Slow-roll Regime Research Articles

On non-Gaussianities in two-field poly-instanton inflation

In the context of Type IIB LARGE volume orientifold setup equipped with poly-instanton corrections, the standard single-field poly-instanton inflation driven by a 'Wilson' divisor volume modulus is generalized by the inclusion of respective axion modulus. This two-field dynamics results in a "Roulette" type inflation with the presence of several inflationary trajectories which could produce 50 (or more) e-foldings. The evolution of various trajectories along with physical observables are studied. The possibility of generating primordial non-Gaussianities in the slow-roll as well as in the beyond slow-roll region is investigated. We find that although the non- linearity parameters are quite small during the slow-roll regime, the same are significantly enhanced in the beyond slow-roll regime investigated up to the end of inflation.

Stability of the 3-form field during inflation

We consider the minimally coupled 3-form field, which has been considered as a candidate for realizing inflation. We have studied the conditions to avoid ghosts and Laplacian instabilities and found that some classes of potentials, e.g., the Mexican-hat, will in general be unstable. We then propose other classes of potentials which are instead free from any instability, drive a long enough slow-roll regime followed by an oscillatory epoch, and as a consequence, can provide successful inflation. Finally, we also provide stable potentials that lead to a small enough propagation speed for the scalar perturbations, making it possible for these models to produce non-Gaussianities.

Dark matter from dark energy-baryonic matter couplings

We present a scenario in which a scalar field dark energy is coupled to the trace of the energy momentum tensor of the baryonic matter fields. In the slow-roll regime, this interaction could give rise to the cosmological features of dark matter. We work out the cosmological background solutions and fit the parameters of the model using the Union 2 supernovae data set. Then, we develop cosmological perturbations up to linear order, and we find that the perturbed variables have an acceptable behavior, in particular, the density contrast of baryonic matter grows similar to that in the $\ensuremath{\Lambda}\mathrm{CDM}$ model for a suitable choice of the strength parameter of the coupling.

Aspects of noncanonical inflation

This paper reviews recent work by the authors on inflation in single-field models with noncanonical (higher-order) kinetic terms. Such terms arise naturally in an EFT approach to modelling inflation, and also from certain string theory embeddings, such as in DBI inflation. Theories containing such terms can support a period of noncanonical inflation which is smoothly connected to the usual slow-roll regime. We give a general formalism for finding solutions of the equations of motion corresponding to noncanonical inflation. However, not every Lagrangian with higher-power kinetic operators supports noncanonical inflation, and not every set of initial conditions in a suitable theory will give rise to an inflationary trajectory. We give some sufficient conditions required for a Lagrangian to support inflation in the non-canonical regime. Further, we investigate the problem of fine-tuning in these models. We find that noncanonical kinetic terms tend to reduce the severity of the fine-tuning problem in general, as long as a regime of noncanonical inflation is present.

Large change in the predicted number of small halos due to a small amplitude oscillating inflaton potential

A smooth inflaton potential is generally assumed when calculating the primordial power spectrum, implicitly assuming that a very small oscillation in the inflaton potential creates a negligible change in the predicted halo mass function. We show that this is not true. We find that a small oscillating perturbation in the inflaton potential in the slow-roll regime can alter significantly the predicted number of small halos. A class of models derived from supergravity theories gives rise to inflaton potentials with a large number of steps and many trans-Planckian effects may generate oscillations in the primordial power spectrum. The potentials we study are the simple quadratic (chaotic inflation) potential with superimposed small oscillations for small field values. Without leaving the slow-roll regime, we find that for a wide choice of parameters, the predicted number of halos change appreciably. For the oscillations beginning in the ${10}^{7}--{10}^{8}{M}_{\ensuremath{\bigodot}}$ range, for example, we find that only a 5% change in the amplitude of the chaotic potential causes a 50% suppression of the number of halos for masses between ${10}^{7}--{10}^{8}{M}_{\ensuremath{\bigodot}}$ and an increase in the number of halos for masses $<{10}^{6}{M}_{\ensuremath{\bigodot}}$ by factors $\ensuremath{\sim}15--50$. We suggest that this might be a solution to the problem of the lack of observed dwarf galaxies in the range ${10}^{7}--{10}^{8}{M}_{\ensuremath{\bigodot}}$. This might also be a solution to the reionization problem where a very large number of Population III stars in low mass halos are required.

Alternative Inflationary Scenario Due to Compact Extra Dimensions

The main goal of this paper is to give an alternative interpretation of space-like and time-like extra dimensions as a primary factor for inflation in the early universe. We introduce the 5-dimensional perfect fluid and compare the energy-momentum tensor for the bulk scalar field with space-like and time-like extra dimensions. It is shown, that additional dimensions can imply to negative pressure in the slow roll regime in the early higher-dimensional world.

Non-Gaussianity beyond slow roll in multi-field inflation

We study the non-Gaussianity generated during multiple-field inflation. We provide an exact expression for the bispectrum parameter fNL which is valid beyond the slow-roll regime, valid for certain classes of inflationary models. We then study a new, exact multi-field inflationary model considering a case where the bispectrum grows to observable values at the end of inflation. We show that in this case the trispectrum is also large and may even provide the dominant signal of non-Gaussianity.

ϕ4inflation is not excluded

We present counterexamples to the claim that the $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ inflaton potential is excluded by recent cosmological data. Finding counterexamples requires that the actually observed primordial fluctuations are generated at the onset of the slow-roll regime of inflation. This setup for the initial conditions is therefore different from the usual scenario of chaotic inflation where inflation starts long before the observed fluctuations are created. The primordial power spectrum of ``just enough'' chaotic inflation violates scale invariance in a way consistent with observations.

A POSSIBLE LATE TIME ΛCDM-LIKE BACKGROUND COSMOLOGY IN RELATIVISTIC MOND THEORY

In the framework of relativistic MOND theory (TeVeS), we show that a late time background ΛCDM cosmology can be attained by choosing a specific F(μ) that also meets the requirement for the existence of Newtonian and MOND limits. We investigate the dynamics of the scalar field ϕ under our chosen F(μ) and show that the slow roll regime of ϕ corresponds to a dynamical attractor, where the whole system reduces to ΛCDM cosmology.

CMB quadrupole depression produced by early fast-roll inflation: Monte Carlo Markov chains analysis of WMAP and SDSS data

Generically, the classical evolution of the inflaton has a brief fast-roll stage that precedes the slow-roll regime. The fast-roll stage leads to a purely attractive potential in the wave equations of curvature and tensor perturbations (while the potential is purely repulsive in the slow-roll stage). This attractive potential leads to a depression of the CMB quadrupole moment for the curvature and $B$-mode angular power spectra. A single new parameter emerges in this way in the early universe model: the comoving wave number ${k}_{1}$ characteristic scale of this attractive potential. This mode ${k}_{1}$ happens to exit the horizon precisely at the transition from the fast-roll to the slow-roll stage. The fast-roll stage dynamically modifies the initial power spectrum by a transfer function $D(k)$. We compute $D(k)$ by solving the inflaton evolution equations. $D(k)$ effectively suppresses the primordial power for $k<{k}_{1}$ and possesses the scaling property $D(k)=\ensuremath{\Psi}(k/{k}_{1})$ where $\ensuremath{\Psi}(x)$ is a universal function. We perform a Monte Carlo Markov chain analysis of the WMAP and SDSS data including the fast-roll stage and find the value ${k}_{1}=0.266\text{ }\text{ }{\mathrm{Gpc}}^{\ensuremath{-}1}$. The quadrupole mode ${k}_{Q}=0.242\text{ }\text{ }{\mathrm{Gpc}}^{\ensuremath{-}1}$ exits the horizon earlier than ${k}_{1}$, about one-tenth of an $e$-fold before the end of fast roll. We compare the fast-roll fit with a fit without fast roll but including a sharp lower cutoff on the primordial power. Fast roll provides a slightly better fit than a sharp cutoff for the temperature--temperature, temperature--$E$ modes, and $E$ modes--$E$ modes. Moreover, our fits provide nonzero lower bounds for $r$, while the values of the other cosmological parameters are essentially those of the pure $\ensuremath{\Lambda}\mathrm{CDM}$ model. We display the real space two point ${C}^{\mathrm{TT}}(\ensuremath{\theta})$ correlator. The fact that ${k}_{Q}$ exits the horizon before the slow-roll stage implies an upper bound in the total number of $e$-folds ${N}_{\mathrm{tot}}$ during inflation. Combining this with estimates during the radiation dominated era we obtain ${N}_{\mathrm{tot}}\ensuremath{\sim}66$, with the bounds $62<{N}_{\mathrm{tot}}<82$. We repeated the same analysis with the WMAP-5, ACBAR-2007, and SDSS data confirming the overall picture.

Inflation at the tip

We study the motion of a (space filling)D3-brane at the tip of a warped deformed conifold, looking for inflationary trajectories. In our set-up noanti-D3-brane is present and the inflaton potential is induced by threshold corrections to thesuperpotential. First we study the slow roll regime and find that, allowing for fine tuning,hilltop inflation compatible with CMB data can take place. Then we consider the DBI regimeand formulate a necessary condition for a phenomenologically viable inflationary stage. Inpassing, we propose a mechanism to cancel the large inflaton mass in the standard radialD3–anti-D3-brane inflation.

Constraints on brane inflation and cosmic strings

By considering simple, but representative, models of brane inflation from a singlebrane–antibrane pair in the slow roll regime, we provide constraints on the parametersof the theory imposed by measurements of the cosmic microwave background(CMB) anisotropies by WMAP (Wilkinson Microwave Anisotropy Probe) includinga cosmic string component. We find that inclusion of the string component iscritical in constraining parameters. In the most general model studied, whichincludes an inflaton mass term, as well as the brane–antibrane attraction, valuesns<1.02 are compatiblewith the data at 95% confidence level. We are also able to constrain the volume of the warped throat region(modulo factors dependent on the warp factor) and the value of the inflaton field to be<0.66MP at horizon exit. We also investigate models with a mass term.These observational considerations suggest that such models haver<2 × 10−5, whichcan only be circumvented in the fast roll regime, or by increasing the number of antibranes. Such a valueof r would not be detectable in any CMB polarization experiment likely in the near future, but theB-mode signal from the cosmic strings could be detectable. We present forecasts of what a similaranalysis using PLANCK data would yield and find that it should be possible to rule outGμ>6.5 × 10−8 usingjust the TT, TE and EE power spectra.

Inflationary perturbations in anisotropic backgrounds and their imprint on the cosmicmicrowave background

We extend the standard theory of cosmological perturbations to homogeneous butanisotropic universes. We present an exhaustive computation for the case of a Bianchi Imodel, with a residual isotropy between two spatial dimensions, which is undergoingcomplete isotropization at the onset of inflation; we also show how the computation can befurther extended to more general backgrounds. In the presence of a single inflaton field,there are three physical perturbations (precisely as in the isotropic case), whichare obtained (i) by removing gauge and non-dynamical degrees of freedom, and(ii) by finding the combinations of the remaining modes in terms of which thequadratic action of the perturbations is canonical. The three perturbations, whichlater in the isotropic regime become a scalar mode and two tensor polarizations(gravitational wave), are coupled to each other already at the linearized level during theanisotropic phase. This generates non-vanishing correlations between different modes ofthe cosmic microwave background (CMB) anisotropies, , which can be particularly relevant at large scales (and, potentially, be related to the largescale anomalies in the WMAP (Wilkinson Microwave Anisotropy Probe) data). As anexample, we compute the spectrum of the perturbations in this Bianchi I geometry,assuming that the inflaton is in a slow roll regime also in the anisotropic phase. For thissimple set-up, fixing the initial conditions for the perturbations appears more difficult thanin the standard case, and additional assumptions seem to be needed to provide predictionsfor the CMB anisotropies.

Evolution of large scale curvature fluctuations during the perturbative decay of the inflaton

We study the evolution of cosmological fluctuations during and after inflation driven by a scalar field coupled to a perfect fluid through a friction term. During the slow-roll regime for the scalar field, the perfect fluid is also frozen and isocurvature perturbations are generated. After the end of inflation, during the decay of the inflaton, we find that a change in the observationally relevant large scale curvature fluctuations is possible.

MSSM flat direction inflation: slow roll, stability, fine-tuning and reheating

We consider low scale slow roll inflation driven by the gauge-invariant flatdirections udd and LLe of the minimally supersymmetric standard model at thevicinity of a saddle point of the scalar potential. We study the stability of thesaddle point and the slow roll regime by considering radiative and supergravitycorrections. The latter are found to be harmless, but the former require a modestfine-tuning of the saddle point condition. We show that, while the inflaton decaysalmost instantly, full thermalization occurs late, typically at a temperatureT≈107 GeV, so that there is no gravitino problem. We also compute the renormalization grouprunning of the inflaton mass and relate it to slepton masses that may be within thereach of the LHC and could be precisely determined in a future linear colliderexperiment.

CMB quadrupole suppression. II. The early fast roll stage

Within the effective field theory of inflation, an initialization of the classical dynamics of the inflaton with approximate equipartition between the kinetic and potential energy of the inflaton leads to a brief fast roll stage that precedes the slow roll regime. The fast roll stage leads to an attractive potential in the wave equations for the mode functions of curvature and tensor perturbations. The evolution of the inflationary perturbations is equivalent to the scattering by this potential and a useful dictionary between the scattering data and observables is established. Implementing methods from scattering theory we prove that this attractive potential leads to a suppression of the quadrupole moment for CMB and B-mode angular power spectra. The scale of the potential is determined by the Hubble parameter during slow roll. Within the effective field theory of inflation at the grand unification (GUT) energy scale we find that if inflation lasts a total number of e-folds N{sub tot}{approx}59, there is a 10%-20% suppression of the CMB quadrupole and about 2%-4% suppression of the tensor quadrupole. The suppression of higher multipoles is smaller, falling off as 1/l{sup 2}. The suppression is much smaller for N{sub tot}>59, therefore if the observable suppression originates inmore » the fast roll stage, there is the upper bound N{sub tot}{approx}59.« less

Phantom without pathologies in the ultraviolet domain

We present a simple model in which the weak energy condition is violated for spatially homogeneous, slowly evolving fields. The excitations in Minkowski space in an external field with violation of the Lorentz invariance do not contain ghosts, tachyons, or superluminal modes at spatial momenta ranging from some low scale ε to the ultraviolet cutoff scale, while tachyons and possibly ghosts do exist for three-dimensional momenta less than ε. We show that in the absence of other matter, a slow-roll cosmological regime is possible. In this regime, the weak energy condition is violated, and yet homogeneity and isotropy are not completely spoiled (at the cost of fine tuning), because for a given conformal momentum, the tachyon mode increases during a sufficiently short time.

RUNNING OF THE SPECTRAL INDEX IN NONCOMMUTATIVE INFLATION

We study the cosmological implications of the space–space noncommutative inflation and present formulae for the spectral index and its running. Our results show that deviations from the spectral index and its running depend on the space–space noncommutativity length scale. We conclude that in the slow-roll regime of a typical inflationary scenario, space–space noncommutativity has negligible effects on both the spectral index and its running. Two classes of examples have been studied and comparisons made with the standard slow-roll formulae. The results show that the correction terms to the commutative case are positive for the spectral index and negative for the running of the spectral index. Nevertheless the spectral index in noncommutative spaces is less than one owing to the very small values of the correction terms.

NONCOMMUTATIVE SCALAR FIELD MINIMALLY COUPLED TO GRAVITY

A model for noncommutative scalar fields coupled to gravity based on the generalization of the Moyal product is proposed. Solutions compatible with homogeneous and isotropic flat Robertson-Walker spaces to first non-trivial order in the perturbation of the star-product are presented. It is shown that in the context of a typical chaotic inflationary scenario, at least in the slow-roll regime, noncommutativity yields no observable effect.

Slow-roll inflation for generalized two-field Lagrangians

We study the slow-roll regime of two-field inflation, in which the two scalar fields are also coupled through their kinetic terms. Such Lagrangians are motivated by particle physics and by scalar-tensor theories studied in the Einstein frame. We compute the power spectra of adiabatic and isocurvature perturbations on large scales to first order in the slow-roll parameters. We discuss the relevance of the extra coupling terms for the amplitude and indexes of the power spectra. Beyond the consistency condition which involves the amplitude of gravitational waves, additional relations may be found in particular models based on such Lagrangians: as an example, we find an additional general consistency condition in implicit form for Brans-Dicke theory in the Einstein frame.