Inflation in an open universe produced by Coleman-De Luccia (CDL) tunneling induces a friction term that is strong enough to allow for successful small-field inflation in models that would otherwise suffer from a severe overshoot problem. In this paper, we present a polynomial scalar potential which allows for a full analysis. This provides a simple model of single-field open inflation on a small-field inflection point after tunneling. We present numerical results and compare them with analytic approximations.
A specific scale factor in Robertson-Walker metric with the prospect of giving the overall cosmic history in a unified picture roughly is considered. The corresponding energy-momentum tensor is identified as that of two scalar fields where one plays the roles of both inflaton and dark matter while the other accounts for dark energy. A preliminary phenomenological analysis gives an order of magnitude agreement with observational data. The resulting picture may be considered as a first step towards a single model for all epochs of cosmic evolution.
The open inflation scenario based on the theory of bubble formation in the models of a single scalar field suffered from a fatal defect. In all the versions of this scenario known so far, the Coleman-De Luccia instantons describing the creation of an open universe did not exist. We propose a simple one-field model where the CDL instanton does exist and the open inflation scenario can be realized.
We propose a toy model for the origin of the universe, where the scale-invariant fluctuations are generated together with the quantum creation process of the universe. The fluctuations arise inside an instanton in the Euclidean domain of time. In the Lorentzian point of view, the universe emerges with passive, coherent and scale-invariant fluctuations present from the beginning, without the need of inflation or a bounce. For this mechanism to work, we need anisotropic scaling in space and time, which is realized in a toy model of Horava-Lifshitz gravity with a Lifshitz scalar field.
Unlike crushing singularities, the so-called Type IV finite-time singularity offers the possibility that the Universe passes smoothly through it, without any catastrophic effects. Then the question is if the effects of a Type IV singularity can be detected in the process of cosmic evolution. In this paper we address this question in the context of $F(R)$ gravity. As we demonstrate, the effects of a Type IV singularity appear in the Hubble flow parameters, which determine the dynamical evolution of the cosmological system. So we study various inflation models incorporating a Type IV singularity…
Discontinuities in non linear field theories propagate through null geodesics in an effective metric that depends on its dynamics and on the background geometry. Once information of the geometry of the universe comes mostly from photons, one should carefully analyze the effects of possible nonlinearities on Electrodynamics in the cosmic geometry. Such phenomenon of induced metric is rather general and may occurs for any nonlinear theory independently of its spin properties. We limit our analysis here to the simplest case of non linear scalar field. We show that a class of theories that have be…
We consider two toy models of open inflation and investigate their ability to give a suppression of scalar power on large scales whilst also satisfying observational constraints on the spatial curvature of the universe. Qualitatively we find that both models are indeed capable of fulfilling these two requirements, but we also see that effects of the quantum tunnelling must be carefully taken into account if we wish to make quantitative predictions.
I present a very simplistic toy model for the inflationary paradigm where the size of the universe undergoes a period of exponential growth. The basic assumption I make use of is that black holes might have a quantized area (mass) spectrum with a stable ground state and that the universe has started with a tightly packed collection of these objects alone.
It has been argued that rather generic features of string-inspired inflationary theories with low-energy supersymmetry (SUSY) make it difficult to achieve inflation with a Hubble scale H > m_{3/2}, where m_{3/2} is the gravitino mass in the SUSY-breaking vacuum state. We present a class of string-inspired supergravity realizations of chaotic inflation where a simple, dynamical mechanism yields hierarchically small scales of post-inflationary supersymmetry breaking. Within these toy models we can easily achieve small ratios between m_{3/2} and the Hubble scale of inflation. This is possible bec…
Inflation is studied in the context of induced gravity (IG) $γσ^2 R$, where $R$ is the Ricci scalar, $σ$ a scalar field and $γ$ a dimensionless constant. We study in detail cosmological perturbations in IG and examine both a Landau-Ginzburg (LG) and a Coleman-Weinberg (CW) potential toy models for small field and large field (chaotic) inflation and find that small field inflationary models in IG are constrained to $γ\lesssim 3 \times 10^{-3}$ by WMAP 5 yrs data. Finally we describe the regime of coherent oscillations in induced gravity by an analytic approximation, showing how the homogeneous …
We reconsider the toy-model of topological inflation, based on the R*4-modified gravity. By using its equivalence to the certain scalar-tensor gravity model in four space-time dimensions, we compute the inflaton scalar potential and investigate a possibility of inflation. We confirm the existence of the slow-roll inflation with an exit. However, the model suffers from the eta-problem that gives rise to the unacceptable value of the spectral index n_s of scalar perturbations.
In this paper we present a simple, toy model of single field inflation in which the standard non-Gaussianity consistency condition is violated. In this model the curvature perturbations on super-horizon scales are not conserved and the decaying modes of perturbations are not negligible in the non-atractor phase. As a result a large local non-Gaussianity can be obtained in the squeezed limit which violates the standard non-Gaussianity consistency condition for the single field models.
We compute analytic expressions for the non-linearity parameters characterizing the bi- and tri-spectrum of primordial curvature perturbations generated during an inflationary epoch of the early universe driven by an arbitrary number of fields. We assume neither slow roll nor a separable potential; instead, to compute Non-Gaussianities, we assume a separable Hubble parameter. We apply the formalism to an exact solvable toy-model and show under which conditions observably large non-Gaussianities are produced.
We analyze a quantized toy model of a universe undergoing eternal inflation using a quantum-field-theoretical formulation of the Wheeler-DeWitt equation. This so-called third quantization method leads to the picture that the eternally inflating universe is converted to a multiverse in which sub-universes are created and exhibit a distinctive phase in their evolution before reaching an asymptotic de Sitter phase. From the perspective of one of these sub-universes, we can thus analyze the pre-inflationary phase that arises naturally. Assuming that our observable universe is represented by one of…
Inspired by the Randall-Sundrum brane-world scenario, we investigate the possibility of brane-world inflation driven not by an inflaton field on the brane, but by a bulk, dilaton-like gravitational field. As a toy model for the dilaton-like gravitational field, we consider a minimally coupled massive scalar field in the bulk 5-dimensional spacetime, and look for a perturbative solution in the anti-de Sitter (AdS) background. For an adequate range of the scalar field mass, we find a unique solution that has non-trivial dependence on the 5th dimensional coordinate and that induces slow-roll infl…
We consider the possibility of realizing inflation in nonlocal field theories containing infinitely many derivatives. Such constructions arise naturally in string field theory and also in a number of toy models, such as the p-adic string. After reviewing the complications (ghosts and instabilities) that arise when working with high derivative theories we discuss the initial value problem and perturbative stability of theories with infinitely many derivatives. Next, we examine the inflationary dynamics and phenomenology of such theories. Nonlocal inflation can proceed even when the potential is…
We consider a phenomenological model of inflation where the inflaton is the phase of a complex scalar field $Φ$. Planck-suppressed operators of $\mathcal O(f^5/M_\mathrm{pl})$ modify the geometry of the vev $\langle Φ\rangle$ at first order in the decay constant $f$, which adds a first order periodic term to the definition of the canonically normalized inflaton $ϕ$. This correction to the inflaton induces a fixed number of extra oscillatory terms in the potential $V \sim θ^p$. We derive the same result in a toy scenario where the vacuum $\langle Φ\rangle$ is an ellipse with an arbitrarily larg…
Primordial black holes (PBH) have been shown to arise from high peaks in the matter power spectra of multi-field models of inflation. Here we show, with a simple toy model, that it is also possible to generate a peak in the curvature power spectrum of single-field inflation. We assume that the effective dynamics of the inflaton field presents a near-inflection point which slows down the field right before the end of inflation and gives rise to a prominent spike in the fluctuation power spectrum at scales much smaller than those probed by Cosmic Microwave Background (CMB) and Large Scale Struct…
On the occasion of a century from the proposal of General relativity by Einstein, I attempt to tackle some open issues in modern cosmology, via a toy but non-trivial model. Specifically, I would like to link together: (i) the smallness of the cosmological constant today, (ii) the evolution of the universe from an inflationary era after the big-bang till now, and (iii) local supersymmetry in the gravitational sector (supergravity) with a broken spectrum at early eras, by making use of the concept of the "running vacuum" in the context of a simple toy model of four-dimensional N=1 supergravity. …
In this paper we consider the influence of transplanckian physics on the CMBR anisotropies produced by inflation. We consider a simple toy model that allows for analytic calculations and argue on general grounds, based on ambiguities in the choice of vacuum, that effects are expected with a magnitude of the order of $H/Λ$, where $H$ is the Hubble constant during inflation and $Λ$ the scale for new physics, e.g. the Planck scale.
Two of the most attractive realizations of inflation in supergravity are based upon the presence of a constant Fayet-Iliopoulos (FI) term. In D-term hybrid inflation it is the FI term itself which sets the energy scale of inflation. Alternatively, the breaking of a U(1) symmetry induced by the FI term can dynamically generate the quadratic potential of chaotic inflation. The purpose of this note is to study the possible UV embedding of these schemes in terms of the `field-dependent FI term' related to a string modulus field which is stabilized by a non-perturbative superpotential. We find that…
We study the possibility of obtaining large nongaussian signatures in the Cosmic Microwave Background in a general class of single-field nonlocal hill-top inflation models. We estimate the nonlinearity parameter f_{NL} which characterizes nongaussianity in such models and show that large nongaussianity is possible. For the recently proposed p-adic inflation model we find that f_{NL} ~ 120 when the string coupling is order unity. We show that large nongaussianity is also possible in a toy model with an action similar to those which arise in string field theory.
Generalized slow roll conditions and parameters are obtained for a general form of scalar-tensor theory (with no external sources), having arbitrary functions describing a nonminimal gravitational coupling F(ϕ), a Kahler-like kinetic function k(ϕ), and a scalar potential V(ϕ). These results are then used to analyze a simple toy model example of chaotic inflation with a single scalar field ϕand a standard Higgs potential and a simple gravitational coupling function. In this type of model inflation can occur with inflaton field values at an intermediate scale of roughly 10^{11} GeV when the part…
In this note we present a simple but exact model of quasi-single field inflation \cite{Chen:2009zp, Chen:2009we}, in which the couplings between perturbations are completely controlled, and for instance can be made constant with any desired value. This provides a way to numerically implement quasi-single field inflation and to test its predictions in various regimes. We confirm that the numerics agree to good accuracy with the analytical predictions for the isosceles bispectrum and the full shape function.
We study the cosmology of a toy modified theory of gravity in which gravity shuts off at short distances, as in the fat graviton scenario of Sundrum. In the weak-field limit, the theory is perturbatively local, ghost-free and unitary, although likely suffers from non-perturbative instabilities. We derive novel self-inflationary solutions from the vacuum equations of the theory, without invoking scalar fields or other forms of stress energy. The modified perturbation equation expressed in terms of the Newtonian potential closely resembles its counterpart for inflaton fluctuations. The resulting…
We study an extension of quasi-single field model of inflation containing multiple semi-heavy isocurvaton fields using the Schwinger-Keldysh mechanism. We calculate the amplitudes and the shapes of the bispectrum and the trispectrum. We show that the diagrammatic approach associated with the Schwinger-Keldysh mechanism simplifies the analysis considerably compared to standard in-in formalism. This method is helpful to study the spectroscopy of masses and couplings of light and semi-heavy fields during inflation.
We perform adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation with varying speed of sound. The subtraction is performed within the framework of earlier study by Urakawa and Starobinsky dealing with the canonical inflation. Inspired by Fakir and Unruh's model on nonminimally coupled chaotic inflation, we find upon imposing near scale-invariant condition, that the subtraction term exponentially decays with the number of $ e $-folds. As in the result for the canonical inflation, the regularized power spectrum tends to the "bare" power spectrum as the…
We compute the non-Gaussianities that arise in single field, slow roll inflationary models arising from arbitrary homogeneous initial states, as well as subleading contributions to the power spectrum. Non Bunch-Davies vacuum initial states can arise if the transition to the single field, slow roll inflation phase occurs only shortly before observable modes left the horizon. They can also arise from new physics at high energies that has been integrated out. Our general result for the bispectrum exhibits several features that were previously seen in special cases.
A toy-model is studied, which considers two flat directions meeting at an enhanced symmetry point such that they realise the usual hybrid inflation mechanism. The kinetic term of the waterfall field features a pole at its Planckian vacuum expectation value (VEV), as with $α$-attractors. Consequently, after the phase transition which terminates hybrid inflation, the waterfall field never rolls to its VEV. Instead, it drives a stiff period, where the barotropic parameter of the Universe $w\approx 1/2$ results in a peak in the spectrum of primordial gravitational waves, which will be observable b…
We study quasi-single field inflation with a warm inflation background. The thermal effects at small scales can sufficiently enhance the magnitude of the primordial standard clock signal. This scenario offers us the possibility of probing the UV physics of the very early universe without the exponentially small Boltzmann factor when the mass of the isocurvaton is much heavier than Hubble. The thermal effects at small scales can be studied using the flat space thermal field theory, connected to an effective description using non-Bunch-Davies vacuum at large scales, with large clock signal.
We study the effective field theory (EFT) description of the virtual particle effects in quasi-single field inflation, which unifies the previous results on large mass and large mixing cases. By using a horizon crossing approximation and matching with known limits, approximate expressions for the power spectrum and the spectral index are obtained. The error of the approximate solution is within 10% in dominate parts of the parameter space, which corresponds to less-than-0.1% error in the $n_s$-$r$ diagram. The quasi-single field corrections on the $n_s$-$r$ diagram are plotted for a few inflat…
Higgs inflation uses the gauge variant Higgs field as the inflaton. During inflation the Higgs field is displaced from its minimum, which results in associated Goldstone bosons that are apparently massive. Working in a minimally coupled U(1) toy model, we use the closed-time-path formalism to show that these Goldstone bosons do contribute to the one-loop effective action. Therefore the computation in unitary gauge gives incorrect results. Our expression for the effective action is gauge invariant upon using the background equations of motion.
We study models of inflation with two scalar fields and non-canonical kinetic terms, focusing on the case in which the curvature and isocurvature perturbations are strongly coupled to each other. In the regime where a heavy mode can be identified and integrated out, we clarify the passage from the full two-field model to an effectively single-field description. However, the strong coupling sets a new scale in the system, and affects the evolution of the perturbations as well as the beginning of the regime of validity of the effective field theory. In particular, the predictions of the model ar…
We review a viable alternative scenario of the inflationary universe in the context of the Randall-Sundrum (RS) braneworld. In this scenario, the dynamics of a 5-dimensional scalar field, which we call a bulk scalar field, plays the central role. Focusing on the second (single-brane) RS model, we discuss braneworld inflation driven by a bulk scalar field without introducing an inflaton on the brane. As a toy model, for the bulk scalar field, we consider a minimally coupled massive scalar field in the 5-dimensional spacetime, and look for a perturbative solution of the field equation in the ant…
We consider toy cosmological models in which a classical, homogeneous, spinor field provides a dominant or sub-dominant contribution to the energy-momentum tensor of a flat Friedmann-Robertson-Walker universe. We find that, if such a field were to exist, appropriate choices of the spinor self-interaction would generate a rich variety of behaviors, quite different from their widely studied scalar field counterparts. We first discuss solutions that incorporate a stage of cosmic inflation and estimate the primordial spectrum of density perturbations seeded during such a stage. Inflation driven by…
Topological defects are generically expected to form in models of brane inflation. Brane-anti-brane annihilation provides a way to gracefully end inflation, and the dynamics of the tachyon field results in defect formation. The formation of defects has been studied mainly from the brane world-volume point of view, but the defects are themselves lower-dimensional branes, and as a result they couple to bulk fields. To investigate the impact of bulk fields on brane defect formation, we construct a toy model that captures the essential features of the tachyon condensation with bulk fields. In this…
We investigate the possibility of embedding the vector curvaton paradigm in D-brane models of inflation in Type IIB string theory in a simple toy model. The vector curvaton is identified with the U(1) gauge field that lives on the world volume of a D3-brane, which may be stationary or undergoing general motion in the internal space. The dilaton is considered as a spectator field which modulates the evolution of the vector field. In this set up, the vector curvaton is able to generate measurable statistical anisotropy in the spectrum and bispectrum of the curvature perturbation assuming that th…
We compute the full bispectra, namely both auto- and cross- bispectra, of primordial curvature and tensor perturbations in the most general single-field inflation model whose scalar and gravitational equations of motion are of second order. The formulae in the limits of k-inflation and potential-driven inflation are also given. These expressions are useful for estimating the full bispectra of temperature and polarization anisotropies of the cosmic microwave background radiation.
Comparisons of cosmological models to current data show that the presence of a non-trivial feature in the primordial power spectrum of fluctuations, around the scale k=0.05 h/Mpc, is an open and exciting possibility, testable in a near future. This could set new constraints on inflationary models. In particular, current data favour a Lambda-CDM model with a steplike spectrum, and more power on small scales. So far, this possibility has been implemented only in toy models of inflation. In this work, we propose a supersymmetric model with two U(1) gauge symmetries, associated with two Fayet-Ilio…
We generalize the consistency condition for the three-point function in single field inflation to the case of dissipative, multi-field, single-clock models. We use the recently introduced extension of the effective field theory of inflation that accounts for dissipative effects, to provide an explicit proof to leading (non-trivial) order in the generalized slow roll parameters and mixing with gravity scales. Our results illustrate the conditions necessary for the validity of the consistency relation in situations with many degrees of freedom relevant during inflation, namely that there is a pr…
We elucidate the counting of the relevant small parameters in inflationary perturbation theory. Doing this allows for an explicit delineation of the domain of validity of the semi-classical approximation to gravity used in the calculation of inflationary correlation functions. We derive an expression for the dependence of correlation functions of inflationary perturbations on the slow-roll parameter $ε= -\dot{H}/H^2$, as well as on $H/M_p$, where $H$ is the Hubble parameter during inflation. Our analysis is valid for single-field models in which the inflaton can traverse a Planck-sized range i…
In single clock models of inflation the coupling between modes of very different scales does not have any significant dynamical effect during inflation. It leads to interesting projection effects. Larger and smaller modes change the relation between the scale a mode of interest will appear in the post-inflationary universe and will also change the time of horizon crossing of that mode. We argue that there are no infrared projection effects in physical questions, that there are no effects from modes of longer wavelength than the one of interest. These potential effects cancel when computing flu…
To understand mechanisms leading to inflation and late acceleration of the Universe it is important to see how one or a set of quantum fields may evolve such that the classical energy-momentum tensor behave similar to a cosmological constant. In this work we consider a toy model including 3 scalar fields with very different masses to study the formation of a light axion-like condensate, presumed to be responsible for inflation and/or late accelerating expansion of the Universe. Despite its simplicity, this model reflects hierarchy of masses and couplings of the Standard Model and its candidate…
We present a series of theoretical constraints on the potentially viable inflation models that might yield a blue spectrum for primordial tensor perturbations. By performing a detailed dynamical analysis we show that, while there exists such possibility, the corresponding phase space is strongly bounded. Our result implies that, in order to achieve a blue tilt for inflationary tensor perturbations, one may either construct a non-canonical inflation model delicately, or study the generation of primordial tensor modes beyond the standard scenario of single slow-roll field.
Applications of Unruh-Fulling (UF) effect are well studied in literature via the interaction of Unruh-DeWitt (UD) detector and {\it single} scalar field. In this work, we investigate a toy model, where the detector is interacting {\it simultaneously} with the {\it multiple} scalar fields. Our study reveals that the transition rate of the system significantly depends on the acceleration of the detector and the number of scalar fields ($n$). For $n\gg1$, there exists a {\it critical acceleration}, beyond which the transition rate becomes drastically high than the accelerations below the critical…
We discuss a new mechanism to enhance the spectrum of primordial tensor fluctuations in single field inflationary scenarios. The enhancement relies on a transitory non-attractor inflationary phase, which amplifies the would-be decaying tensor mode, and gives rise to a growth of tensor fluctuations at superhorizon scales. We show that the enhancement produced during this phase can be neatly treated via a tensor duality between an attractor and non-attractor phase, which we introduce. We illustrate the mechanism and duality in a kinetically driven scenario of inflation, with non-minimal coupling…
We study a toy model of a multiverse consisting of canonically quantized universes that interact with each other on a quantum level based on a field-theoretical formulation of the Wheeler-DeWitt equation. This interaction leads to the appearance of a pre-inflationary phase in the evolution of the individual universes. We analyze scalar perturbations within the model and calculate the influence of the pre-inflationary phase onto the power spectrum of these perturbations. The result is that there is a suppression of power on large scales, which can describe well the Planck 2018 data for the cosm…
We construct an analytically solvable simplified model that captures the essential features for primordial black hole (PBH) production in most models of single-field inflation. The construction makes use of the Wands duality between the constant-roll (or slow-roll) and the preceding ultra-slow-roll phases and can be realized by a simple inflaton potential of two joined parabolas. Within this framework, it is possible to formulate explicit inflationary scenarios consistent with the CMB observations and copious production of PBHs of arbitrary mass. We quantify the variability of the shape of the…
We apply the effective field theory approach to quasi-single field inflation, which contains an additional scalar field with Hubble scale mass other than inflaton. Based on the time-dependent spatial diffeomorphism, which is not broken by the time-dependent background evolution, the most generic action of quasi-single field inflation is constructed up to third order fluctuations. Using the obtained action, the effects of the additional massive scalar field on the primordial curvature perturbations are discussed. In particular, we calculate the power spectrum and discuss the momentum-dependence…
We investigate the non-Gaussian signatures of ultra slow-roll inflation. The bispectrum and the trispectrum are calculated with general initial conditions. The trispectrum is of local shape, as in the case of the bispectrum. We show that the prediction of local non-Gaussianity is robust again generalizing the Bunch-Davies vacuum. The Suyama-Yamaguchi relation is saturated in this scenario.
We consider "new inflation" inflationary models at small fields, embedded in minimal ${\cal N}=1$ supergravity with a single chiral superfield. Imposing a period of inflation compatible with experiment severely restricts possible models, classified in perturbation theory. If moreover we impose that the field goes to large values and very small potential at the current time, like would be needed for instance for the inflaton being the volume modulus in large extra dimensional scenarios, the possible models are restricted to very contrived superpotentials.
We have calculated the third order moments of scalar curvature perturbations in configuration space for different inflationary models. We developed a robust numerical technique to compute the bispectrum for different models that have some features in the inflationary potential. From the bispectrum we evaluated moments analytically in the slow roll regime while we devised a numerical mechanism to calculated these moments for non slow roll single field inflationary models with standard kinetic term that are minimally coupled to gravity. With help of these third order moments one can directly pre…
A naive computation of the correlation functions of fluctuations generated during inflation suffers from logarithmic divergences in the infrared (IR) limit. In this paper, we propose one way to solve this IR divergence problem in the single-field inflation model. The key observation is that the variables that are commonly used in describing fluctuations are influenced by what we cannot observe. Introducing a new perturbation variable which mimics what we actually observe, we propose a new prescription to solve the time evolution of perturbation in which this leakage of information from the uno…
Quantization implies independent degrees of freedom that do not appear in the classical theory, given by fluctuations, correlations, and higher moments of a state. A systematic derivation of the resulting dynamical systems is presented here in a cosmological application for near-Gaussian states of a single-field inflation model. As a consequence, single-field Higgs inflation is made viable observationally by becoming a multi-field model with a specific potential for a fluctuation field interacting with the inflaton expectation value. Crucially, non-adiabatic methods of semiclassical quantum dy…
