Phase Of Slow-roll Inflation Research Articles

Exploring the pre-inflationary dynamics in loop quantum cosmology with a DBI scalar field

Loop quantum cosmology is a symmetry-reduced application of loop quantum gravity. The theory predicts a bounce for the universe at the Planck scale and resolves the singularity of standard cosmology. The dynamics is also governed by an effective Hamiltonian, which predicts a modified Friedmann equation containing the quadratic terms of the energy density. The term plays an essential role in the high energy regime, but the equations return to the standard form in the low energy regime. The evolution of the universe in the pre-inflationary period is studied in the framework of loop quantum cosmology, where the DBI scalar field is assumed to be the dominant component of the universe. Using the numerical method, we provide the evolution of the DBI field. The background evolution shows that there are three phases as: bouncing phase, transition phase and slow-roll inflationary phase. There is also a short period of super-inflation just at the beginning of the bounce phase. The field first climbs the potential and then reaches the turning point where ϕ̇ disappears and the potential energy becomes the dominant part of the energy density. This is the time when the slow roll inflation begins and the field slowly rolls down the potential. The results indicate that there are a few e-fold expansions in the bounce phase, about N = 3.5–4, and the universe experiences about N = 59 e-fold expansions in the slow-roll inflation phase.

Novel higher-curvature variations of R2 inflation

We put forward novel extensions of Starobinsky inflation, involving a class of 'geometric' higher-curvature corrections that yield second-order Friedmann-Lema\^itre equations and second-order-in-time linearized equations around cosmological backgrounds. We determine the range of models within this class that admit an extended phase of slow roll inflation as an attractor. By embedding these theories in anti-de Sitter space, we derive holographic 'unitarity' bounds on the two dominant higher-order curvature corrections. Finally we compute the leading corrections to the spectral properties of scalar and tensor primordial perturbations, including the modified consistency relation $r=-8n_{T}$. Remarkably, the range of models singled out by holography nearly coincides with the current observational bounds on the scalar spectral tilt. Our results indicate that future observations have the potential to discriminate between different higher-curvature corrections considered here.

Pre-inflation dynamical behavior of warm inflation in loop quantum cosmology

Considering a constant dissipative coefficient [Formula: see text], the pre-inflation dynamical behaviors of warm inflation in the loop quantum cosmology scenario are discussed. We consider three sets of initial conditions. The evolution of the background can always be divided into three phases, namely super-inflation, damping, and slow-roll inflation phases, with the duration of each phase depending on the initial conditions. As an example, we compare the background evolution between [Formula: see text] and [Formula: see text] under special initial conditions and find that there is no slow-roll inflation phase for [Formula: see text] while the number of e-folds is about 60.209 for [Formula: see text].

Observational consequences of Bianchi I spacetimes in loop quantum cosmology

Anisotropies generically dominate the earliest stages of expansion of a homogeneous universe. They are particularly relevant in bouncing models, since shears grow in the contracting phase of the cosmos, making the isotropic situation unstable. This paper extends the study of cosmological perturbations in loop quantum cosmology (LQC) to anisotropic Bianchi I models that contain a bounce followed by a phase of slow-roll inflation. We show that, although the shear tensor dilutes and the universe isotropizes soon after the bounce, cosmic perturbations retain memory of this short anisotropic phase. We develop the formalism needed to describe perturbations in anisotropic, effective LQC, and apply it to make predictions for the cosmic microwave background (CMB), while respecting current observational constraints. We show that the anisotropic bounce induces: (i) anisotropic features in all angular correlation functions in the CMB, and in particular a quadrupolar modulation that can account for a similar feature observed in the temperature map by the Planck satellite, and (ii) quantum entanglement between scalar and tensor modes, that manifests itself in temperature-polarization (T-B and E-B) correlations in the CMB.

Galileon inflation field with three dark eras of the universe

In this paper, we discuss possible three early eras of the universe in the theoretical context of the Galilean cosmology. The first phase is a slow-roll inflation phase in which the friction term in the equations of motion dominates over the kinetic term. This is the initial vacuum state leading to quasi-de Sitter expansion. The second phase is where the cosmological perturbations are supposed to be generated. In this phase, the friction term is supposed to be negligible which leads to the appearance of the Galileon inflation field. The third phase is the reheating phase in the standard cosmology, where the oscillations of a canonical scalar field in the model lead to this phase. These three eras for the early universe are shown by a single master equation of the theory. However, we compute observational indices (the scalar spectral index parameter and the tensor-to-scalar ratio) for the era where the era that the perturbations are produced. Finally, we compare viability of the theoretical findings with the latest Planck observational data.

Inflation in loop quantum cosmology

We develop a consistent analytic approach to determine the conditions under which slow roll inflation can arise when the inflaton is the same scalar field that is responsible for the bounce in Loop Quantum Cosmology (LQC). We find that the requirement that the energy density of the field is fixed at the bounce having to match a critical density has important consequences for its future evolution. For a generic potential with a minimum, we find different scenarios depending on the initial velocity of the field and whether it begins life in a kinetic or potential energy dominated regime. For chaotic potentials that start in a kinetic dominated regime, we find an initial phase of superinflation independent of the shape of the potential followed by a damping phase which slows the inflaton down, forcing it to turnaround and naturally enter a phase of slow-roll inflation. If we begin in a potential energy dominated regime, then the field undergoes a period where the corrections present in LQC damp its evolution once again forcing it to turnaround and enter a phase of slow roll inflation. On the other hand we show for the Starobinsky potential that inflation never occurs when we begin in a potential dominated regime. In fact traditional Starobinsky inflation has to start in a kinetic energy dominated regime, with corresponding tighter constraints on the initial value of the field for successful inflation than in the conventional case. Comparing our analytic results to published numerical ones, we find remarkable agreement especially when we consider the different epochs that are involved. In particular the values of key observables obtained from the two approaches are in excellent agreement, opening up the possibility of obtaining analytic results for the evolution of the density perturbations in these models.

Tensor perturbations during inflation in a spatially closed Universe

In a recent paper [1], we studied the evolution of the background geometry and scalar perturbations in an inflationary, spatially closed Friedmann-Lemaȋtre-Robertson-Walker (FLRW) model having constant positive spatial curvature and spatial topology S3. Due to the spatial curvature, the early phase of slow-roll inflation is modified, leading to suppression of power in the scalar power spectrum at large angular scales. In this paper, we extend the analysis to include tensor perturbations. We find that, similarly to the scalar perturbations, the tensor power spectrum also shows suppression for long wavelength modes. The correction to the tensor spectrum is limited to the very long wavelength modes, therefore the resulting observable CMB B-mode polarization spectrum remains practically the same as in the standard scenario with flat spatial sections. However, since both the tensor and scalar power spectra are modified, there are scale dependent corrections to the tensor-to-scalar ratio that leads to violation of the standard slow-roll consistency relation.

Eternal inflation with noninflationary pocket universes

Eternal inflation produces pocket universes with all physically allowed vacua and histories. Some of these pocket universes might contain a phase of slow-roll inflation, some might undergo cycles of cosmological evolution and some might look like the galilean genesis or other "emergent" universe scenarios. Which one of these types of universe we are most likely to inhabit depends on the measure we choose in order to regulate the infinities inherent in eternal inflation. We show that the currently leading measure proposals, namely the global light-cone cut-off and its local counterpart, the causal diamond measure, as well as closely related proposals, all predict that we should live in a pocket universe that starts out with a small Hubble rate, thus favoring emergent and cyclic models. Pocket universes which undergo cycles are further preferred, because they produce habitable conditions repeatedly inside each pocket.

Observational hints on the Big Bounce

In this paper we study possible observational consequences of the bouncing cosmology. We consider a model where a phase of inflation is preceded by a cosmic bounce. While we consider in this paper only that the bounce is due to loop quantum gravity, most of the results presented here can be applied for different bouncing cosmologies. We concentrate on the scenario where the scalar field, as the result of contraction of the universe, is driven from the bottom of the potential well. The field is amplified, and finally the phase of the standard slow-roll inflation is realized. Such an evolution modifies the standard inflationary spectrum of perturbations by the additional oscillations and dampingon the large scales. We extract the parameters of the model from the observationsof the cosmic microwave background radiation. In particular, the value of inflaton mass is equal to m = (1.7±0.6)·1013 GeV. In our considerations we base on the seven years of observations made by the WMAP satellite. We propose the new observational consistency check forthe phase of slow-roll inflation. We investigate the conditions which have to be fulfilled to make the observations of the Big Bounce effects possible. We translate them to the requirements on the parameters of the model andthen put the observational constraints on the model. Based on assumption usually made in loop quantum cosmology, the Barbero-Immirzi parameter was shown to be constrained by γ < 1100 from the cosmological observations. We have compared the Big Bounce model with the standard Big Bang scenario and showed that the present observational data is not informative enough to distinguish these models.

Phase diagram for Nflation

Recently, it was showed that there is a large N phase transition in Nflation, in which when the number of fields is large enough, the slow roll inflation phase will disappear. In this brief report, we illustrate the phase diagram for Nflation, and discuss the entropy bound and some relevant results. It is found that near the critical point the number of fields saturates dS entropy.

Stretching the inflaton potential with kinetic energy

Inflation near a maximum of the potential is studied when nonlocal derivative operators are included in the inflaton Lagrangian. Such terms can impose additional sources of friction on the field. For an arbitrary spacetime geometry, these effects can be quantified in terms of a local field theory with a potential whose curvature around the turning point is strongly suppressed. This implies that a prolonged phase of slow-roll inflation can be achieved with potentials that are otherwise too steep to drive quasiexponential expansion. We illustrate this mechanism within the context of $p$-adic string theory.

Leading order corrections to the cosmological evolution of tensor perturbations inbraneworld

Tensor-type perturbations in the expanding braneworld of the Randall–Sundrum type areinvestigated. We consider a model composed of a slow-roll inflation phase and thesucceeding radiation phase. The effect of the presence of an extra dimension through thetransition to the radiation phase is studied, giving an analytic formula for leading ordercorrections.

Inflationary cosmology and quantization ambiguities in semiclassical loop quantum gravity

In loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar field to accelerate away from a minimum of its potential. In principle, this mechanism can generate the conditions that subsequently lead to slow-roll inflation. The consequences for this mechanism of various quantization ambiguities arising within loop quantum cosmology are considered. For the case of a quadratic potential, it is found that some quantization procedures are more likely to generate a phase of slow-roll inflation. In general, however, loop quantum cosmology is robust to ambiguities in the quantization and extends the range of initial conditions for inflation.

Particle production and symmetry restoration in collisions of vacuum bubbles

NASA/Fermilab Astrophysics CenterFermi National Accelerator Laboratory, Batavia, Illinois 60510In first-order inflation a phase transition is completed by the collisionsof expanding true-vacuum bubbles. If bubble collisions produce large num-bers of soft scalar particles carrying quantum numbers associated with aspontaneously broken symmetry, then symmetry restoration may occur ina “pre-heating” phase in a manner similar to symmetry restoration in thepre-heating phase of slow-roll inflation. Since bubble collisions lead to inho-mogeneities, there is the possibility of inhomogeneous symmetry restorationwhere restoration occurs only in the regions of wall collisions.PACS number(s): 98.80.Cq, 11.27.+d