We derive all single-field cosmologies with unit sound speed that generate scale invariant curvature perturbations on a dynamical attractor background. We identify three distinct phases: slow-roll inflation; a slowly contracting adiabatic ekpyrotic phase, described by a rapidly-varying equation of state; and a novel adiabatic ekpyrotic phase on a slowly expanding background. All of these yield identical power spectra. The degeneracy is broken at the 3-point level: unlike the nearly gaussian spectrum of slow-roll inflation, adiabatic ekpyrosis predicts large non-gaussianities on small scales.
I consider the generic model independent predictions of the theory of quantum cosmological perturbations. To describe the stage of cosmic inflation, where these perturbations are amplified, the hydrodynamical approch is used. The inflationary stage is completely characterized by the deviation of the equation of state from cosmological constant which is a smooth function of the number of e-folds until the end of inflation. It is shown that in this case the spectral index should deviate from the flat one at least by 3 percent irrespective of any particular scenario. Given the value of the spectr…
We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the initial condition for inflation and therefore as a quantum cosmological prediction for its energy scale. This energy scale is also a genuine prediction of any inflationary model by itself, as the primordial gravitons generated during inflation leave their imprint in the B-polarization of the cosmic microwave background. In this way, one can derive a consist…
We obtain cosmological constraints on models of inflation which exhibit rapid roll solutions. Rapid roll attractors exist for potentials with large mass terms and are thus of interest for inflationary model building within string theory. We constrain a general ansatz for the power spectrum arising from rapid roll inflation that, in the small field limit, can be associated with tree level hybrid potentials with variable mass terms and nonminimal gravitational coupling $ξRϕ^2$. We consider perturbations generated through modulated reheating and/or curvaton mechanisms in place of the observationa…
A particular compensation-type solution of the main cosmological constant problem has been proposed recently, with two massless vector fields dynamically canceling an arbitrary cosmological constant Λ. The naive expectation is that such a compensation mechanism does not allow for the existence of an inflationary phase in the very early Universe. However, it is shown that certain initial boundary conditions on the vector fields can in fact give rise to an inflationary phase.
By making a suitable generalization of the Starobinsky stochastic inflation, we propose a classical phase space formulation of stochastic inflation which may be used for a quantitative study of decoherence of cosmological perturbations during inflation. The precise knowledge of how much cosmological perturbations have decohered is essential to the understanding of acoustic oscillations of cosmological microwave background (CMB) photons. In order to show how the method works, we provide the relevant equations for a self-interacting inflaton field. For pedagogical reasons and to provide a link t…
We review recent developments in the theory of inflation and cosmological perturbations produced from inflation. After a brief introduction of the standard, single-field slow-roll inflation, and the curvature and tensor perturbations produced from it, we discuss possible sources of nonlinear, non-Gaussian perturbations in other models of inflation. Then we describe the so-called $δN$ formalism, which is a powerful tool for evaluating nonlinear curvature perturbations on super Hubble scales.
Cosmological history after higher dimensional inflation
Lehman College, City University of New York（纽约市立大学莱曼学院）；Graduate Center, City University of New York（纽约市立大学研究生院）；American Museum of Natural History（美国自然历史博物馆）；Institute for Advanced Study, Princeton（普林斯顿高等研究院）；Sorbonne Université（索邦大学）；Chulalongkorn University（朱拉隆功大学）
In this paper we show how the string landscape can be constrained using observational data. We illustrate this idea by focusing on Fibre Inflation which is a promising class of string inflationary models in type IIB flux compactifications. We determine the values of the microscopic flux-dependent parameters which yield the best fit to the most recent cosmological datasets.
We show how cosmological correlation functions of massless fields can be rewritten in terms of Minkowski correlation functions, by extracting symmetry-breaking operators from the cosmological correlators. This technique simplifies some cosmological calculations. Also, known properties of Minkowski correlation functions can be translated to non-trivial properties of cosmological correlations. To illustrate this idea, inflation to Minkowski and matter bounce to Minkowski relations are presented for the interactions of general single field inflation. And a Minkowski recursion relation is translat…
We study whether the relaxion mechanism solves the Higgs hierarchy problem against a high scale inflation or a high reheating temperature. To accomplish the mechanism, we consider the scenario that the Higgs vacuum expectation value is determined after inflation. We take into account the effects of the Hubble induced mass and thermal one in the dynamics of the relaxion.
An inflationary universe scenario in the context of tachyon field is studied. This study is done from an ansantz for the effective potential of cosmological perturbations $U(η)$. We describe in great detail the analytical solutions of the scalar and tensor perturbations for two different ansantz in the effective potential of cosmological perturbations; the Easther's model and an effective potential similar to power law inflation. Also we find from the background equations that the effective tachyonic potential $V(φ)$, in both models satisfy the properties of a tachyonic potential. We consider …
The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameter values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary p…
Cosmological inflation is discussed in the framework of $F(R,{\cal G})$ gravity where $F$ is a generic function of the curvature scalar $R$ and the Gauss-Bonnet topological invariant $\cal G$. The main feature that emerges in this analysis is the fact that this kind of theory can exhaust all the curvature budget related to curvature invariants without considering derivatives of $R,$ $R_{μν}$, $R^λ_{σμν}$ etc. in the action. Cosmological dynamics results driven by two effective masses (lenghts) related to the $R$ scalaron and the $\cal G$ scalaron working respectively at early and very early ep…
Phase-plane stability analysis of a dynamical system describing the Universe as a two-fraction fluid containing baryonic dust and real virial gas quintessence is presented. Existence of a stable periodic solution experiencing inflationary periods is shown. A van der Waals quintessence model is revisited and cyclic Universe solution again found.
We consider a broad class of inflationary models of two unconstrained chiral superfields, the stabilizer $S$ and the inflaton $Φ$, which can describe inflationary models with nearly arbitrary potentials. These models include, in particular, the recently introduced theories of cosmological attractors, which provide an excellent fit to the latest Planck data. We show that by adding to the superpotential of the fields $S$ and $Φ$ a small term depending on a nilpotent chiral superfield $P$ one can break SUSY and introduce a small cosmological constant without affecting main predictions of the orig…
The inflationary paradigm, although very successful phenomenologically, suffers from several conceptual problems which motivate the search for alternative scenarios of early universe cosmology. Here, two possible alternatives will be reviewed. - "string gas cosmology" and the "matter bounce". Their successes and problems will be pointed out.
We discuss implications of the large eigenvalue of the cosmological constant seesaw mechanism extending hep-th/0602112 and hep-th/0604108. While the previous papers focused on the small eigenvalue as a cosmological constant associated with the accelerating Universe, here we draw attention to the physical implications of the large eigenvalue. In particular we find that the large eigenvalue can give rise to a period of inflation terminated by Universe decay. The mechanism involves quantum tunneling and mixing and introduces parameters $Γ$, the decay constant, and $θ$, the mixing angle. We discus…
We present a cosmological model arising from a gravitational theory with an infinite tower of higher-order curvature invariants that can reproduce the entire evolution of the Universe: from inflation to late-time acceleration, without invoking an inflaton nor a cosmological constant. The theory is Einsteinian-like. The field equations for a Friedmann-Lemaître-Robertson-Walker metric are of second-order and can reproduce a late-time evolution that is consistent with the acceleration provided by the cosmological constant at low redshift. Our results force us to reinterpret the nature of dark ene…
Introducing a variable cosmological parameter $Λ(t)$ in a geometrical manner from a 5D Riemann-flat metric, we investigate the origin and evolution of primordial magnetic fields in the early universe, when the expansion is governed by a cosmological parameter $Λ(t)$ that decreases with time. Using the gravitoelectromagnetic inflationary formalism, but without the Feynman gauge, we obtain the power of spectrums for large-scale magnetic fields and the inflaton field fluctuations during inflation. A very important fact is that our formalism is {\em naturally non-conformally invariant}.
Why the cosmological constant $Λ$ observed today is so much smaller than the Planck scale or why the universe is accelerating at present? This is so-called the cosmological constant fine-tuning problem. In this paper, we find that this problem is solved with the help of Higgs inflation by simply assuming a variable cosmological "constant" during the inflation epoch. In the meanwhile, it could predict a large tensor-to-scalar ratio $r\approx 0.20$ and a large running of spectral index $n'_s \approx -0.028$ with a red-tilt spectrum $n_s \approx 0.96$, as well as a big enough number of e-folds $N…
We provide a concise review on multi-field inflation and cosmological perturbations. We discuss convenient and physically meaningful bases in terms of which perturbations can be systematically studied. We give formal accounts on the gauge fixing conditions and present the perturbation action in two gauges. We also briefly review non-linear perturbations.
The purpose of these lectures is to give a pedagogical introduction to inflation and the production of primordial perturbations, as well as a review of some of the latest developments in this domain. After a short introduction, we review the main principles of the Hot Big Bang model, as well as its limitations. This motivates the study of cosmological inflation induced by a slow-rolling scalar field. We then turn to the analysis of cosmological perturbations, and explain how the vacuum quantum fluctuations are amplified during an inflationary phase. The next step consists in relating the pertu…
We find a unique way of realizing inflation through cyclic phases in an universe with negative vacuum energy. According to the second law of thermodynamics entropy monotonically increases from cycle to cycle, typically by a constant factor. This means that the scale factor at the same energy density in consecutive cycles also increases by a constant factor. If the time period of the oscillations remain approximately constant then this leads to an ``over all'' exponential growth of the scale factor, mimicking inflation. A graceful exit from this inflationary phase is possible as a dynamical sca…
Scalar field cosmological inflation has a first integral relating the Hubble function and the lagrangian of the scalar field(s), which is known under the names of "Hamilton-Jacobi approach" or "superpotential equation". Here we exploit the simplicity of this superpotential equation and use it as an alternative but equivalent cosmological evolution equation during inflation, replacing the Friedman-Robertson-Walker (FRW) equations. It turns out that all inflationary observables can be calculated directly from its solution (the superpotential). Further, the superpotential equation allows for a si…
We show that S-dual inflationary potentials solve the unlikeliness problem manifested in Planck data and explain the excess B-mode power observed by the BICEP2 experiment as arising from primordial tensor fluctuations.
We study the backreaction problem in a mechanism of magnetogenesis from inflation. In usual analysis, it has been assumed that the backreaction due to electromagnetic fields spoils inflation once it becomes important. However, there exists no justification for this assumption. Hence, we analyze magnetogenesis from inflation by taking into account the backreaction. On the contrary to the naive expectation, we show that inflation still continues even after the backreaction begins to work. Nevertheless, it turns out that creation of primordial magnetic fields is significantly suppressed due to th…
Quantum fluctuation of unstable modes about gravitational instantons causes the instability of flat space at finite temperature, leading to the spontaneous process of nucleating quantum black holes. The density of vacuum energy-gain in such process gives the cosmological term in the Einstein equation. This naturally results in the inflationary phase of Early Universe. While the reheating phase is attributed to the Hawking radiation of these quantum black holes. In the Standard cosmology era, this cosmological term depends on the reheating temperature and asymptotically approaches to the cosmol…
This thesis is centered on three main subjects within the theory of inflation and cosmological perturbations: loop corrections to the power spectrum of curvature fluctuations generated during inflation; evolution of cosmological fluctuations in anisotropic pre-inflationary cosmologies; statistical anisotropy and non-Gaussianity predictions of models of inflation populated with vector fields. Currently, what makes even more interesting the study of 2-nd and higher order corrections to cosmological correlation functions as well as the computation of higher-than-two order correlators, is the almo…
The detection of B-mode shows a very powerful constraint to theoretical inflation models through the measurement of the tensor-to-scalar ratio $r$. Higgs boson is the most likely candidate of the inflaton field. But usually, Higgs inflation models predict a small value of $r$, which is not quite consistent with the recent results from BICEP2. In this paper, we explored whether a cosmological constant energy component is needed to improve the situation. And we found the answer is yes. For the so-called Higgs chaotic inflation model with a quadratic potential, it predicts $r\approx 0.2$, $n_s\ap…
We study the cosmological perturbations created during the New Higgs inflationary phase. In the New Higgs Inflation, the Higgs boson is kinetically coupled to the Einstein tensor and only three perturbative degrees of freedom, a scalar and two tensorial (gravitational waves), propagate during Inflation. Scalar perturbations are found to match the latest WMAP-7yrs data within Standard Model Higgs parameters. Primordial gravitational waves also, although propagating with superluminal speed, are consistent with present data. Finally, we estimate the values of the parameter of the New Higgs Inflat…
Standard inflationary models yield a characteristic signature of a primordial power spectrum with a red tensor and scalar tilt. Nevertheless, Cannone et al recently suggested that, by breaking the assumption of spatial diffeomorphism invariance in the context of the effective field theory of inflation, a blue tensor spectrum can be achieved without violating the Null Energy Condition. In this context, we explore in which cases a blue tensor tilt can be obtained along with a red tilt in the scalar spectrum. Ultimately, we analyze under which conditions this model can reproduce the specific cons…
We analyze the behavior of linear perturbations in vector inflation. In contrast to the scalar field inflation, the linearized theory with vector fields contains couplings between scalar, vector and tensor modes. The perturbations decouple only in the ultraviolet limit, which allows us to carry out the canonical quantization. Superhorizon perturbations can be approximately analyzed due to suppressed mixing between different modes in the small fields models. We find that the vector perturbations of the metric decay exponentially, but the scalar and tensor modes could remain weakly coupled throu…
Nonthermal leptogenesis via cosmological gravitational particle production is tested by inflationary gravitational waves
University of Manitoba（曼尼托巴大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；The University of Chicago（芝加哥大学）；Rice University（莱斯大学）；University of Winnipeg（温尼伯大学）
We study gravitational waves generated during the inflationary epoch in presence of a decaying cosmological parameter on a 5D geometrical background which is Riemann flat. Two examples are considered, one with a constant cosmological parameter and the second with a decreasing one.
After a brief summary of general relativity and cosmology, we present the basic concepts underlying inflation, the currently best motivated models for the early Universe. We describe the simplest inflation models, based on a single scalar field, and discuss how primordial cosmological perturbations are generated. We then review some recent developments concerning multi-field inflation models, in particular multi-field Dirac-Born-Infeld inflation.
We investigate one-loop quantum corrections to the power spectrum of adiabatic perturbation from entropy modes/adiabatic mode cross-interactions in multiple DBI inflationary models. We find that due to the non-canonical kinetic term in DBI models, the loop corrections are enhanced by slow-varying parameter $ε$ and small sound speed $c_s$. Thus, in general the loop-corrections in multi-DBI models can be large. Moreover, we find that the loop-corrections from adiabatic/entropy cross-interaction vertices are IR finite.
Swampland Conjectures have attracted quite some interest in the Cosmological Community. They have been shown to have wide ranging implications , like Constraints on Inflationary Models, Primordial Black Holes etc. to name a few. A particularly revealing insight on dark energy also shows that one can have the dark energy equation of state for a quintessence scenario to be signficantly different than -1 after one takes into account the refined dS conjecture. Another interesting issue with the swampland conjectures is that they have been shown to be incompatible with single field inflationary mod…
Applying the anholonomic frame deformation method, we construct various classes of cosmological solutions for effective Einstein -- Yang-Mills -- Higgs, and two measure theories. The types of models considered are Freedman-Lemaître-Robertson-Walker, Bianchi, Kasner and models with attractor configurations. The various regimes pertaining to plateau--type inflation, quadratic inflation, Starobinsky type and Higgs type inflation are presented.
We show that in generic supergravity theories the mass of the moduli during inflation is larger (or at least of the same order of magnitude) than the Hubble constant. This fact does not depends on the details of the inflation and on the value of the Hubble parameter during it. The reason is that inflationary universe is dominated by large F-term (or D-term) density which is higher than the SUSY breaking scale in the present minimum and stabilizes the flat directions of the supersymmetric vacua. Therefore, in general even standard inflationary scenarios (with large H) may solve the cosmological…
We propose a paradigm for the inflation and the vanishing cosmological constant in a unified way with the self-tuning solutions of the cosmological constant problem. Here, we consider a time-varying cosmological constant in self-tuning models of the cosmological constant. As a specific example, we demonstrate it with a 3-form field in 5D.
The physical history of the Universe is completed by including the quantum planckian and trans-planckian phase before Inflation in the Standard Model of the Universe in agreement with observations. A new quantum precursor phase appears beyond the Planck scale. We extend de Sitter universe to the quantum domain: classical-quantum de Sitter duality. As a result: The classical and quantum dual de Sitter Temperatures and Entropies are naturally included, and the different (classical, semiclassical, quantum planckian and super-planckian) de Sitter regimes characterized in a precise and unifying way…
We show that a pair of field theory monodromies in which the shift symmetry is broken by small, well motivated deformations, naturally incorporates a mechanism for cancelling off radiative corrections to the cosmological constant. The lighter monodromy sector plays the role of inflation as well as providing a rigid degree of freedom that acts as a dynamical counterterm for the cosmological constant. The heavier monodromy sector includes a rigid dilaton that forces a global constraint on the system and the cancellation of vacuum energy loops occurs at low energies via the sequestering mechanism…
From the viewpoint of no-cloning theorem we postulate a relation between the current accelerated expansion of our universe and the inflationary expansion in the very early universe. It implies that the fate of our universe should be in a state with accelerated expansion. Quantitatively we find that the no-cloning theorem leads to a lower bound on the cosmological constant which is compatible with observations.
We show that the cosmological abundance of string axions is much smaller than naive estimates if the Hubble scale of inflation, $H_{\rm inf}$, is sufficiently low (but can still be much higher than the axion masses) and if the inflation lasts sufficiently long. The reason is that the initial misalignment angles of the string axions follow the Bunch-Davies distribution peaked at the potential minima. As a result, the cosmological moduli problem induced by the string axions can be significantly relaxed by low-scale inflation, and astrophysical and cosmological bounds are satisfied over a wide ra…
Inflationary scenarios motivated by the Minimal Supersymmetric Standard Model (MSSM) where five scalar fields are non-minimally coupled to gravity are considered. The potential of the model and the function of non-minimal coupling are polynomials of two Higgs doublet convolutions. We show that the use of the strong coupling approximation allows to obtain inflationary parameters in the case when a combination of the four scalar fields plays a role of inflaton. Numerical calculations show that the cosmological evolution leads to inflationary scenarios fully compatible with observational data for…
We investigate scalar perturbations from inflation in a bulk inflaton braneworld model. Using the generalized longitudinal gauge, we derive and solve the full set of scalar perturbation equations. Our exact results support the recent argument that for the de Sitter brane the square of the radion mass is not positive, showing that unlike the flat brane case, the de Sitter brane is not stable.
Recently a new kind of quintessential inflation coming from the Lorentzian distribution has been introduced in [1,2]. The model leads to a very simple potential, which basically depends on two parameters, belonging to the class of $α$-attractors and depicting correctly the early and late time accelerations of our universe. The potential emphasizes a {\it cosmological seesaw mechanism} (CSSM) that produces a large inflationary vacuum energy in one side of the potential and a very small value of dark energy on the right hand side of the potential. {Here we show that the model agrees with the rec…
We briefly review the standard derivation of the spectra of cosmological perturbations in the simplest models of inflation. We then consider models with several scalar fields, described by Lagrangians with an arbitrary dependence on the kinetic terms. We illustrate our general formalism with the case of multi-field DBI inflation.
We study the emission of large-scales wavelength space-time waves during the inflationary expansion of the universe, produced by back-reaction effects. As an example, we study an inflationary model with variable time scale, where the scale factor of the universe grows as a power of time. The coarse-grained field to describe space-time waves is defined by using the Levy distribution, on the wavenumber space. The evolution for the norm of these waves on cosmological scales is calculated, and it is shown that decreases with time.
The cosmological constant problem is how one chooses, without fine-tuning, one singular point $Λ_{eff}=0$ for the 4D cosmological constant. We argue that some recently discovered {\it weak self-tuning} solutions can be viewed as blowing-up this one point into a band of some parameter. These weak self-tuning solutions may have a virtue that only de Sitter space solutions are allowed outside this band, allowing an inflationary period. We adopt the hybrid inflation at the brane to exit from this inflationary phase and to enter into the standard Big Bang cosmology.
Heavy-ion colliders have revealed the process of "fast thermalization". This experimental breakthrough has led to new theoretical tools to study the thermalization process at both weak and strong coupling. We apply this to the reheating epoch of inflationary cosmology, and the formation of a cosmological quark gluon plasma (QGP). We compute the thermalization time of the QGP at reheating, and find it is determined by the energy scale of inflation and the shear viscosity to entropy ratio $η/s$; or equivalently, the tensor-to-scalar ratio and the strong coupling constant at the epoch of thermali…
These lectures are intended to give a pedagogical introduction to the main current picture of the very early universe. After elementary reviews of general relativity and of the standard Big Bang model, the following subjects are discussed: inflation, the classical relativistic theory of cosmological perturbations and the generation of perturbations from scalar field quantum fluctuations during inflation.
Cosmological inflation is studied in the case where the inflaton is the overall modulus $T$ for an orbifold. General forms of the (non-perturbative) superpotential are considered to ensure that $G=K+{\rm ln}|W|^2$ is modular invariant. We find generically that these models do not produce a potential flat enough for slow roll to a supersymmetric minimum, although we do find a model which produces up to 20 e-folds of inflation to a non-supersymmetric minimum.
Cosmological inflation, if it occurred, radically alters the picture of the `big bang', which would merely point to reheating at the end of inflation. Moreover, this reheating may be only local, so that inflation continues elsewhere and forever, continually spawning big-bang-like regions. This chapter reviews this idea of `eternal inflation', then focuses on what this may mean for the ultimate beginning of the universe. In particular, I will argue that given eternal inflation, the universe may be free of a cosmological initial singularity, might be eternal (and eternally inflating) to the past…
This paper considers Einstein-Brans-Dicke action being coupled with a Higgs sector. It is shown that classically graceful exit from inflation is not possible in principle, rejecting the claim of La and Steinhardt. Further, wormhole solutions with and without conserved charges are explored. Finally, the wavefunction of the universe in this model is constructed with the boundary condition, as proposed by Vilenkin. The interesting feature of the wavefunction is that it has been constructed for an arbitrary factor-ordering index.
