Adiabatic and entropy perturbations from inflation

We explore the homogeneous background dynamics and the evolution of generated perturbations of cosmological inflation that is driven by multiple scalar fields interacting with a perfect fluid.Then we apply the method to warm inflation driven by two scalar fields and a radiation fluid, and present general results about the evolution of the inflaton and radiation. After decomposing the perturbations into adiabatic and entropy modes, we give the equation of motion of adiabatic and entropy perturbations on large scales. Then, we give numerical results of background and perturbation equations in a concrete model (the dissipative coefficient $\Gamma \propto H$). At last, we use the most recent observational data to constrain our models and give the observationally allowed regions of parameters. This work is a natural extension of warm inflation to multi-field cases.

Cosmological perturbations

Long wavelength limit of evolution of cosmological perturbations in the universe where scalar fields and fluids coexist

The cosmological birefringence caused by the coupling between the cosmic\nscalar field and the cosmic microwave background (CMB) photons through the\nChern-Simons term can rotate the polarization planes of the photons, and mix\nthe CMB E-mode and B-mode polarizations. The rotation angle induced by the\ndynamical scalar field can be separated into the isotropic background part and\nthe anisotropic fluctuations. The effect of the background part has been be\nstudied in the previous work (Zhao & Li, arXiv:1402.4324). In this paper, we\nfocus on the influence of the anisotropies of the rotation angle. We first\nassume that the cosmic scalar field is massless, consistent with other works,\nwe find that the rotation spectrum can be quite large, which may be detected by\nthe potential CMB observations. However, if the scalar field is identified as\nthe quintessence field, by detailed discussing both the entropy and adiabatic\nperturbation modes for the first time, we find that the anisotropies of the\nrotation angle are always too small to be detectable.In addition, as the main\ngoal of this paper, we investigate the effect of rotated polarization power\nspectrum on the detection of relic gravitational waves. we find that, the\nrotated B-mode polarization could be fairly large, and comparable with those\ngenerated by the gravitational waves. This forms a new contamination for the\ndetection of relic gravitational waves in the CMB. In particular, we also\npropose the method to reconstruct and subtract the rotated B-mode polarization,\nby which the residuals become negligible for the gravitational-wave detection.\n

We study Dirac-Born-Infeld inflation models with multiple scalar fields. We show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at the sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We show that this could strongly affect the observable curvature power spectrum as well as the amplitude of non-Gaussianities, although their shape remains as in the single-field Dirac-Born-Infeld case.

Exact models for Bianchi VI0 spacetimes with multiple scalar fields with exponential potentials have been derived and analysed. It has been shown that these solutions, when they exist, attract neighbouring solutions in the two cases corresponding to interacting and non-interacting fields. Unlike the results obtained in a previous work dealing with the late-time inflationary behaviour of Bianchi VI0 cosmologies, the knowledge of exact solutions has made possible to study in detail the occurrence of inflation before the asymptotic regime. As happened in preceding works, here as well inflation is more likely to happen with a higher number of non-interacting fields or a lower number of interacting scalar fields.

In low-density universe models the gravitational growth of density perturbations are slower than that in the Einstein–de Sitter critical model, and larger amplitudes are required at the decoupling time, in order that protoclusters may form to the present epoch. In this paper it is shown that, if the thermal model without secondary heating is assumed, the required amplitudes of entropy perturbations exceed the observational limit derived from the high degree of isotropy of the cosmic background radiation, as well as those of adiabatic perturbations.

Current data are in good agreement with the predictions of single field inflation. However, the hemispherical asymmetry, seen in the cosmic microwave background data, may hint at a potential problem. Generalizing to multi-field models may provide one possible explanation. A useful way of modeling perturbations in multi-field inflation is to investigate the projection of the perturbation along and perpendicular to the background fields' trajectory. These correspond to the adiabatic and isocurvature perturbations. However, it is important to note that in general there are no corresponding adiabatic and isocurvature fields. The purpose of this article is to highlight the distinction between a field redefinition and a perturbation projection. We provide a detailed derivation of the evolution of the isocurvature perturbation to show that no assumption of an adiabatic or isocurvature field is needed. We also show how this evolution equation is consistent with the field covariant evolution equations for the adiabatic perturbation in the flat field space limit.

The role of cosmic-ray-modified contact discontinuities and pressure balance structures in two-fluid cosmic-ray hydrodynamics in one Cartesian space dimension are investigated by means of analytic and numerical solution examples, as well as by weakly nonlinear asymptotics. The fundamental wave modes of the two-fluid cosmic-ray hydrodynamic equations in the long-wavelength limit consist of the backward and forward propagating cosmic-ray-modified sound waves, with sound speed dependent on both the cosmic-ray and thermal gas pressures; the contact discontinuity; and a pressure balance mode in which the sum ofthe cosmic ray and thermal gas pressure perturbations is zero. The pressure balance mode, like the contact discontinuity is advected with the background flow. The interaction of the pressure balance mode with the contact discontinuity is investigated by means of the method of multiple scales. The thermal gas and cosmic-ray pressure perturbations satisfy a linear diffusion equation, and entropy perturbations arising from nonisentropic initial conditions for the thermal gas are frozen into the fluid. The contact discontinuity and pressure balance eigenmodes both admit nonzero perturbations in the thermal gas, whereas the cosmic-ray-modified sound waves are isentropic. The total entropy perturbation is shared between the contact discontinuity and pressure balance eigenmodes, and examples are given in which there is a transfer of entropy between the two modes. In particular, N-wave type density disturbances are obtained which arise as a result of the entropy transfer between the two modes. A weakly nonlinear geometric optics perturbation expansion is used to study the long timescale evolution of the short-wavelength entropy wave and the thermal gas sound waves in a slowly varying, large-scale background flow. The weakly nonlinear geometric optics expansion is also used to generalize previous studies of squeezing instability for short-wavelength sound waves in the two fluid model, by including a weakly nonlinear wave steepening term that leads to shock formation, as well as the effect of long time and space dependence of the background flow. Implications of cosmic-ray-modified pressure balance structures and contact discontinuities in models of the interaction of traveling interplanetary shocks and compression and rarefraction waves with the solar wind termination shock are briefly discussed.

The dynamics of closed quantum systems may be manipulated by using an applied field to achieve a control objective value for a physical goal. The functional relationship between the applied field and the objective value forms a quantum control landscape, and the optimization process consists of a guided climb up the landscape from the bottom to the top. Two classes of landscape features are important for understanding the ease of finding an optimal control field. The first class of topological landscape features has been proven to be especially simple in that no suboptimal local maxima exist (upon satisfaction of certain assumptions), which partially accounts for the ease of finding optimal fields. Complementary to the topology, the second class of features entails the landscape structure, characterizing the sinuous nature of the paths leading to an optimal control field. Previous work found that the landscape structure is also particularly simple, as excursions up the landscape guided by a gradient algorithm correspond to nearly straight paths through the space of control fields. In this paper we take an alternative approach to examining landscape structure by constructing, and then following, exactly straight trajectories in control space. Each trajectory starts at a corresponding point on the bottom of the landscape and ends at an associated point on the top, with the observable values taken either as the state-to-state transition probability, the expectation value of a general observable, or the distance from a desired unitary transformation. In some cases the starting point is at a suboptimal critical-point saddle, with the goal, again, of following a straight field path to the optimal objective yield or another suboptimal critical point. We find that the objective value almost always rises monotonically upon following a straight control path from one critical point to another, which shows that landscape structure is very simple, being devoid of rough bumps and gnarled ``twists and turns''. An analysis reveals that the generally featureless nature of quantum control landscapes can be understood in terms of the occurrence of many interfering quantum pathways contributing while traversing the landscape, essentially smoothing out the terrain. These results also provide a basis for further studies to seek a new efficient algorithm to discover optimal fields by means of taking into account the inherently smooth landscape structure.

This paper demonstrates that existing upper bounds on the magnitude of cosmological dark matter and baryon isocurvature fluctuations can be translated into stringent constraints on the parameter space of moduli fields of supersymmetric theories, defined in terms of mσ (modulus mass) and σinf (modulus vacuum expectation value at the end of inflation). For the sake of concreteness, we assume here a quadractic modulus potential and we focus on high-scale inflationary models. These constraints are complementary to previously existing bounds from big-bang nucleosynthesis, therefore the moduli problem becomes worse at the level of cosmological perturbations. In particular, if the inflationary scale Hinf∼1013 GeV, particle physics scenarios which predict high moduli masses mσ ≳ 10–100 TeV are plagued by the perturbative moduli problem, even though they evade big-bang nucleosynthesis constraints. This perturbative moduli problem is somewhat relaxed if the modulus is made heavy during inflation, with effective mass ≳Hinf.

In brane-world cosmologies of Randall-Sundrum type, we show that evolution of large-scale curvature perturbations may be determined on the brane, without solving the bulk perturbation equations. The influence of the bulk gravitational field on the brane is felt through a projected Weyl tensor which behaves effectively like an imperfect radiation fluid with anisotropic stress. We define curvature perturbations on uniform density surfaces for both the matter and Weyl fluids, and show that their evolution on large scales follows directly from the energy conservation equations for each fluid. The total curvature perturbation is not necessarily constant for adiabatic matter perturbations, but can change due to the Weyl entropy perturbation. To relate this curvature perturbation to the longitudinal gauge metric potentials requires knowledge of the Weyl anisotropic stress which is not determined by the equations on the brane. We discuss the implications for large-angle anisotropies on the cosmic microwave background sky.

In this paper we wish to point out the possibility of using a complex scalar field in a constant roll inflationary model, as needed for observational viability. We extend the idea of real field inflaton with constant rate of roll to a complex field, showing the feasibility of solving Einstein Klein-Gordon equations constrained by an appropriate form of constant roll definition. As compared to the well known (two-parametric class of) real field models, there is one more degree of flexibility in constant roll inflationary solutions which is represented by an arbitrary function of time, γ(t). We work with an arbitrary but constant function γ (where γ = 0 refers to the corresponding real field model) and find new inflationary class of potentials. In this class of models, the behavior of real and complex field models are similar in some aspects, for example the solutions with large constant roll parameter are not stable and should be considered as early time transients. These field solutions relax at late time on a dual attractor trajectory. However, complex fields phase space trajectories reach this stable regime after real fields. We performed the stability analysis on γ function space solutions and found that dynamically stable trajectories in phase space are stable under γ variations. We extended this study by considering multifield models of constant roll inflation with non-canonical kinetic terms. By enlarging the size of field space, we showed that a multifield constant roll model is dynamically a single field effective theory. If field space is parametrized by N non-canonical fields, there will be N free parameters in the potential that can be attributed to the interaction between the fields.

We propose a scenario for realizing inflation in the framework of supersymmetric $B\ensuremath{-}L$ extension of the standard model. We find that one of the associated right-handed sneutrinos (the superpartner of the standard model singlet fermion) can provide a new nontrivial inflationary trajectory at tree level (therefore breaking $B\ensuremath{-}L$ during inflation). As soon as the inflation ends, the right-handed sneutrino falls into the supersymmetric vacuum, with a vanishing vacuum expectation value, so that $B\ensuremath{-}L$ symmetry is restored. In this class of models, the $B\ensuremath{-}L$ gauge symmetry will be radiatively broken at a TeV scale and light neutrino masses are generated through the inverse seesaw mechanism.

We introduce a frame-covariant formalism for inflation of scalar-curvature theories by adopting a differential geometric approach which treats the scalar fields as coordinates living on a field-space manifold. This ensures that our description of inflation is both conformally and reparameterization covariant. Our formulation gives rise to extensions of the usual Hubble and potential slow-roll parameters to generalized fully frame-covariant forms, which allow us to provide manifestly frame-invariant predictions for cosmological observables, such as the tensor-to-scalar ratio r, the spectral indices nR and nT, their runnings αR and αT, the non-Gaussianity parameter fNL, and the isocurvature fraction βiso. We examine the role of the field space curvature in the generation and transfer of isocurvature modes, and we investigate the effect of boundary conditions for the scalar fields at the end of inflation on the observable inflationary quantities. We explore the stability of the trajectories with respect to the boundary conditions by using a suitable sensitivity parameter. To illustrate our approach, we first analyze a simple minimal two-field scenario before studying a more realistic nonminimal model inspired by Higgs inflation. We find that isocurvature effects are greatly enhanced in the latter scenario and must be taken into account for certain values in the parameter space such that the model is properly normalized to the observed scalar power spectrum PR. Finally, we outline how our frame-covariant approach may be extended beyond the tree-level approximation through the Vilkovisky–De Witt formalism, which we generalize to take into account conformal transformations, thereby leading to a fully frame-invariant effective action at the one-loop level.