We study higher curvature corrections to the scalar spectral index, the tensor spectral index, the tensor-to-scalar ratio, and the polarization of gravitational waves. We find that the higher curvature corrections can not be negligible in the dynamics of the scalar field, although they are energetically negligible. Indeed, it turns out that the tensor-to-scalar ratio could be enhanced and the tensor spectral index could be blue due to the Gauss-Bonnet term. We estimate the degree of circular polarization of gravitational waves generated during the slow-roll inflation. We argue that the circular polarization can be observable with the help both of the Gauss-Bonnet and parity violating terms. We also present several examples to reveal observational implications of higher curvature corrections for chaotic inflationary models.
Using the nonlinear $δN$ formalism, we consider a simple exactly soluble model of multi-component slow-roll inflation in which the nonlinear curvature perturbation can be evaluated analytically.
We study a double inflation model (a hybrid inflation + a new inflation) in supergravity and discuss the formation of primordial black holes (PBHs) with mass \sim 10^{-20}-10^{5}M_{\odot}. We find that in a wide range of parameter space, we obtain PBHs which amount to Ω\simeq 1, i.e., PBH dark matter. Also, we find a set of inflation parameters which produces PBHs evaporating now. Those PBHs may be responsible for antiproton fluxes observed by the BESS experiment.
As an extension of our previous study, we derive slow-roll conditions for multiple scalar fields which are non-minimally coupled with gravity and for generalized gravity theories of the form $f(ϕ,R)$. We provide simple formulae of the spectral indices of scalar/tensor perturbations in terms of the slow-roll parameters.
We re-examine approximations in the analytical calculation of the primordial spectrum of cosmological perturbation produced during inflation. Taking two inflation models (chaotic inflation and natural inflation) as examples, we numerically verify the accuracy of these approximations.
We propose an explanation for the present accelerated expansion of the universe that does not invoke dark energy or a modification of gravity and is firmly rooted in inflationary cosmology.
In this talk we propose a natural double inflation model in supergravity. Chaotic inflation first takes place by virtue of the Nambu-Goldstone-like shift symmetry. During chaotic inflation, an initial value of second inflation (new inflation) is set, which is adequately far from the local maximum of the potential due to the small linear term in the Kähler potential. Then, primordial fluctuations within the present horizon scale may be produced during both inflations. Primordial fluctuations responsible for anisotropies of the cosmic microwave background radiation and the large scale structure …
Inflation predicts the generation of cosmological perturbations. Usually, the power spectra for the scalar and tensor modes are calculated with help of the slow roll approximation. In the case of power law inflation an exact result is available. We compare the predictions for the cosmic microwave background anisotropies from the slow roll approximation with the exact results from power law inflation. We find that the so-called consistency check from the slow roll approximation, $C_2^T/C_2^S \approx -6.93 n_T$, may differ considerably from the exact result.
We investigate the recently proposed natural double inflation model in supergravity. Chaotic inflation first takes place by virtue of the Nambu-Goldstone-like shift symmetry. During chaotic inflation, an initial value of second inflation (new inflation) is set, which is adequately far from the local maximum of the potential due to the small linear term in the Kähler potential. Then, primordial fluctuations within the present horizon scale may be produced during both inflations. Primordial fluctuations responsible for anisotropies of the cosmic microwave background radiation and the large scale…
Using a recently introduced formalism we discuss slow-roll inflaton from Kaluza-Klein theory without the cylinder condition. In particular, some examples corresponding to polynomic and hyperbolic $ϕ$-potentials are studied. We find that the evolution of the fifth coordinate should be determinant for both, the evolution of the early inflationary universe and the quantum fluctuations.
We calculate the power spectra of primordial curvature and isocurvature perturbations from a general two field inflation model at next-to-leading order correction in a slow-roll expansion. In particular we calculate the spectral indices to second order in slow-roll parameters. We show that the cross-correlation of the curvature and isocurvature perturbations at the time of Hubble-exit during inflation is non-zero at first-order in slow-roll parameters. We apply our results to different classes of inflation, including inflaton and curvaton scenarios. The spectrum of primordial gravitational wav…
It is shown that in a number of scalar potentials with an unstable local maximum at the origin chaotic inflation is followed by new inflation if model parameters are appropriately chosen. In this model density fluctuation can have a large-amplitude peak on the comoving Hubble scale at the onset of the slow-roll new inflation and can result in formation of appreciable amount of primordial black holes on astrophysically interesting mass scales.
I describe a general approach to characterizing cosmological inflation outside the standard slow-roll approximation, based on the Hamilton-Jacobi formulation of scalar field dynamics. The basic idea is to view the equation of state of the scalar field matter as the fundamental dynamical variable, as opposed to the field value or the expansion rate. I discuss how to formulate the equations of motion for scalar and tensor fluctuations in situations where the assumption of slow roll is not valid. I apply the general results to the simple case of inflation from an ``inverted'' polynomial potential…
In this note we argue that the breaking of conformal invariance because of the coupling of a charged scalar field to gravity is not sufficient for the production of seed galactic magnetic fields during inflation.
We study an inflationary scenario where thermal inflation is followed by fast-roll inflation. This is a rather generic possibility based on the effective potentials of spontaneous symmetry breaking in the context of particle physics models. We show that a large enough expansion could be achieved to solve cosmological problems. However, the power spectrum of primordial density perturbations from the quantum fluctuations in the inflaton field is not scale invariant and thus inconsistent with observations. Using the curvaton mechanism instead, we can obtain a nearly scale invariant spectrum, prov…
I discuss folded inflation, an inflationary model embedded in a multi-dimensional scalar potential, such as the stringy landscape. During folded inflation, the field point evolves along a path that turns several corners in the potential. Folded inflation can lead to a relatively large tensor contribution to the Cosmic Microwave Background, while keeping all fields smaller than the Planck scale. I conjecture that if folded inflation generates a significant primordial tensor amplitude, this will generically be associated with non-trivial scale dependence in the spectrum of primordial scalar pert…
We draw attention to the possibility that inflation (i.e. accelerated expansion) might continue after the end of slow roll, during a period of fast oscillations of the inflaton field ϕ. This phenomenon takes place when a mild non-convexity inequality is satisfied by the potential V(ϕ). The presence of such a period of ϕ-oscillation-driven inflation can substantially modify reheating scenarios. In some models the effect of these fast oscillations might be imprinted on the primordial perturbation spectrum at cosmological scales.
The slow-roll approximation to inflation is ultimately justified by the presence of inflationary attractors for the orbits of the solutions of the dynamical equations in phase space. There are many indications that the inflaton field couples nonminimally to the spacetime curvature: the existence of attractor points for inflation with nonminimal coupling is demonstrated, subject to a condition on the inflaton potential and the value of the coupling constant.
We show that in the simplest theories of spontaneous symmetry breaking one can have a stage of a fast-roll inflation. In this regime the standard slow-roll condition |m^2| << H^2 is violated. Nevertheless, this stage can be rather long if |m| is sufficiently small. Fast-roll inflation can be useful for generating proper initial conditions for the subsequent stage of slow-roll inflation in the very early universe. It may also be responsible for the present stage of accelerated expansion of the universe. We also make two observations of a more general nature. First of all, the universe after a l…
We analyze the weak (2 sigma) evidence for a running spectral index seen in the three-year WMAP dataset and its implications for single field, slow roll inflation. We assume that the running is comparable to the central value found from the WMAP data analysis, and use the Hubble Slow Roll formalism to follow the evolution of the slow roll parameters. For all parameter choices consistent with a large, negative running, single field, slow roll inflation lasts less than 30 efolds after CMB scales leave the horizon. Thus, a definitive observation of a large negative running would imply that any in…
There are many inflationary models in which inflaton field does not satisfy the slow-roll condition. However, in such models, it is always difficult to generate the curvature perturbation during inflation. Thus, to generate the curvature perturbation, one must introduce another component to the theory. To cite a case, curvatons may generate dominant part of the curvature perturbation after inflation. However, we have a question whether it is unrealistic to consider the generation of the curvature perturbation during inflation without slow-roll. Assuming multi-field inflation, we encounter the …
The scenario of brane inflation without using the conventional slow-roll approximations has been investigated. Based on the mechanism of generating the curvature perturbations at the end of inflation, a new brane inflation paradigm was developed. The conditions for making a sufficiently large enough number of e-foldings and for generating the curvature perturbations without producing dangerous relics were also examined. Benefits of our scenario are subsequently discussed in detail.
The scale--independence of the primordial curvature perturbation suggests that it comes from the vacuum fluctuation during inflation of a light scalar field. This field may be the inflaton, or a different `curvaton' field. The observation of primordial non--gaussianity would be a smoking gun for the curvaton model, while the observation of gravitational waves originating during slow--roll inflation would rule out the model.
We study the WKB approximation beyond leading order for cosmological perturbations during inflation. To first order in the slow-roll parameters, we show that an improved WKB approximation leads to analytical results agreeing to within 0.1% with the standard slow-roll results. Moreover, the leading WKB approximation to second order in the slow-roll parameters leads to analytical predictions in qualitative agreement with those obtained by the Green's function method.
We not only reconstruct the slow-roll parameters for fit to the running spectral index from WMAP three-year data in the usual slow-roll inflation model and noncommutative inflation model, but also investigate the evolution of these slow-roll parameters. Requiring slow-roll inflation lasts more than 20 e-folds after CMB scales leave the horizon suggests that the potential at the last stage of inflation takes the form $V(ϕ)=V_0(1+{η_c\over 2}{(ϕ-ϕ_c)^2\over M_p^2})$, where $η_c$ is a constant. A natural mechanism to end inflation at $ϕ=ϕ_c$ is hybrid type inflation.
We extend the WKB method for the computation of cosmological perturbations during inflation beyond leading order and provide the power spectra of scalar and tensor perturbations to second order in the slow-roll parameters. Our method does not require that the slow-roll parameters be constant. Although leading and next-to-leading results in the slow-roll parameters depend on the approximation technique used in the computation, we find that the inflationary theoretical predictions obtained may reach the accuracy required by planned observations. In two technical appendices, we compare our techni…
We invert the second order, single field, general slow-roll formula for the power spectrum, to obtain a second order formula for inflationary parameters in terms of the primordial power spectrum.
We analyze the non-Gaussianity for primordial curvature perturbations generated in multi-scalar slow-roll inflation model including the model with non-separable potential by making use of $δN$ formalism. Many authors have investigated the possibility of large non-Gaussianity for the models with separable potential, and they have found that the non-linear parameter, $f_{NL}$, is suppressed by the slow-roll parameters. We show that for the non-separable models $f_{NL}$ is given by the product of a factor which is suppressed by the slow-roll parameters and a possible enhancement factor which is g…
We quantify the slow-roll corrections to primordial density perturbations arising from inflation driven by a four-dimensional scalar field with a monomial potential in a five-dimensional non-compact bulk spacetime. Although the difference between the classical brane-world solutions and standard four-dimensional solutions is large at early times, the change to the amplitude at late times of perturbations generated from quantum fluctuations is first-order in slow-roll parameters, leading to second-order slow-roll corrections to the spectral index. This confirms that the leading-order effects are…
In this paper we study the inflation model driven by the phantom field. We propose a possible exit from phantom inflation to our observational cosmology by introducing an additional normal scalar field, similar to hybrid inflation model. Then we discuss the primordial perturbation spectra from various phantom inflation models and give an interesting compare with those of normal scalar field inflation models.
I generalize the inflationary flow equations of Hoffman and Turner to arbitrary order in slow roll. This makes it possible to study the predictions of slow roll inflation in the full observable parameter space of tensor/scalar ratio $r$, spectral index $n$, and running $d n / d \ln k$. It also becomes possible to identify exact fixed points in the parameter flow. I numerically evaluate the flow equations to fifth order in slow roll for a set of randomly chosen initial conditions and find that the models cluster strongly in the observable parameter space, indicating a ``generic'' set of predict…
We study the level of primordial non-Gaussianity in slow-roll two-field inflation. Using an analytic formula for the nonlinear parameter f_nl in the case of a sum or product separable potential, we find that it is possible to generate significant non-Gaussianity even during slow-roll inflation with Gaussian perturbations at Hubble exit. In this paper we give the general conditions to obtain large non-Gaussianity and calculate the level of fine-tuning required to obtain this. We present explicit models in which the non-Gaussianity at the end of inflation can exceed the current observational bou…
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…
Improved general slow-roll formulae giving the primordial gravitational wave spectrum are derived in the present work. Also the first and second order general slow-roll inverse formulae giving the Hubble parameter $H$ in terms of the gravitational wave spectrum are derived. Moreover, the general slow-roll consistency condition relating the scalar and tensor spectra is obtained.
We comment on the choice of the quintessence potential, examining the slow-roll approximation in a minimally coupled theory of gravity. We make some considerations on the potential behaviors, the related γparameter, and their relationships to phantom cosmology.
Black hole formation in the framework of hybrid inflation is considered. It is shown that this model of inflation provides conditions for multiple black hole production.
As a nonbaryonic explanation of massive compact halo objects, a phenomenological model is presented which predicts formation of primordial black holes at a desired mass scale. The required feature of initial density fluctuation is realized making use of the primordially isocurvature fluctuation generated in an inflationary universe model with multiple scalar fields.
Recent observations suggest that the spectral index of the primordial perturbations is very close to unity, as expected in models of slow roll inflation. It is still possible for such models to produce spectra which are scale dependent. We present a formula for the spectrum produced by an arbitrary inflaton potential (within the context of slow roll models); this formula explicitly illustrates and accounts for the possiblity of scale dependence. A class of examples are studied and comparisons made with the standard slow roll formula.
The meaning of the inflationary slow-roll approximation is formalised. Comparisons are made between an approach based on the Hamilton-Jacobi equations, governing the evolution of the Hubble parameter, and the usual scenario based on the evolution of the potential energy density. The vital role of the inflationary attractor solution is emphasised, and some of its properties described. We propose a new measure of inflation, based upon contraction of the comoving Hubble length as opposed to the usual e-foldings of physical expansion, and derive relevant formulae. We introduce an infinite hierarch…
The standard calculation of the spectrum of density perturbations produced during inflation assumes (i) |n-1| << 1 and (ii) |dn/dlnk| << |n-1|. Slow-roll predicts and observations require (i), but neither slow-roll nor observations require (ii). In this paper I derive formulae for the spectrum, spectral index, and running of the spectral index, assuming only (i) and not (ii). I give a large class of observationally viable examples in which these general slow-roll formulae are accurate but the standard slow-roll formulae for the spectral index and running are incorrect.
We propose a general inverse formula for extracting inflationary parameters from the observed power spectrum of cosmological perturbations. Under the general slow-roll scheme, which helps to probe the properties of inflation in a model independent way, we invert the leading order, single field, power spectrum formula. We also give some physically interesting examples to demonstrate its wide applicability and illuminate its properties.
We examine the dynamics of inflation driven by multiple, interacting scalar fields and derive a multi field version of the Hubble slow roll expansion. We show that the properties of this expansion naturally generalize those of the single field case. We present an analogous hierarchy of slow roll parameters, and derive the system of ``flow'' equations that describes their evolution, and show that when this system is truncated at finite order, it can always be solved exactly. Lastly, we express the scalar and tensor perturbation spectra in terms of the slow roll parameters.
In addition to generating the appropriate perturbation power spectrum, an inflationary scenario must take into account the need for inflation to end subsequently. In the context of single-field inflation models where inflation ends by breaking of the slow-roll condition, we constrain the first and second derivatives of the inflaton potential using this additional requirement. We compare this with current observational constraints from the primordial spectrum and discuss several issues relating to our results.
I argue that the proposition that primordial perturbations were produced by inflation is most definitely falsifyable. Far from ``predicting anything you want'', the Gaussianity and passivity of inflationary perturbations strongly constrain the possible outcomes. For example, the next generation of CMB satellites could easily prove that the perturbations do not have an inflationary origin.
The dependence of cosmological and inflationary parameters on time during the last 60 e-folds in inflation is investigated using a slow-roll inflation model. The time dependence of the inflaton field is calculated for the case of chaotic inflation by a numerical method rather than the familiar approximations. It is found that the Hubble parameter and the spectral index decrease in the last 60 e-folds. The dependence of the power spectrum of the curvature perturbation on the size perturbation k is calculated numerically, and it is shown that the overall constant value of the power spectrum thus…
We investigate the accuracy of the slow-roll approximation for calculating perturbation spectra generated during inflation. The Hamilton-Jacobi formalism is used to evolve inflationary models with different histories. Models are identified for which the scalar power spectra computed using the Stewart-Lyth slow-roll approximation differ from exact numerical calculations using the Mukhanov perturbation equation. We then revisit the problem of primordial black holes generated by inflation. Hybrid-type inflationary models, in which the inflaton is trapped in the minimum of a potential, can produce…
We show how the quantum-to-classical transition of the cosmological fluctuations produced during an inflationary stage can be described using the consistent histories approach. We identify the corresponding histories in the limit of infinite squeezing. To take the decaying mode into account, we propose an extension to coarse-grained histories.
B-Pol is a medium-class space mission aimed at detecting the primordial gravitational waves generated during inflation through high accuracy measurements of the Cosmic Microwave Background (CMB) polarization. We discuss the scientific background, feasibility of the experiment, and implementation developed in response to the ESA Cosmic Vision 2015-2025 Call for Proposals.
We formalize the Hubble slow-roll formalism for inflationary dynamics in Randall-Sundrum Type II braneworld cosmologies, defining Hubble slow-roll parameters which can be used along with the Hamilton-Jacobi formalism. Focussing on the high-energy limit, we use these to calculate the exact power spectrum for power-law inflation, and then perturb around this solution to derive the higher-order expression for the density perturbations (sometimes called the Stewart-Lyth correction) of slow-roll braneworld models. Finally we apply our result to specific examples of potentials to calculate the corre…
An inflationary single field model with a non-trivial kinetic term for the inflaton is discussed. It is shown that it is possible to have large primordial non-gaussianities and large tensor-to-scalar ratio in a simple concrete model with just a scalar field and a generalized kinetic term for the inflaton field. This is potentially interesting in the prospect of new forthcoming observations.
We study how the noncommutative spacetime affects on inflation. First we obtain the noncommutative power spectrum of the curvature perturbations produced during inflation in the slow-roll approximation. This is the explicit $k$-dependent power spectrum up to first order in slow-roll parameters $ε_1 δ_1$ including the noncommutative parameter $μ$. In order to test the role of $μ$ further, we calculate the noncommutative power spectrum using the slow-roll expansion. We find corrections which arise from the change of pivot scale and a noncommutative parameter with $μ\not=$ constant. It turns out …
In this paper we investigate how the energy density due to a non-standard choice of initial vacuum affects the expansion of the universe during inflation. To do this we introduce source terms in the Friedmann equations making sure that we respect the relation between gravity and thermodynamics. We find that the energy production automatically implies a slow rolling cosmological constant. Hence we also conclude that there is no well defined value for the cosmological constant in the presence of sources. We speculate that a non-standard vacuum can provide slow roll inflation on its own.
