In the recent years the quantization methods of Loop Quantum Gravity have been successfully applied to the homogeneous and isotropic Friedmann-Robertson-Walker space-times. The resulting theory, called Loop Quantum Cosmology (LQC), resolves the Big Bang singularity by replacing it with the Big Bounce. We argue that LQC generates also certain corrections to field theoretical inflationary scenarios. These corrections imply that in the LQC the effective sonic horizon becomes infinite at some point after the bounce and that the scale of the inflationary potential implied by the COBE normalisation increases. The evolution of scalar fields immediately after the Bounce becomes modified in an interesting way. We point out that one can use COBE normalisation to establish an upper bound on the quantum of length of LQG.
Classical string cosmology consists of two branches related to each other by scale-factor duality: a super-inflation branch and a Friedmann-Robertson-Walker (FRW) branch. Curvature and string coupling singularity separates the two branches, hence posing `graceful exit problem' to super-inflationary string cosmology. In an exactly soluble two-dimensional compactification model it is shown that quantum back reaction retards curvature and string coupling growth and connects the super-inflation branch to the FRW branch without encountering a singularity. This may offer an attractive solution to th…
In this paper we describe in detail how to solve the problems of pre-inflationary cosmology within the holographic cosmology model of McFadden and Skenderis \cite{McFadden:2009fg}. The solutions of the smoothness and horizon problems, the flatness problem, the entropy and perturbation problems and the baryon asymmetry problem are shown, and the mechanisms for them complement the inflationary solutions. Most of the paper is devoted to the solution of the monopole relic problem, through a detailed calculation of 2-loop correlators of currents in a toy model which we perform in $d$ dimensions, in…
Physical scenarios, leading to highly energetic stochastic gravitational waves backgrounds (for frequencies ranging from the $μ$Hz up to the GHz) are examined. In some cases the typical amplitude of the logarithmic energy spectrum can be even eight orders of magnitude larger than the ordinary inflationary prediction. Scaling violations in the frequency dependence of the energy density of the produced gravitons are discussed.
The brane cosmology has invoked new challenges to the usual Big Bang cosmology. In this paper we present a brief account on thermal history of the post-inflationary brane cosmology. We have realized that it is not obvious that the post-inflationary brane cosmology would always deviate from the standard Big Bang cosmology. However, if it deviates some stringent conditions on the brane tension are to be satisfied. In this regard we study various implications on gravitino production and its abundance. We discuss Affleck-Dine mechanism for baryogenesis and make some comments on moduli and dilaton …
We show that the constraints which follow from the {\it Trans-Planckian Censorship Conjecture} for inflationary cosmology can be strengthened if the pre-inflationary universe was dominated by radiation. The resulting upper bound on the energy scale of inflation is $η\sim 10^4 {\rm GeV}$, close to the scale accessible to accelerator experiments.
Inflationary cosmology has provided a predictive and phenomenologically very successful scenario for early universe cosmology. Attempts to implement inflation using scalar fields, however, lead to models with serious conceptual problems. I will discuss some of the problems, explain why string theory could provide solutions to a subset of these problems, and give a brief overview of ``string gas cosmology'', one of the approaches to merge string theory and early universe cosmology.
A general overview of the history and present status of inflationary cosmology is given. Recent developments discussed in this paper include the hybrid inflation scenario, the theory of reheating, and the theory of inflating tolopogical defects. We also discuss the theory of a stationary self-reproducing inflationary universe, and its possible implications for evaluating the most probable values of the gravitational and cosmological constants. Finally, we discuss some preliminary results concerning possible nonperturbative large-scale deviations of density from the critical density in inflatio…
We review inflationary cosmology in modified gravity such as $R^2$ gravity with its extensions in order to generalize the Starobinsky inflation model. In particular, we explore inflation realized by three kinds of effects: modification of gravity, the quantum anomaly, and the $R^2$ term in loop quantum cosmology. It is explicitly demonstrated that in these inflationary models, the spectral index of scalar modes of the density perturbations and the tensor-to-scalar ratio can be consistent with the Planck results. Bounce cosmology in $F(R)$ gravity is also explained.
These lecture notes intend to form a short pedagogical introduction to inflationary cosmology, highlighting selected areas of recent progress such as reheating and the theory of cosmological perturbations. Problems of principle for inflationary cosmology are pointed out, and some new attempts at solving them are indicated, including a nonsingular Universe construction by means of higher derivative terms in the gravitational action, and the study of back-reaction of cosmological perturbations.
In this review I briefly describe the evolution of the inflationary theory from the scenario based on the idea of supercooling and expansion in the false vacuum toward the theory of eternally expanding self-reproducing inflationary universe. I describe recent development of inflationary cosmology with Omega < 1, and then discuss some issues related to the possibility to verify inflation by comparing its predictions with observational data. I argue that it is possible to verify and disprove many particular models of inflationary cosmology, but it is very difficult to kill the basic idea of infl…
A warm inflationary universe model in loop quantum cosmology is studied. In general we discuss the condition of inflation in this framework. By using a chaotic potential, $V(ϕ)\propto ϕ^2$, we develop a model where the dissipation coefficient $Γ=Γ_0=$ constant. We use recent astronomical observations for constraining the parameters appearing in our model.
We analyze the impact of certain modifications to short distance physics on the inflationary perturbation spectrum. For the specific case of power-law inflation, we find distinctive -- and possibly observable -- effects on the spectrum of density perturbations.
The first aim of this lecture is to highlight two areas of recent progress in inflationary cosmology, namely reheating and the quantum theory of cosmological perturbations. The second aim is to discuss important conceptual problems for the current realizations of inflation based on fundamental scalar matter fields, and to present some new approaches at solving these problems.
This paper is intended to offer a pedagogical treatment of cosmological modeling and inflationary cosmology. In recent years, inflation has become accepted as a standard scenario making predictions that are testable by observations of the cosmic background. It is therefore manifest that anyone wishing to pursue the study of cosmology and large-scale structure should have this scenario at their disposal. The author hopes this paper will serve to `bridge the gap' between technical and popular accounts of the subject.
In this review I consider several different issues related to inflation. I will begin with the wave function of the Universe. This issue is pretty old, but recently there were some new insights based on the theory of the self-reproducing inflationary universe. Then we will discuss stationarity of inflationary universe and the possibility to make predictions in the context of quantum cosmology using stochastic approach to inflation. Returning to more pragmatic aspects of inflationary theory, we will discuss inflationary models with $Ω< 1$. Finally, we will describe several aspects of the theory…
We study the implications of the recently proposed Trans-Planckian Censorship Conjecture (TCC) for early universe cosmology and in particular inflationary cosmology. The TCC leads to the conclusion that if we want inflationary cosmology to provide a successful scenario for cosmological structure formation, the energy scale of inflation has to be lower than $10^9$ GeV. Demanding the correct amplitude of the cosmological perturbations then forces the generalized slow-roll parameter $ε$ of the model to be very small ($<10^{-31}$). This leads to the prediction of a negligible amplitude of primordi…
Super--inflation driven by dilaton/moduli kinetic energy is naturally realized in compactified string theory. Discussed are selected topics of recent development in string inflationary cosmology: kinematics of super-inflation, graceful exit triggered by quantum back reaction, and clasical and quantum power spectra of density and metric perturbations.
Inflationary cosmology has become one of the cornerstones of modern cosmology. Inflation was the first theory within which it was possible to make predictions about the structure of the Universe on large scales, based on causal physics. The development of the inflationary Universe scenario has opened up a new and extremely promising avenue for connecting fundamental physics with experiment. This article summarizes the principles of inflationary cosmology, discusses progress in the field, focusing in particular on the mechanism by which initial quantum vacuum fluctuations develop into the seeds…
I study the power-law and de Sitter expansions for the universe during inflation from the STM theory of gravity. In a de Sitter expansion the additional dimension is related to the cosmological constant. I find from experimental data that the mass of the inflaton field is $m^2=2/(3Ψ^2)$. In power-law expansion, the fifth coordinate appears to be a dimensionless constant. The interesting here is that the $Ψ$-value depends on the initial conditions. I find the 5D line element for this inflationary expansion, which is a function of the classical component of the inflaton.
A formalization of the recently introduced formalism for inflation is developed from noncompact Kaluza-Klein theory. In particular, the case for a single scalar field inflationary model is studied. We obtain that the scalar potential, which assume different representations in different frames, has a geometrical origin.
We review some recent progress in the extraction of inflationary observables in loop quantum cosmology. Inverse-volume quantum corrections induce a growth of power in the large-scale cosmological spectra and are constrained by observations.
Cosmological solutions are obtained by continuation of black D-brane solutions into the region between the horizons. It is investigated whether one can find exponential expansion when probing the cosmology with D-branes. A unique configuration exhibiting exponential expansion is discussed.
The accelerated expansion of space during the period of cosmological inflation leads to trans-Planckian issues which need to be addressed. Most importantly, the physical wavelength of fluctuations which are studied at the present time by means of cosmological observations may well originate with a wavelength smaller than the Planck length at the beginning of the inflationary phase. Thus, questions arise as to whether the usual predictions of inflationary cosmology are robust considering our ignorance of physics on trans-Planckian scales, and whether the imprints of Planck-scale physics are at …
A bouncing cosmology with an initial matter-dominated phase of contraction during which scales which are currently probed with cosmological observations exit the Hubble radius provides a mechanism alternative to inflation for producing a nearly scale-invariant spectrum of cosmological perturbations. In this review article I first discuss the evolution of cosmological fluctuations in the matter bounce scenario, and then discuss various attempts at realizing such a scenario. Observational signatures which will allow the matter bounce to be distinguished from the inflationary paradigm are also di…
In this article we study closed inflationary universe models proposed by Linde in a brane world cosmological context. In this scenario we determine and characterize the existence of a closed universe, in presence of one self-interacting scalar field with an inflationary stage. Our results are compared to those found in General Relativity.
Loop quantum cosmology provides a nice solution of avoiding the big bang singularity through a big bounce mechanism in the high energy region. In loop quantum cosmology an inflationary universe is emergent after the big bounce, no matter what matter component is filled in the universe. A super-inflation phase without phantom matter will appear in a certain way in the initial stage after the bounce; then the universe will undergo a normal inflation stage. We discuss the condition of inflation in detail in this framework. Also, for slow-roll inflation, we expect the imprint from the effects of t…
Reheating is an important part of inflationary cosmology. It describes the production of Standard Matter particles after the phase of accelerated expansion. We give a review of the reheating process, focusing on an in-depth discussion of the preheating stage which is characterized by exponential particle production due to a parametric resonance or tachyonic instability. We give a brief overview of the thermalization process after preheating and end with a survey of some applications to supersymmetric theories and to other issues in cosmology such as baryogenesis, dark matter and metric preheat…
We investigate the holographic quantum entanglement of a visible universe in an inflationary cosmology. To do so, we consider an AdS space with a dS boundary which represents an expanding space in time. In an inflationary cosmology, there exists a natural entangling surface called a cosmic event horizon which divides a universe into visible and invisible parts. In this model, cosmic event horizon monotonically decreases and approaches a constant value proportional to the inverse of Hubble constant. We show that the quantum entanglement between the visible and invisible universes divided by cos…
In this letter, we propose a model of inflationary cosmology with a bounce preceded and study its primordial curvature perturbations. Our model gives rise to a primordial power spectrum with a feature of oscillation on large scales compared with the nearly scale-invariant spectrum generated by the traditional slow rolling inflation model. We will show this effect changes the Cosmic Microwave Background (CMB) temperature power spectrum and the Large Scale Structure (LSS) matter power spectrum. And further with a detailed simulation we will point out this signal is detectable to the forthcoming …
In spite of its great phenomenological success, current models of scalar field-driven inflation suffer from important unresolved conceptual issues. New fundamental physics will be required to address these questions. String theory is a candidate for a unified quantum theory of all four forces of nature. As will be shown, string theory may lead to a cosmological background quite different from an inflationary cosmology, and may admit a new stringy mechanism for the origin of a roughly scale-invariant spectrum of cosmological fluctuations.
In the framework of the Connes-Lott model based on noncommutative geometry, the basic features of a gauge theory in the presence of gravity are reviewed, in order to show the possible physical relevance of this scheme for inflationary cosmology. These models naturally contain at least two scalar fields, interacting with each other whenever more than one fermion generation is assumed. In this paper we propose to investigate the behaviour of these two fields (one of which represents the distance between the copies of a two-sheeted space-time) in the early stages of the universe evolution. In par…
We investigate inflationary cosmology by solving the effective action of the M-theory, which consists of the 11 dimensional supergravity and quartic terms of the Weyl tensor. The metric is simply expressed by two scale factors, one for the spatial directions and the other for the internal directions. Since the effective action of the M-theory is constructed perturbatively, we also solve the equations of motion perturbatively. We will show that the classical solution of the 11 dimensional supergravity does not represent the inflationary expansion, but if we include the quantum corrections, the …
We investigate observational constraints on inflationary parameters in the context of an holographic cosmology with an induced gravity correction. We consider two situations where a universe is firstly filled with a scalar field and secondly with a tachyon field. Both cases are investigated in a slow-roll regime. We adopt a quadratic potential and an exponential potential for the scalar and the tachyon inflation respectively. In this regard, the standard background and perturbative parameters characterizing the inflationary era are modified by correction terms. We show a good agreement between…
It is stressed that the kinematical problems of the standard cosmological model can be solved by a phase of accelerated contraction of the cosmic scale factor. Such a behaviour is only a particular case of a more general ``pre-big-bang" inflationary scenario, arising naturally in a string cosmology context, and driven asymptotically by the free dilaton field without any self-interaction potential and/or vacuum contribution.
I give a general review of inflationary cosmology and of its present status, in view of the 2013 data release by the Planck satellite. A specific emphasis is given to the new broad class of theories, the cosmological attractors, which have nearly model-independent predictions converging at the sweet spot of the Planck data in the (n_s,r) plane. I also discuss the problem of initial conditions for the theories favored by the Planck data.
We consider the effective evolution of a phenomenological model from FLRW supersymmetric quantum cosmology with a scalar field. The scalar field acts as a clock and inflaton. We examine a family of simple superpotentials that produce an inflation whose virtual effect on inhomogeneous fluctuations shows very good agreement with PLANCK observational evidence for the tensor-to-scalar ratio and the scalar spectral index.
In this article, we study a type of one-field approach for open inflationary universe scenario in the context of braneworld models with a Gauss-Bonnet correction term. For a one-bubble universe model, we determine and characterize the existence of the Coleman-De Lucia instanton together with the period of inflation after tunneling has occurred. Our results are compared those analogous obtained when the usual Einstein Theory of Gravitation is used.
Cosmological equations for homogeneous isotropic models filled by scalar fields and ultrarelativistic matter are investigated in the framework of gauge theories of gravity. Regular inflationary cosmological models of flat, closed and open type with dominating ultrarelativistic matter at a bounce are discussed. It is shown that essential part of inflationary cosmological models has bouncing character.
We derive an analogue of the Berry phase associated with inflationary cosmological perturbations of quantum mechanical origin by obtaining the corresponding wavefunction. We have further shown that cosmological Berry phase can be completely envisioned through the observable parameters, viz. spectral indices. Finally, physical significance of this phase is discussed from the point of view of theoretical and observational aspects with some possible consequences of this quantity in inflationary cosmology.
Problem of cosmological singularity of general relativity theory is discussed. The possible resolution of this problem in the framework of inflationary cosmology is proposed. Physical conditions leading to bouncing inflationary solutions in the frame of general relativity theory and gauge theories of gravitation are compared. It is shown that gauge theories of gravitation allow to build regular inflationary cosmological models of closed, open and flat type with dominating ultrarelativistic matter at a bounce.
Equipped with concrete examples of Type IIB orientifolds featuring poly-instanton corrections to the superpotential, the effects on moduli stabilization and inflationary cosmology are analyzed. Working in the framework of the LARGE volume scenario, the Kaehler modulus related to the size of the four-cycle supporting the poly-instanton contributes sub-dominantly to the scalar potential. It is shown that this Kaehler modulus gets stabilized and, by displacing it from its minimum, can play the role of an inflaton. Subsequent cosmological implications are discussed and compared to experimental dat…
For most initial conditions, cosmologically relevant physical modes were trans-planckian at the bounce time, often by many magnitude orders. We improve the usual loop quantum cosmology calculation of the primordial power spectra -- in the inflationary framework -- by accounting for those trans-planckian effects through modified dispersion relations. This can induce drastic changes in the spectrum, making it either compatible or incompatible with observational data, depending on the details of the choices operated.
We demonstrate that the strict upper bounds on the energy scale of inflation and on the tensor-to-scalar ratio can be somewhat relaxed if we assume that - after an initial period of slow rolling when scales probed today in CMB experiments exit the Hubble radius - the equation of state of the background changes to correspond to an almost marginally accelerating universe. Constructing an actual model in which this happens appears, however, to be unnatural.
This paper presents a review of the basic, model-independent differences between the pre-big bang scenario, arising naturally in a string cosmology context, and the standard inflationary scenario. We use an unconventional approach in which the introduction of technical details is avoided as much as possible, trying to focus the reader's attention on the main conceptual aspects of both scenarios. The aim of the paper is not to conclude in favour either of one or of the other scenario, but to raise questions that are left to the reader's meditation. Warnings: the paper does not contain equations…
The holographic protection due to inflationary cosmology is a conse- quence of a quantum tricritical point. In this scenario a closed spacetime solution transitions into an inflationary de Sitter spacetime. Saturation of the holographic entropy bound is prevented by the phase change in the topology of the early universe.
An intriguing hypothesis is that gravity may be non-perturbatively renormalizable via the notion of asymptotic safety. We show that the Higgs sector of the SM minimally coupled to asymptotically safe gravity can generate the observed near scale-invariant spectrum of the Cosmic Microwave Background through the curvaton mechanism. The resulting primordial power spectrum places an upper bound on the Higgs mass, which for finely tuned values of the curvaton parameters, is compatible with the recently released Large Hadron Collider data.
In this paper, we study the pre-inflationary dynamics for the power-law potential $(V(ϕ) \propto ϕ^n)$ with $n<2$ in the framework of loop quantum cosmology. In the case where the kinetic energy of the inflaton dominates at the initial, the evolution of the universe can always be divided into three different phases prior to preheating: {\em bouncing, transition and slow-roll inflation}. During the bouncing phase, the evolution of the expansion factor is independent not only on the initial conditions but also the inflationary potentials, and is given explicitly by an analytical solution. In con…
Using the factorization approach of quantum mechanics, we obtain a family of isospectral scalar potentials for power law inflationary cosmology. The construction is based on a scattering Wheeler-DeWitt solution. These iso-spectrals have new features, they give a mechanism to end inflation, as well as the possibility to have new inflationary epochs. The procedure can be extended to other cosmological models.
Problem of cosmological singularity is discussed in the framework of gauge theories of gravitation. Generalizing cosmological Friedmann equations (GCFE) for homogeneous isotropic models including scalar fields and usual gravitating matter are introduced. It is shown that by certain restrictions on equation of state of gravitating matter and indefinite parameter of GCFE generic feature of inflationary cosmological models of flat, open and closed type is their regular bouncing character.
After 25 years of its existence, inflationary theory gradually becomes the standard cosmological paradigm. However, we still do not know which of the many versions of inflationary cosmology will be favored by the future observational data. Moreover, it may be quite nontrivial to obtain a natural realization of inflationary theory in the context of the ever changing theory of all fundamental interactions. In this paper I will describe the history and the present status of inflationary cosmology, including recent attempts to implement inflation in the context of string theory.
Models of inflationary cosmology can lead to variation of observable parameters ("constants of Nature") on extremely large scales. The question of making probabilistic predictions for today's observables in such models has been investigated in the literature. Because of the infinite thermalized volume resulting from eternal inflation, it has proven difficult to obtain a meaningful and unambiguous probability distribution for observables, in particular due to the gauge dependence. In the present paper, we further develop the gauge-invariant procedure proposed in a previous work for models with …
Due to the quasi-exponential red-shifting which occurs during an inflationary period in the very early Universe, wavelengths which at the present time correspond to cosmological lengths are in general sub-Planckian during the early stages of inflation. This talk discusses two approaches to addressing this issue which both indicate that the standard predictions of inflationary cosmology - made using classical general relativity and weakly coupled scalar matter field theory - are not robust against changes in the physics on trans-Planckian scales. One approach makes use of modified dispersion re…
After a brief review of the theory of cosmological perturbations, I highlight some recent progress in the area of reheating in inflationary cosmology, focusing in particular on parametric amplification of super-Hubble cosmological fluctuations, and on the role of noise in the resonance dynamics (yielding a new proof of Anderson localization). I then discuss several important conceptual problems for the current realizations of inflation based on fundamental scalar matter fields, and review some new approaches at solving these problems.
The stability analysis of an anisotropic inflationary universe of the four dimensional Neveu-Schwarz--Neveu-Schwarz string model with a nonvanishing cosmological constant is discussed in this paper. The accelerating expansion solution found earlier is shown to be stable against the perturbations with respect to the dilaton and axion fields once the dilaton field falls close to the local minimum of the symmetry-breaking potential. This indicates that the Bianchi I space tends to evolve to an isotropic flat Friedmann-Robertson-Walker space. This expanding solution is also shown to be stable agai…
We consider an alternative higher order gravity theory which is non-analytic in the Ricci curvature. It has power-law inflationary behaviour. This is further evidence that inflation is a general property of higher derivative gravity theories.
