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 the loop quantum cosmology should be left in the primordial perturbation power spectrum. However, we show that this imprint is too weak to be observed.
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 …
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…
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…
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…
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…
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 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 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…
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.
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 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.
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…
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.
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…
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 consider a minimum uncertainty vacuum choice at a fixed energy scale Lambda as an effective description of trans-Planckian physics, and discuss its implications for the linear perturbations of a massless scalar field in power-law inflationary models. We find possible effects with a magnitude of order H/Λin the power spectrum, in analogy with previous results for de-Sitter space-time.
The curvaton in an intermediate inflationary universe model is studied. This study has allowed us to find some interesting constraints on different parameters that appear in the model.
This is the LaTeX version of my book "Particle Physics and Inflationary Cosmology'' (Harwood, Chur, Switzerland, 1990). I decided to put it to hep-th, to make it easily available. Many things happened during the 15 years since the time when it was written. In particular, we have learned a lot about the high temperature behavior in the electroweak theory and about baryogenesis. A discovery of the acceleration of the universe has changed the way we are thinking about the problem of the vacuum energy: Instead of trying to explain why it is zero, we are trying to understand why it is anomalously s…
Tachyonic inflationary universe model in the context of a Chaplygin gas equation of state is studied. General conditions for this model to be realizable are discussed. By using an effective exponential potential we describe in great details the characteristic of the inflationary universe model. The parameters of the model are restricted by using recent astronomical observations.
We study the spectrum of gravitational waves generated from inflation in the Randall-Sundrum braneworld. Since the inflationary gravitational waves are of quantum-mechanical origin, the initial configuration of perturbations in the bulk includes Kaluza-Klein quantum fluctuations as well as fluctuations in the zero mode. We show, however, that the initial fluctuations in Kaluza-Klein modes have no significant effect on the late time spectrum, irrespective of the energy scale of inflation and the equation of state parameter in the post-inflationary stage. This is done numerically, using the Wron…
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…
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.
We discuss two important modifications of inflationary paradigm. Until very recently we believed that inflation automatically leads to flatness of the universe, Omega = 1. We also thought that post-inflationary phase transitions in GUTs may occur only after thermalization, which made it very difficult to have baryogenesis in GUTs and to obtain superheavy topological defects after inflation. We will describe a very simple version of chaotic inflation which leads to a division of the universe into infinitely many open universes with all possible values of Omega from 1 to 0. We will show also tha…
If inflation can occur only at the energy density V much smaller than the Planck density, which is the case for many inflationary models based on string theory, then the probability of quantum creation of a closed or an infinitely large open inflationary universe is exponentially suppressed for all known choices of the wave function of the universe. Meanwhile under certain conditions there is no exponential suppression for creation of topologically nontrivial compact flat or open inflationary universes. This suggests, contrary to the standard textbook lore, that compact flat or open universes …
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.
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 …
Warm inflationary universe models in a tachyon field theory are studied. General conditions required for these models to be realizable are derived and discussed. We describe scalar perturbations (in the longitudinal gauge) and tensor perturbations for these scenarios. We develop our models for a constant dissipation parameter $Γ$ in one case and one dependent on $ϕ$ in the other case. We have been successful in describing such of inflationary universe models. We use recent astronomical observations for constraining the parameters appearing in our model. Also, our results are compared with thei…
We describe several different regimes which are possible in inflationary cosmology. The simplest one is inflation without self-reproduction of the universe. In this scenario the universe is not stationary. The second regime, which exists in a broad class of inflationary models, is eternal inflation with the self-reproduction of inflationary domains. In this regime local properties of domains with a given density and given values of fields do not depend on the time when these domains were produced. The probability distribution to find a domain with given properties in a self-reproducing univers…
We describe a scenario for inflation in the framework of non-critical string theory, which does not employ an inflaton field. There is an exponential expansion of the volume of the Universe, induced by enormous entropy production in the early stages of cosmological evolution. This is associated with the loss of information carried by global string modes that cross the particle horizon. It is the same loss of information that induces irreversible time flow when target time is identified with the world-sheet Liouville mode. The resulting scenario for inflation is described by a string analogue o…
We further clarify how scalar metric perturbations are amplified in an inflationary cosmology. We first construct a simple, analytic model of an inflationary cosmology in which the expansion scale factor evolves continuously from an inflationary era to a radiation-dominated era. From this model, it is clear to see how scalar perturbations are amplified. Second, we examine the recent claims of Grishchuk, and the reply by Deruelle and Mukhanov, regarding the evolution of scalar perturbations through an abrupt transition in the equation of state of the cosmological fluid. We demonstrate that the …
We study inflationary cosmology and the late-time accelerated expansion of the universe in non-minimal Yang-Mills (YM) theory, in which the YM field couples to a function of the scalar curvature. It is shown that power-law inflation can be realized due to the non-minimal YM field-gravitational coupling which maybe caused by quantum corrections. Moreover, it is demonstrated that both inflation and the late-time accelerated expansion of the universe can be realized in a modified YM-$F(R)$ gravity which is consistent with solar system tests. Furthermore, it is shown that this result can be realiz…
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 …
We show that there exists a large class of regularization schemes for probabilistic predictions in the theory of a self-reproducing inflationary univere, all of which eliminate the apparent dependence on the time reparametrization. However, all these schemes lead to different answers for relative probabilities of finding various types of post-inflationary universes. Besides, all these schemes fail to be reparametrization invariant beyond the range of the inflaton field close to end of inflation boundary. Therefore, we argue that at the current level of understanding, the simple regularization …
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.
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.
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 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 loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar field to accelerate away from a minimum of its potential. In principle, this mechanism can generate the conditions that subsequently lead to slow-roll inflation. The consequences for this mechanism of various quantization ambiguities arising within loop quantum cosmology are considered. For the case of a quadratic potential, it is found that some quantization procedures are more likely to generate a phase of slow--roll inflation. In general, however, loop quantum cosmology is robust to ambiguities…
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.
In the context of loop quantum cosmology, we consider an inflationary era driven by a canonical scalar field and occurring in the semiclassical regime, where spacetime is a continuum but quantum gravitational effects are important. The spectral amplitude and index of scalar perturbations on an unperturbed de Sitter background are computed at lowest order in the slow-roll parameters. The scalar spectrum can be blue-tilted and far from scale invariance, and tuning of the quantization ambiguities is necessary for agreement with observations. The results are extended to a generalized quantization …
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…
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.
Recently Hollands and Wald argued that inflation does not solve any of the major cosmological problems. We explain why we disagree with their arguments. They also proposed a new speculative mechanism of generation of density perturbations. We show that in their scenario the inhomogeneities responsible for the large scale structure observed today were generated at an epoch when the energy density of the hot universe was 10^{95} times greater than the Planck density. The only way to avoid this problem is to assume that there was a stage of inflation in the early universe.
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.
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…
