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 perturbations generated during inflation to the perturbations of the cosmological fluid in the radiation dominated phase. The final part of these lectures gives a review of more general models of inflation, involving multiple fields or non standard kinetic terms. Although more complicated, these models are usually motivated by high energy physics and they can lead to specific signatures that are not expected in the simplest models of inflation. After introducing a very general formalism to describe perturbations in multi-field models with arbitrary kinetic terms, several interesting cases are presented. We also stress the role of entropy perturbations in the context of multi-field models. Finally, we discuss in detail the non-Gaussianities of the primordial perturbations and some models that could produce a detectable level of non-Gaussianities.
In a series of five lectures I review inflationary cosmology. I begin with a description of the initial conditions problems of the Friedmann-Robertson-Walker (FRW) cosmology and then explain how inflation, an early period of accelerated expansion, solves these problems. Next, I describe how inflation transforms microscopic quantum fluctuations into macroscopic seeds for cosmological structure formation. I present in full detail the famous calculation for the primordial spectra of scalar and tensor fluctuations. I then define the inverse problem of extracting information on the inflationary era…
This lecture note provides a generic introduction to reheating after inflation, covering theoretical, phenomenological and observational aspects of the process.
These lectures cover the theoretical structure and phenomenology of some basic mechanisms for inflation. A full treatment of the problem requires `ultraviolet completion' because of the sensitivity of inflation to quantum gravity effects, while the observables are elegantly parameterized using low energy field theory. String theory provides novel mechanisms for inflation, some subject to significant observational tests, with highly UV-sensitive tensor mode measurements being a prime example. Although the ultraviolet completion is not directly accessible experimentally, some of these mechanisms…
This series of lectures gives a pedagogical review of the subject of cosmological inflation. I discuss Friedmann-Robertson-Walker cosmology and the horizon and flatness problems of the standard hot Big Bang, and introduce inflation as a solution to those problems, focusing on the simple scenario of inflation from a single scalar field. I discuss quantum modes in inflation and the generation of primordial tensor and scalar fluctuations. Finally, I provide comparison of inflationary models to the WMAP satellite measurement of the Cosmic Microwave Background, and briefly discuss future directions…
These lectures, presented at TASI 2018, provide a concise introduction to inflation, baryogenesis, and aspects of dark matter not covered by the other lectures. The emphasis for inflation is an intuitive understanding and techniques for constraining inflationary models. For baryogenesis we focus on two examples, leptogenesis and electroweak baryogenesis, with attention to singlet-assisted two-step phase transitions. Concerning dark matter, we review different classes of models distinguished by their mechanisms for obtaining the observed relic density, including thermal freeze-out, asymmetric d…
These lecture notes introduce the reader to the hot big bang model, cosmological perturbations, gravitational waves, the cosmic microwave background, inflation, the singularity problem, the cosmological constant problem and the cosmology of quantum gravity.
These lectures provide an updated pedagogical treatment of the theoretical structure and phenomenology of some basic mechanisms for inflation, along with an overview of the structure of cosmological uplifts of holographic duality. A full treatment of the problem requires `ultraviolet completion' because of the sensitivity of inflation to quantum gravity effects, including back reaction and non-adiabatic production of heavy degrees of freedom. Cosmological observations imply accelerated expansion of the late universe, and provide increasingly precise constraints and discovery potential on the a…
These lecture notes are based on those presented at the Theoretical Aspects of Astroparticle Physics, Cosmology and Gravitation School at the Galileo Galilee Institute in Florence in 2021, https://agenda.infn.it/event/24368/. They aim to provide a pedagogical introduction and basic working knowledge of single-field inflation including the ultra-slow-roll regime, where the perturbations grow exponentially. This rapid growth is connected to the formation of primordial black holes (PBHs), a special dark matter candidate and probe of the initial conditions of the early universe. Although there are…
These lectures on the cosmological constant problem were prepared for the X Mexican School on Gravitation and Mathematical Physics. The problem itself is explained in detail, emphasising the importance of radiative instability and the need to repeatedly fine tune as we change our effective description. Weinberg's no go theorem is worked through in detail. I review a number of proposals including Linde's universe multiplication, Coleman's wormholes, the fat graviton, and SLED, to name a few. Large distance modifications of gravity are also discussed, with causality considerations pointing towar…
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…
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.
These notes present an introduction to $Λ$CDM cosmology and its possible inflationary precursor, with an emphasis on some of the ways effective field theories are used in its analysis. The intended audience are graduate students in particle physics, such as attended the lectures (prepared for the Les Houches Summer School, Effective Field Theory in Particle Physics and Cosmology, July 2017).
We present a self-contained summary of the theory of linear cosmological perturbations. We emphasize the effect of the six parameters of the minimal cosmological model, first, on the spectrum of Cosmic Microwave Background temperature anisotropies, and second, on the linear matter power spectrum. We briefly review at the end the possible impact of a few non-minimal dark matter and dark energy models.
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 …
In these lectures, after a short introduction to cosmology, we discuss the supergravity embedding of higher curvature models of inflation. The supergravity description of such models is presented for the two different formulations of minimal supergravity.
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…
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 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…
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 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 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 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.
In order to solve the fine-tuning problem of the cosmological constant, we propose a simple model with the vacuum energy non-minimally coupled to the inflaton field. In this model, the vacuum energy decays to the inflaton during pre-inflation and inflation eras, so that the cosmological constant effectively deflates from the Planck mass scale to a much smaller one after inflation and plays the role of dark energy in the late-time of the universe. We show that our deflationary scenario is applicable to arbitrary slow-roll inflation models. We also take two specific inflation potentials to illus…
We study the dynamics of two concrete inflationary models, namely Spontaneous Symmetry Breaking Inflation as well as Loop Inflation. We constrain the parameters for which a viable inflationary Universe emerges using the latest PLANCK results of last year, and we give predictions for the duration of reheating as well as for the reheating temperature after inflation. Our numerical results show that baryogenesis via leptogenesis may be realized within the inflationary models considered in this work.
We discuss how primordial non-Gaussianity of the curvature perturbation helps to constrain models of the early universe. Observations are consistent with Gaussian initial conditions, compatible with the predictions of the simplest models of inflation. Deviations are constrained to be at the sub percent level, constraining alternative models such as those with multiple fields, non-canonical kinetic terms or breaking the slow-roll conditions. We introduce some of the most important models of inflation which generate non-Gaussian perturbations and provide practical tools on how to calculate the t…
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…
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…
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…
The constant mean extrinsic curvature on a spacelike slice may constitute a physically preferred time coordinate, `York time'. One line of enquiry to probe this idea is to understand processes in our cosmological history in terms of York time. Following a review of the theoretical motivations, we focus on slow-roll inflation and the freezing and Hubble re-entry of cosmological perturbations. We show how the mathematical account of these processes is distinct from the conventional account in terms of standard cosmological or conformal time. We also consider the cosmological York-timeline more b…
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）
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…
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…
Dynamics of the inflaton scalar field oscillating around a minimum of the singular potentials in the expanding Universe is investigated. Asymptotic formulas are obtained describing the cosmological expansion at the late times. The problem of stability of the oscillations considered and the related phenomenon of the field fragmentation are briefly discussed.
Assuming the existence of a cosmological constant depending on time, we study the evolution of this field in a local region of spacetime. Solving the standard equations of Einstein Relativity in the weak field approximation we find two asymptotes in the behavior of the cosmological constant. Their meaning is the existence of an inflationary era both in the far past and in the future. A trace of the initial acceleration of the Universe can be found also in the local behavior of cosmological constant.
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 study some aspects of cosmological inflation in the framework of unimodular $f(R)$ gravity. To be more clarified, we consider a generic $f(R)$ of the type $f(R)=R+αR^{n}$. By considering Einstein frame counterpart of the unimodular $f(R)$ gravity, we set the scalaron to be responsible for cosmological inflation in this setup. We confront our model parameters space with observational data and impose some constraints on the value of $n$ in this manner. We show that for the number of e-folds $N=60$, the model is consistent with observation if $1.89<n<1.918$.
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 propose a mechanism for generating an inflationary phase in the early universe without resorting to any type of scalar field(s). Instead, this accelerated expansion is driven by a dynamical "cosmological constant" in the framework of unimodular gravity. The time dependent cosmological constant can be related to an energy diffusion term that arises naturally in unimodular gravity due to its restrictive diffeomorphism invariance. We derive the generic conditions required for any type of diffusion to generate a realistic inflationary epoch. Furthermore, for a given parameterization of inflatio…
A model of a universe without big bang singularity is presented, which displaysanearly inflationary period ending just before a phase transition to a deflationary epoch. The model produces enough heavy particles so as to reheat the universe at temperatures in the MeV regime. After the reheating, it smoothly matches the standard $Λ$CDM scenario.
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…
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.
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 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.
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.
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…
In this series of lectures we review observational evidence for, and theoretical investigations into, cosmic acceleration and dark energy. The notes are in four sections. First I review the basic cosmological formalism to describe the expansion history of the universe and how distance measures are defined. The second section covers the evidence for cosmic acceleration from cosmic distance measurements. Section 3 discusses the theoretical avenues being considered to explain the cosmological observations and section 4 discusses how the growth of inhomogeneities and large scale structure observat…
In this work, we revisit the non-minimally coupled Higgs Inflation scenario and investigate its observational viability in light of the current Cosmic Microwave Background, Baryon Acoustic Oscillation and type Ia Supernovae data. We explore the effects of the Coleman-Weinberg approximation to the Higgs potential in the primordial universe, connecting the predictions for the Lagrangian parameters at inflationary scales to the electroweak observables through Renormalization Group methods at two-loop order. As the main result, we find that observations on the electroweak scale are in disagreement…
