The vector curvaton

Statistical anisotropy from vector curvaton in D-brane inflation

We derive analytical expressions for the power spectra at the end of inflation in theories with two inflaton fields and non-canonical kinetic terms. We find that going beyond the slow-roll approximation is necessary and that the nature of the non-canonical terms have an important impact on the final power spectra at the end of inflation. We study five models numerically and find excellent agreement with our analytical results. Our results emphasise the fact that going beyond the slow-roll approximation is important in times of high-precision data coming from cosmological observations.

We investigate the dynamics of inflation models driven by multiple, decoupled scalar fields and calculate the Hubble parameter and the amplitude of the lightest field at the end of inflation. The results are very simple and similar to those of the single field inflation, mainly depending on the underlying spectrum of the masses. The mass distribution is heavily constrained by the power spectrum of density perturbations P and the spectral index ns. The overall mass scale gives the amplitude of P and ns is affected by the number of fields and the spacing between masses in the distribution. The drop‐out effect of the massive fields makes the perturbation spectrum typically redder than the single field inflation spectrum. We illustrate this using two different mass distributions.

With the enhancement mechanism provided by a noncanonical kinetic term with a peak, the amplitude of primordial curvature perturbations can be enhanced by seven orders of magnitude at small scales while keeping to be consistent with observations at large scales. The peak function and inflationary potential are not restricted in this mechanism. We use the Higgs model and T-model as examples to show how abundant primordial black hole dark matter with different mass and scalar induced secondary gravitational waves with different peak frequency are generated. We also show that the enhanced power spectrum for the primordial curvature perturbations and the energy density of the scalar induced secondary gravitational waves can have either a sharp peak or a broad peak. The primordial black holes with the mass around $10^{-14}-10^{-12} M_{\odot}$ produced with the enhancement mechanism can make up almost all dark matter, and the scalar induced secondary gravitational waves accompanied with the production of primordial black holes can be tested by the pulsar timing arrays and spaced based gravitational wave observatory. Therefore, the mechanism can be tested by primordial black hole dark matter and gravitational wave observations.

We study the generation of the primordial curvature perturbation in multi-field inflation. Considering both the evolution of the perturbation during inflation and the effects generated at the end of inflation, we present a general formula for the curvature perturbation. We provide the analytic expressions of the power spectrum, spectral tilt and non-Gaussianity for the separable potentials of two inflaton scalars, and apply them to some specific models.

We investigate the perturbation theory of a fixed-norm, timelike\nLorentz-violating vector field. After consistently quantizing the vector field\nto put constraints on its parameters, we compute the primordial spectra of\nperturbations generated by inflation in the presence of this vector field. We\nfind that its perturbations are sourced by the perturbations of the inflaton;\nwithout the inflaton perturbation the vector field perturbations decay away\nleaving no primordial spectra of perturbations. Since the inflaton perturbation\ndoes not have a spin-1 component, the vector field generically does not\ngenerate any spin-1 ``vector-type'' perturbations. Nevertheless, it will modify\nthe amplitude of both the spin-0 ``scalar-type'' and spin-2 ``tensor-type''\nperturbation spectra, leading to violations of the inflationary consistency\nrelationship.\n

Scalar-induced gravitational waves (SIGWs) are attracting growing attention for probing extremely short-scale scalar perturbations via gravitational wave measurements. In this paper, we investigate the SIGWs from statistically anisotropic scalar perturbations, which are motivated in inflationary scenarios in the presence of, e.g., a vector field. While the ensemble average of the SIGW energy spectrum is isotropic for the standard statistically isotropic scalar perturbations, the statistical anisotropy in the source introduces the multipole moments of the differential SIGW energy spectrum. We consider quadrupole anisotropy in the scalar power spectrum and show that the SIGW spectrum has anisotropies up to $\ensuremath{\ell}=4$. We present generic formulas of the multipole moments and then apply them to the delta-function-like and log-normal source spectra. We find analytic expressions for the former case and show that the infrared scalings of the multipole moments are the same as the isotropic SIGWs. Interestingly, the monopole has an additional local minimum in the high-$k$ tail, a key feature to distinguish from the isotropic SIGWs. The latter log-normal case is analytic for the narrow-peak source, and we perform the numerical calculation for the broad peak. As one expects, the multipole moments become broader with increasing source width. Our results are helpful to test the isotropy of primordial density perturbations at extremely small scales through SIGWs.

We study the instability of a scalar field at the end of hybrid inflation, using both analytical techniques and numerical simulations. We improve previous studies by taking the inflaton field fully into account, and show that the range of unstable modes depends sensitively on the velocity of the inflaton field, and thereby on the Hubble rate, at the end of inflation. If topological defects are formed, their number density is determined by the shortest unstable wavelength. Finally, we show that the oscillations of the inflaton field amplify the inhomogeneities in the energy density, leading to local symmetry restoration and faster thermalization. We believe this explains why tachyonic preheating is so effective in transferring energy away from the inflaton zero mode.

It is natural to ask what happened, between the end of inflation and the beginning of the known history. To answer that question, we have to make assumptions which may or may not be correct. Most importantly, we have to make an assumption about the energy density at the end of inflation. As we saw in Chap. 14, the energy density at the end of inflation might be anything up to 1064 times as big as at the beginning of the known history.

Well-known causality arguments show that events occurring during or at the end of inflation, associated with reheating or preheating, could contribute a blue component to the spectrum of primordial curvature perturbations, with the dependence k3. We explore the possibility that they could be observably large in CMB, LSS, and Lyman-α data. We find that a k3 component with a cutoff at some maximum k can modestly improve the fits (Δχ2 = 2.0, 5.4) of the low multipoles (ℓ ~ 10–50) or the second peak (ℓ ~ 540) of the CMB angular spectrum when the three-year WMAP data are used. Moreover, the results from WMAP are consistent with the CBI, ACBAR, 2dFGRS, and SDSS data when they are included in the analysis. Including the SDSS galaxy clustering power spectrum, we find weak positive evidence for the k3 component at the level of Δχ2′ = 2.4, with the caveat that the nonlinear evolution of the power spectrum may not be properly treated in the presence of the k3 distortion. To investigate the high-k regime, we use the Lyman-α forest data (LUQAS, Croft et al., and SDSS Lyman-α); here we find evidence at the level Δχ2′ = 3.8. Considering that there are two additional free parameters in the model, the above results do not give a strong evidence for features; however, they show that surprisingly large bumps are not ruled out. We give constraints on the ratio between the k3 component and the nearly scale-invariant component, r3 < 1.5, over the range of wave numbers 2.3 × 10-3 Mpc -1 < k < 8.2 Mpc -1. We also discuss theoretical models which could lead to the k3 effect, including ordinary hybrid inflation and double D-term inflation models. We show that the well-motivated k3 component is also a good representative of the generic spikelike feature in the primordial perturbation power spectrum.

We discuss new models of an “affine” theory of gravity in multidimensional space-times with symmetric connections. We use and develop ideas of Weyl, Eddington, and Einstein, in particular, Einstein’s proposal to specify the space-time geometry by the use of the Hamilton principle. More specifically, the connection coefficients are determined using a “geometric” Lagrangian that is an arbitrary function of the generalized (nonsymmetric) Ricci curvature tensor (and, possibly, of other fundamental tensors) expressed in terms of the connection coefficients regarded as independent variables. Such a theory supplements the standard Einstein gravity with dark energy (the cosmological constant, in the first approximation), a neutral massive (or tachyonic) vector field (vecton), and massive (or tachyonic) scalar fields. These fields couple only to gravity and can generate dark matter and/or inflation. The new field masses (real or imaginary) have a geometric origin and must appear in any concrete model. The concrete choice of the geometric Lagrangian determines further details of the theory, for example, the nature of the vector and scalar fields that can describe massive particles, tachyons, or even “phantoms.” In “natural” geometric theories, which are discussed here, dark energy must also arise. We mainly focus on intricate relations between geometry and dynamics while only very briefly considering approximate cosmological models inspired by the geometric approach.

We study the development of entropy fluctuations in brane inflation in a warped throat, including the brane–antibrane tachyon as the waterfall field. We find that there is a period at the end of inflation during which the entropy mode associated with the tachyon field increases exponentially. In turn, the induced entropy seeds a contribution to the curvature fluctuation on cosmological scales which grows rapidly and could exceed the primordial curvature perturbation. We identify parameter values for which in the absence of backreaction the induced curvature fluctuations are larger than the primordial adiabatic ones. In the specific model we study, however, backreaction limits the growth of the entropy fluctuations. We discuss situations in which backreaction effects are less constraining. The lesson of our investigation is that the study of the development of entropy fluctuations at the end of the period of inflation can lead to constraints on models of brane inflation and suggests that the curvaton mechanism may contribute significantly to the spectrum of cosmological perturbations.

According to the literature, there is a significant number of inflationary models that lack observational and conceptual support. Such is the case with recent observations regarding a possible preferred direction in the universe, which imply that scalar fields are not suitable as generators of inflation. On the other hand, recent inflationary models that employ vector fields require a modification of gravity and/or fine-tuning in order to have the appropriate behaviour; besides, they lack naturalness and do not exhibit one of the most important properties of theories in modern physics: the existence of internal symmetries. In this paper, we present a vector inflationary model embodied in a SU(2) gauge theory composed of three vector fields over which we make a well supported assumption about their direction, their norm, and their time dependence. Such an assumption allows us to obtain isotropic inflation in a rotationally invariant background if we take into account the homomorphic relation between SU(2) and O(3) groups. In this scenario, we study the dynamics of the vector fields and the conditions to obtain accelerated expansion; we also analyze the evolution of the system in the slow-roll regime and obtain numerical solutions for the equations of motion. Due to the naturalness of the model, the observed numerical results and the generality of the proposed assumption, we conclude that this type of inflation represents well the behaviour of the primordial universe in view of the most recent observations.

We consider a scenario in which primordial scalar perturbations aregenerated when complex conformal scalar field rolls down its negativequartic potential. Initially, these are the perturbations of thephase of this field; they are converted into the adiabaticperturbations at a later stage. A potentially dangerous feature ofthis scenario is the existence of perturbations in the radial fielddirection, which have red power spectrum. We show, however, that tothe linear order in the small parameter — the quartic self-coupling— the infrared effects are completely harmless, as they can beabsorbed into field redefinition. We then evaluate the statisticalanisotropy inherent in the model due to the existence of thelong-ranged radial perturbations. To the linear order in the quarticself-coupling the statistical anisotropy is free of the infraredeffects. The latter show up at the quadratic order in theself-coupling and result in the mild (logarithmic) enhancement of thecorresponding contribution to the statistical anisotropy. Theresulting statistical anisotropy is a combination of a larger termwhich, however, decays as momentum increases, and a smaller termwhich is independent of momentum.

We investigate the production of dark matter from metric perturbations produced during inflation or in standard cosmology. Perturbations break Weyl flatness of the Friedmann-Lemaître-Robertson-Walker metric, allowing conformally coupled fields-in particular, fermions studied here-to be produced even when their mass is negligible. Particle production can be computed by studying the Bogoliubov transformation induced by the stochastic background. For perturbations generated during inflation, we present a closed formula for the resulting abundance of particles that depends solely on the power spectrum of curvature perturbations at the end of inflation. This production mechanism can be dominant especially if the amplitude of curvature perturbations is enhanced for modes that exit the horizon toward the end of inflation. In the simplest scenario, the critical dark matter abundance is reproduced for M≳10^{6} GeV.