quadratic in derivatives. We consider both the case when the torsion is determined by the field equations and the case when it is assumed to be zero a priori. We find the metric derivative terms can significantly modify inflationary predictions. We specialise to Higgs inflation and terms of only up to …
We systematically investigate the preheating behavior of single field inflation with an oscillon-supporting potential. We compute the properties of the emitted gravitational waves (GWs) and the number density and characteristics of the produced oscillons. By performing numerical simulations for a variety of potential types, we divide the analyzed potentials in two families, each of them containing potentials with varying large- or small-field dependence. We find that the shape and amplitude of the emitted GW spectrum have a universal feature, with the peak around the physical wavenumber $k/a \…
The recent astonishing realization of the negative absolute temperature (NAT) for motional degrees of freedom \cite{Braun_ea13} inspires its possible application to the early universe. The existence of the upper bound on the energy of the system is the sufficient requirement for a NAT and this might correspond to the Planck scale at the Big Bang model. It has been argued that standard inflation requires an initial patch that is smooth over distance scales a bit larger than the causal horizon at the onset of inflation. We show that this initial condition problem can be solved if the NAT fermion…
Three channel dissipative warm Higgs inflation with global inference via genetic algorithms
School of Science, Chongqing University of Posts and Telecommunications（重庆邮电大学理学院）；Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University（重庆大学物理学院与强耦合物理学重庆市重点实验室）
During inflation, there is a preferred reference frame in which the expansion of the background spacetime is spatially isotropic. In contrast to Minkowski spacetime, observables can depend on the velocity of the system with respect to this cosmic rest frame. We derive new constraints from radiative stability and unitarity on effective field theories with such spontaneously broken Lorentz symmetry. In addition to a maximum energy scale, there is now also a critical velocity at which the theory breaks down. The theory therefore has different resolving power in time and in space, and we show that…
We calculate the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ in a class of recently proposed two-field no-scale inflationary models in supergravity. We show that, in order to obtain correct predictions, it is crucial to take into account the coupling between the curvature and the isocurvature perturbations induced by the noncanonical form of the kinetic terms. This coupling enhances the curvature perturbation and suppresses the resulting tensor-to-scalar ratio to the per mille level even for values of the slow-roll parameter $ε\sim 0.01$. Beyond these particular models, we e…
We study the tensor spectral index $n_t$ and the tensor-to-scalar ratio $r$ in the simplest multifield extension to single-field, slow-roll inflation models. We show that multifield models with potentials $V \sim \sum_i λ_i |ϕ_i|^p$ have different predictions for $n_t/r$ than single-field models, even when all the couplings are equal $λ_i=λ_j$, due to the probabilistic nature of the fields' initial values. We analyze well-motivated prior probabilities for the $λ_i$ and initial conditions to make detailed predictions for the marginalized probability distribution of $n_t/r$. With $\mathcal O(100…
At the beginning of inflation there could be extra dynamical scalar fields that will soon disappear (become static) before the end of inflation. In the light of multi-field inflation, those extra degrees of freedom may alter the time-dependence of the original spectrum of the curvature perturbation. It is possible to remove such fields introducing extra number of e-foldings prior to $N_e\sim 60$, however such extra e-foldings may make the trans-Planckian problem worse due to the Lyth bound. We show that such extra scalar fields can change the running of the spectral index to give correction of…
Spontaneously broken supersymmetry (SUSY) and a vanishingly small cosmological constant imply that R symmetry must be spontaneously broken at low energies. Based on this observation, we suppose that, in the sector responsible for low-energy R symmetry breaking, a discrete R symmetry remains preserved at high energies and only becomes dynamically broken at relatively late times in the cosmological evolution, i.e., after the dynamical breaking of SUSY. Prior to R symmetry breaking, the Universe is then bound to be in a quasi-de Sitter phase---which offers a dynamical explanation for the occurren…
We investigate the prior dependence on the inferred spectrum of primordial tensor perturbations, in light of recent results from BICEP2 and taking into account a possible dust contribution to polarized anisotropies. We highlight an optimized parameterization of the tensor power spectrum, and adoption of a logarithmic prior on its amplitude $A_T$, leading to results that transform more evenly under change of pivot scale. In the absence of foregrounds the tension between the results of BICEP2 and Planck drives the tensor spectral index $n_T$ to be blue-tilted in a joint analysis, which would be …
We constrain several models in Tachyonic Inflation derived from the large-$N$ formalism by considering theoretical aspects as well as the latest observational data. On the theoretical side, we assess the field range of our models by means of the excursion of the equivalent canonical field. On the observational side, we employ BK14+PLANCK+BAO data to perform a parameter estimation analysis as well as a Bayesian model selection to distinguish the most favoured models among all four classes here presented. We observe that the original potential $V \propto \textrm{sech}(T)$ is strongly disfavoured…
We explore inflation via the effective potential of the minimal Wess-Zumino model, considering both the real and imaginary components of the complex field. Using transport techniques, we calculate the full allowed range of $n_s$, $r$ and $f_{\rm NL}$ for different choices of the single free parameter, $v$, and present the probability distribution of these signatures given a simple choice for the prior distribution of initial conditions. Our work provides a case study of multi-field inflation in a simple but realistic setting, with important lessons that are likely to apply more generally. For …
In this thesis we will primarily demonstrate how additional scalar degrees of freedom - which are motivated from many high-energy embeddings - open up new observational windows onto the physics of inflation. We construct a Bayesian framework to statistically compare models with additional fields given the current astronomical data. Putting inflation to the test, we perform our analysis on the quadratic curvaton accompanying a range of inflationary potentials, where we find that only one potential remains as a viable candidate. Furthermore, if the curvaton mechanism were to be confirmed by futu…
Recent cosmic microwave background observations favor low energy scale inflationary models in a closed universe. However, onset of inflation in such models for a closed universe is known to be severely problematic. In particular, such a universe recollapses within a few Planck seconds and encounters a big crunch singularity when initial conditions are given in the Planck regime. We show that this problem of onset of inflation in low energy scale inflationary models can be successfully overcome in a quantum gravitational framework where the big bang/big crunch singularities are resolved and a n…
We investigate the observational constraints on three typical brane inflation models by considering the latest local measurement of the Hubble constant in the global fit. We also employ other observational data, including the Planck 2015 CMB data, the BICEP2/Keck Array B-mode data, and the baryon acoustic oscillations data, in our analysis. Previous studies have shown that the addition of the latest local $H_{0}$ measurement favors a larger spectral index, and can exert a significant influence on the model selection of inflation. In this work, we investigate its impacts on the status of brane …
