We present an inflationary model that is geodesically complete and does not suffer from the transplanckian problem. In most inflationary models, massless (conformal) scalar field fluctuations in a deSitter background gives rise to a scale-invariant spectrum. In this work, we realize scale invariant perturbations from thermal fluctuations in (conformal) radiation during a radiation dominated contraction era prior to inflation. As the modes exit the Hubble radius during the contraction phase, scale invariant fluctuations are indeed generated. After many cycles, we enter into a power-law inflationary phase, that stretches the modes produced in the previous contraction phase to scales that we observe today.
We study analytically and numerically the inflationary solutions for various type scalar potentials in the nonminimally coupled scalar field theory. The Hamilton-Jacobi equation is used to deal with nonlinear evolutions of inhomogeneous spacetimes and the long-wavelength approximation is employed. The constraints that lead to a sufficient inflation are found for the nonminimal coupling constant and initial conditions of the scalar field for inflation potentials. In particular, we numerically find an inflationary solution in the new inflation model of a nonminimal scalar field.
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…
The inflationary scenario for the brane world driven by the bulk inflaton is proposed. The quantum fluctuations of the inflaton is calculated and compared to those of the conventional 4-dimensional inflationary scenario. It is shown that the deviation of the primordial spectrum of this model from that of the conventional one is too small to be observed even if $AdS$ radius is very large. Hence, it turns out that the inflation caused by the bulk inflaton is viable in the context of brane world cosmology.
We show that particle production during the expansion of bubbles of true vacuum in the sea of false vacuum is possible and calculate the resulting rate. As a result the nucleated bubbles cannot expand due to the transfer of false vacuum energy to the created particles inside the bubbles. Therefore all the inflationary models dealing with the nucleation and expansion of the bubbles (including extended inflation) may not be viable.
How sensitive are the predictions of inflation to pre-inflationary conditions when the number of efolds of inflation is not too large? In an attempt to address this question, we consider a simple model where the inflationary era is preceded by an era dominated by a radiation fluid, which is coupled to the inflaton only gravitationally and which extends back to the Planck era. We show that there is a natural generalized Bunch-Davies vacuum state for perturbations to the coupled inflaton-gravity-fluid system at early times. With this choice of initial state the model predicts interesting deviati…
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…
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…
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 introduce the concept of inflationary twin models, that is, a class of generalized (kinetic or "K-inflation") field theories which lead exactly to the same cosmological evolution during the inflationary period as a given standard scalar field theory of inflation. The twin concept permits to introduce generalized, K-inflation theories in a controlled manner, maintaining some inflationary predictions unaltered. Further, this concept allows to extend analytical tools like the slow-roll expansion to the realm of K-inflation theories, facilitating their investigation. Twins of a standard scalar …
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.
Starobinsky inflation and Higgs inflation in gravity, and their equivalence based on the common inflationary potential are extended to supergravity in the proper framework, where the Starobinsky and Higgs descriptions of inflation arise in two different gauges of the same supergravity model.
Curvature perturbations generated after the end of inflation are estimated for a generic multi-field inflationary potential. The curvature perturbations are generated by conversion of inflationary isocurvature perturbations, similar to curvaton and inhomogeneous reheating scenarios. During inflation, the trajectory along which the fields are rolling down will fluctuate. When inflation ends, the fields enter the oscillatory phase along different directions in different parts of the universe. Different oscillatory trajectories can have different effective equations of state and reheating rates, …
We show a model-independent fine-tuning issue in the DBI inflationary mechanism. DBI inflation requires a warp factor h small enough to sufficiently slow down the inflaton. On the other hand, the Einstein equation in extra dimensions under the inflationary background deforms the warp space in the IR side. Generically these two locations coincide with each other, spoiling the DBI inflation. The origin and tuning of this ``h-problem'' is closely related, through the AdS/CFT duality, to those of the well-known ``eta-problem'' in the slow-roll inflationary mechanism.
We examine some inflationary models based on modifications of gravity in the light of Planck 2015 data, such as the generalised Chaplygin inspired inflation, models based in $N=1$ supergravity and braneworld scenarios. We also show that, conversely, potentials with a very flat plateau yield a primordial spectrum similar to that of the Starobinsky model with no need to modify general relativity.
Recently, the nonperturbative quantization scheme of loop quantum gravity has been extended to the Brans-Dicke theory and the corresponding loop quantum Brans-Dicke cosmology has been derived, which provides an essential platform to explore inflationary models in this framework. In this paper, we consider two inflation models, the Starobinsky and $α$-attractor inflation whose cosmological predictions are in excellent agreement with Planck data, and study systematically their pre-inflationary dynamics as well as the slow-roll inflation. We show that for both models, the background evolution of …
A simple inflationary model based on loop quantum cosmology is considered. Within this framework, we show that inflation does not necessarily erase the infor- mation prior to its onset, but that such information may leave its imprint in the energy-spectrum of the gravitational-waves generated at these earliest of times.
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…
A reformulation of inflationary model analyses appeared recently, in which inflationary observables are determined by the structure of a pole in the inflaton kinetic term rather than the shape of the inflaton potential. We comprehensively study this framework with an arbitrary order of the pole taking into account possible additional poles in the kinetic term or in the potential. Depending on the setup, the canonical potential becomes the form of hilltop or plateau models, variants of natural inflation, power-law inflation, or monomial/polynomial chaotic inflation. We demonstrate attractor beh…
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 investigate the nucleation of circular cosmic strings in models of generalized inflationary universes with an accelerating scale factor. We consider toy cosmological models of a smooth inflationary exit and transition into a flat Minkowski spacetime. Our results establish that an inflationary expanding phase is necessary but not sufficient for quantum nucleation of circular cosmic strings to occur.
We consider constraints on inflation driven by a single, minimally coupled scalar field in the light of the WMAP5 dataset, as well as ACBAR and the SuperNova Legacy Survey. We use the Slow Roll Reconstruction algorithm to derive optimal constraints on the inflationary parameter space. The scale dependence in the slope of the scalar spectrum permitted by WMAP5 is large enough to lead to viable models where the small scale perturbations have a substantial amplitude when extrapolated to the end of inflation. We find that excluding parameter values which would cause the overproduction of primordia…
We show how the inclusion of non-perturbative, {\em dynamical} quantum effects on the evolution of the inflaton can allow for an inflationary phase that is both consistent with cosmological constraints {\em and} avoids the problems associated with the so-called swampland conditions. In particular, for concave potentials such as those preferred by the Planck data, spinodal instabilities associated with tachyonic masses for long wavelength modes induce a second round of inflation, which in essence decouples the tree-level potential from the inflationary phase. We illustrate these points using na…
The large-scale power deficit in the cosmic microwave background fluctuations might be relevant with the physics of pre-inflation, a bounce, or a superinflationary phase preceding slow-roll inflation, which can provide a singular-free realization of inflation. We investigate the primordial perturbations from such pre-inflationary evolutions, which generally may consist of multiple phases with different background dynamics, and give a universal formula for the power spectrum of primordial perturbations in terms of the recursive Bogoliubov coefficients. We also apply our formula to corresponding…
Inflation solves several cosmological problems at the classical and quantum level, with a strong agreement between the theoretical predictions of well-motivated inflationary models and observations. In this work, we study the corrections induced by dynamical collapse models, which phenomenologically solve the quantum measurement problem, to the power spectrum of the comoving curvature perturbation during inflation and the radiation dominated era. We find that the corrections are strongly negligible for the reference values of the collapse parameters.
We study the dynamics of scalar metric fluctuations in a non-perturbative variational formalism recently introduced, by which the dynamics of an geometrical scalar field $θ$, describes the quantum geometrical effects on a Weylian-like manifold with respect to a background Riemannian space-time. In this letter we have examined an example in the framework of inflationary cosmology. The resulting spectral predictions are in very good agreement with observations and other models of inflation.
Scalar fields provide attractive modifications of pre-BBN cosmology, which have interesting implications for dark matter abundances. We analyse the effect of these modifications on the number of e-foldings between horizon exit of CMB modes and the end of inflation $(N_k)$, and examine the consequences for inflationary predictions of various models. We find significant effects in the predictions in the $(n_s, r)$ plane. For a large part of the parameter space, the shift in $N_k$ is positive; this ameliorates the tension of $m^{2} φ^{2}$ and natural inflation with data.
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.
We study an inflationary scenario with a vector field coupled with an inflaton field and show that the inflationary universe is endowed with anisotropy for a wide range of coupling functions. This anisotropic inflation is a tracking solution where the energy density of the vector field follows that of the inflaton field irrespective of initial conditions. We find a universal relation between the anisotropy and a slow-roll parameter of inflation. Our finding has observational implications and gives a counter example to the cosmic no-hair conjecture.
We analyse slow-roll inflationary cosmologies that are holographically dual to a three-dimensional conformal field theory deformed by a nearly marginal scalar operator. We show the cosmological power spectrum is inversely proportional to the spectral density associated with the 2-point function of the trace of the stress tensor in the deformed CFT. Computing this quantity using second-order conformal perturbation theory, we obtain a holographic power spectrum in exact agreement with the expected inflationary power spectrum to second order in slow roll.
We introduce the relation between the holographic entropy bounds and the inflationary universe. First the holographic entropy bounds for radiation-dominated universe, radiation-dominated universe with a positive cosmological constant are introduced. For an exact de Sitter phase, we use the maximal entropy bound. We classify the inflation based on the quasi-de Sitter spacetime into three steps: slow-roll period of inflation, epoch of reheating, and radiation-dominated era. Then we study how to apply three entropy bounds to the three steps of the inflation. Finally we discuss our results.
We work out the Standard Model (SM) mass spectrum during inflation with quantum corrections, and explore its observable consequences in the squeezed limit of non-Gaussianity. Both non-Higgs and Higgs inflation models are studied in detail. We also illustrate how some inflationary loop diagrams can be computed neatly by Wick-rotating the inflation background to Euclidean signature and by dimensional regularization.
Multi-Stage and Multi-Field Inflation in Random Inflationary Landscapes
Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）；Laboratoire de Physique de l’École Normale Supérieure, ENS, CNRS, Université PSL, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，ENS，CNRS，PSL大学，索邦大学，巴黎西岱大学）；Tsinghua University（清华大学）
We reconsider magnetogenesis in the context of three-form inflation, and its backreaction. In particular, we focus on first order perturbation theory during inflation and subsequent radiation era: we discuss the consistency of the perturbative approach, and elaborate on the possible non-Gaussian signatures of the model.
A new family of inflationary models is introduced and analysed. The behaviour of the parameters characterising the models suggest preferred values, which generate the most interesting testable predictions. Results are further improved if late reheating and/or a subsequent period of thermal inflation is taken into account. Specific model realisations consider a sub-Planckian inflaton variation or a potential without fine-tuning of mass scales, based on the Planck and grand unified theory scales. A toy model realisation in the context of global and local supersymmetry is examined and results fit…
