We study non-linear primordial adiabatic and isocurvature perturbations and their non-Gaussianity. After giving a general formulation in the context of an extended delta N-formalism, we analyse in detail two illustrative examples. The first is a mixed curvaton-inflaton scenario in which fluctuations of both the inflaton and a curvaton (a light isocurvature field during inflation) contribute to the primordial density perturbation. The second example is that of double inflation involving two decoupled massive scalar fields during inflation. In the mixed curvaton-inflaton scenario we find that the bispectrum of primordial isocurvature perturbations may be large and comparable to the bispectrum of adiabatic curvature perturbations.
We analyze the trajectories for multifield DBI inflation, which can arise in brane inflation models, and show that the trajectories are the same as in typical slow roll inflation. We calculate the power spectrum and find that the higher derivative terms of the DBI action lead to a suppression of the contribution from the isocurvature perturbations. We also calculate the bispectrum generated by the isocurvature perturbation, and find that it leads to distinctive features.
We develop a formalism to study non-Gaussianity in both curvature and isocurvature perturbations. It is shown that non-Gaussianity in the isocurvature perturbation between dark matter and photons leaves distinct signatures in the CMB temperature fluctuations, which may be confirmed in future experiments, or possibly, even in the currently available observational data. As an explicit example, we consider the QCD axion and show that it can actually induce sizable non-Gaussianity for the inflationary scale, H_{inf} = O(10^9 - 10^{11})GeV.
We study the effect of primordial isocurvature perturbations on non-Gaussian properties of CMB temperature anisotropies. We consider generic forms of the non-linearity of isocurvature perturbations which can be applied to a wide range of theoretical models. We derive analytical expressions for the bispectrum and the Minkowski Functionals for CMB temperature fluctuations to describe the non-Gaussianity from isocurvature perturbations. We find that the isocurvature non-Gaussianity in the quadratic isocurvature model, where the isocurvature perturbation S is written as a quadratic function of the…
Low energy effective field theories motivated by string theory will likely contain several scalar moduli fields which will be relevant to early Universe cosmology. Some of these fields are expected to couple with non-standard kinetic terms to gravity. In this paper, we study the splitting into adiabatic and isocurvature perturbations for a model with two scalar fields, one of which has a non-standard kinetic term in the Einstein-frame action. Such actions can arise, e.g., in the Pre-Big-Bang and Ekpyrotic scenarios. The presence of a non-standard kinetic term induces a new coupling between adi…
We study cosmological perturbations in two-field inflation, allowing for non-standard kinetic terms. We calculate analytically the spectra of curvature and isocurvature modes at Hubble crossing, up to first order in the slow-roll parameters. We also compute numerically the evolution of the curvature and isocurvature modes from well within the Hubble radius until the end of inflation. We show explicitly for a few examples, including the recently proposed model of `roulette' inflation, how isocurvature perturbations affect significantly the curvature perturbation between Hubble crossing and the …
We investigate the evolution of cosmological perturbations in scenarios with a quintessence scalar field, both analytically and numerically. In the tracking regime for quintessence, we find the long wavelength solutions for quintessential perturbations. We discuss the possibility of isocurvature modes generated by the quintessence sector and their impact on observations.
We study adiabatic and isocurvature perturbations produced during a period of cosmological inflation. We compute the power spectra and cross spectra of the curvature and isocurvature modes, as well as the tensor perturbation spectrum in terms of the slow-roll parameters. We provide two consistency relations for the amplitudes and spectral indices of the corresponding power spectra. These relations represent a definite prediction and a test of inflationary models which should be adopted when studying cosmological perturbations through the Cosmic Microwave Background in forthcoming satellite exp…
Light scalars may be ubiquitous in nature, and their quantum fluctuations can produce large non-Gaussianity in the cosmic microwave background temperature anisotropy. The non-Gaussianity may be accompanied with a small admixture of isocurvature perturbations, which often have correlations with the curvature perturbations. We present a general method to calculate the non-Gaussianity in the adiabatic and isocurvature perturbations with and without correlations, and see how it works in several explicit examples. We also show that they leave distinct signatures on the bispectrum of the cosmic micr…
The Ekpyrotic scenario assumes that our visible Universe is a boundary brane in a five-dimensional bulk and that the hot Big Bang occurs when a nearly supersymmetric five-brane travelling along the fifth dimension collides with our visible brane. We show that the generation of isocurvature perturbations is a generic prediction of the Ekpyrotic Universe. This is due to the interactions in the kinetic terms between the brane modulus parametrizing the position of the five-brane in the bulk and the dilaton and volume moduli. We show how to separate explicitly the adiabatic and isorcuvature modes b…
We present a class of very simple inflationary models of two scalar fields which leads to nongaussian isothermal perturbations with "blue" spectrum, n > 1. One of the models is inspired by supersymmetric theories where light scalar fields naturally acquire masses of the order of the Hubble constant H during inflation. Another model presumes that one of the fields has a nonminimal interaction with gravity. By a slight modification of parameters of these models one can obtain either gaussian isothermal perturbations, or nongaussian adiabatic perturbations with n > 1.
We discuss the residual isocurvature perturbations, fully-correlated with the curvature perturbation, that are automatic in the curvaton scenario if curvaton decay is sufficiently late. We contrast these residual isocurvature perturbations with the generally un-correlated `intrinsic' isocurvature perturbation generated by an additional field such as the axion. We present a general formula for the residual isocurvature perturbations, referring only to the generation of the relevant quantity (Cold Dark Matter, baryon number or lepton number) in an unperturbed universe. Specific formulas for the …
We investigate the isocurvaton model, in which the isocurvature perturbation plays a role in suppressing the curvature perturbation, and large non-Gaussianity and gravitational waves can be produced with no isocurvature perturbation for dark matter. We show that in the slow roll non-interacting multi-field theory, the isocurvaton mechanism can not be realized. This result can also be generalized to most of the studied models with generalized kinetic terms. We also study the implications for the curvaton model. We show that there is a combined constraint for curvaton on non-Gaussianity, gravita…
It is shown that double inflation (two minimally coupled massive scalar fields) can produce correlated adiabatic and isocurvature primordial perturbations. Depending on the two relevant parameters of the model, the contributions to the primordial perturbations are computed, with special emphasis on the correlation, which can be quantitatively represented by a correlation spectrum. Finally the primordial spectra are evolved numerically to obtain the CMBR anisotropy multipole expectation values. It turns out that the existence of mixing and correlation can alter very significantly the temperatur…
In a recent paper of Linde and Mukhanov, a hybrid inflationary model with nongaussian density perturbations and a ``blue'' spectral index n > 1 was presented. In this comment we point out that this model can be considered as a particular realization of the general framework for the spectrum and statistics of the CMBR we proposed in astro-ph/9611208, based on the hypothesis of conformal invariance. The implication of this hypothesis is that density perturbations are nongaussian with a spectral index n > 1.
We investigate the noncommutative effect on the non-Gaussianities of primordial cosmological perturbation. In the lowest order of string length and slow-roll parameter, we find that in the models with small speed of sound the noncommutative modifications could be observable if assuming a relatively low string scale. In particular, the dominant modification of non-Gaussianity estimator f_{NL} could reach O(1) in DBI inflation and K-inflation. The corrections are sensitive to the speed of sound and the choice of string length scale. Moreover the shapes of the corrected non-Gaussianities are dist…
Recently high quality data of the cosmic microwave background anisotropies have been published. In this work we study to which extent the cosmological parameters determined by using this data depend on assumptions about the initial conditions. We show that for generic initial conditions, not only the best fit values are very different but, and this is our main result, the allowed parameter range enlarges dramatically.
In D-term inflation models, Affleck-Dine baryogenesis produces isocurvature density fluctuations. These can be perturbations in the baryon number, or, in the case where the present neutralino density comes directly from B-ball decay, perturbations in the number of dark matter neutralinos. The latter case results in a large enhancement of the isocurvature perturbation. The requirement that the deviation of the adiabatic perturbations from scale invariance due to the Affleck-Dine field is not too large then imposes a lower bound on the magnitude of the isocurvature fluctuation of about $10^{-2}$…
We propose a primeval baryon isocurvature model in the context of the Affleck-Dine (AD) baryogenesis mechanism. Quantum fluctuations of the AD field during inflation produce fluctuations in the baryon number. We obtain a model which gives both the appropriate baryon to entropy ratio of the order $10^{-11}$ and the gaussian baryon isocurvature perturbation of the order $10^{-3}$ at the break of the spectrum 1 Mpc with the steep spectrum $n=-1.5$ on large scales >1 Mpc.
We obtain very stringent bounds on the possible cold dark matter, baryon and neutrino isocurvature contributions to the primordial fluctuations in the Universe, using recent cosmic microwave background and large scale structure data. In particular, we include the measured temperature and polarization power spectra from WMAP and ACBAR, as well as the matter power spectrum from the 2dF galaxy redshift survey. Neglecting the possible effects of spatial curvature, tensor perturbations and reionization, we perform a Bayesian likelihood analysis with nine free parameters, and find that the amplitude…
We consider the detection possibilities of isocurvature fluctuations in the future CMB satellite experiments MAP and Planck for different cosmological reference models. We present a simultaneous 10 parameter fit (8 for the case of open model) to determine the correlations between the cosmological parameters, including isocurvature cold dark matter contribution to the anisotropy. Assuming that polarization information can be fully exploited, we find that an isocurvature perturbation can be detected by the Planck Surveyor if the ratio of the initial isocurvature and adiabatic perturbation amplit…
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…
The observed CMBR dipole, generally interpreted as the consequence of the peculiar motion of the Sun with respect to the reference frame of the CMBR, can also be explained by the presence of ultra large scale (of the order of $100H_0^{-1}$) isocurvature perturbations. Moreover, the simplest model of inflation with several scalar fields, namely that of double inflation, with appropriate parameters, can produce such perturbations.
We consider the evolution of the Affleck-Dine scalar during D-term and F-term inflation and solve the combined slow-roll equations of motion. We show that for a typical case, where both the Affleck-Dine scalar and inflaton initially have large values, in D-term inflation the Affleck-Dine scalar is driven to a fixed value, with only a very slight dependence on the number of e-foldings. As a result, there is a definite prediction for the ratio of the baryonic isocurvature perturbation to the adiabatic perturbation. In minimal (d=4) Affleck-Dine baryogenesis the relative isocurvature contribution…
Isentropic and isocurvature axion inflationary perturbations are studied in detail. If isocurvature perturbations are present, COBE requires the inflationary Hubble constant to be rather small, $H_{I} \stackrel{<}{\sim} 10^{12}$GeV, regardless of the inflation model. Microwave background anisotropies are calculated for CDM models with a mixture of axion and supersymmetric CDM. The angular power spectrum of the microwave background depends not only on the amplitude of the isocurvature power spectrum but also on $Ω_{a}$. The Saskatoon data and $σ_{8}$ are used to constrain the contribution of ax…
We compute the non-Gaussianity of the curvature perturbation generated by ekpyrotic collapse with multiple fields. The transition from the multi-field scaling solution to a single-field dominated regime converts initial isocurvature field perturbations to an almost scale-invariant comoving curvature perturbation. In the specific model of two fields, $ϕ_1$ and $ϕ_2$, with exponential potentials, $-V_i \exp (-c_i ϕ_i)$, we calculate the bispectrum of the resulting curvature perturbation. We find that the non-Gaussianity is dominated by non-linear evolution on super-Hubble scales and hence is of …
Using both cosmic microwave background and large scale structure data, we put stringent bounds on the possible cold dark matter, baryon and neutrino isocurvature contributions to primordial fluctuations in the Universe. Neglecting the possible effects of spatial curvature, tensor perturbations and reionization, we perform a Bayesian likelihood analysis with nine free parameters, and find that the relative amplitude of the isocurvature component cannot be larger than about a few percent for uncorrelated models. On the other hand, for correlated adiabatic and isocurvature components, the ratio c…
Dynamics of long-wave isocurvature perturbations during an inflationary stage in multiple (multi-component) inflationary models is calculated analytically for the case where scalar fields producing this stage interact between themselves through gravity only. This enables to determine correct amplitudes of such perturbations produced by vacuum quantum fluctuations of the scalar fields during the multiple inflationary stage. Exact matching to a post-inflationary evolution that gives the amplitude of isocurvature perturbations in the cold dark matter model with radiation is performed in the case …
We study the evolution of the cosmological perturbations after inflation in curvaton models where the non-relativistic curvaton decays into both radiation and a cold dark matter component. We calculate the primordial curvature and correlated isocurvature perturbations inherited by the radiation and cold dark matter after the curvaton has decayed. We give the transfer coefficient in terms of the initial curvaton density relative to the curvaton decay rate.
We investigate cosmological constraints on primordial isocurvature and tensor perturbations, using recent observations of the cosmic microwave background and the large scale structure. We find that present observations are consistent with purely adiabatic initial conditions for the structure formation under any priors on correlations of isocurvature modes, and upper limits on the contribution of isocurvature and tensor perturbations are presented. We also apply the obtained constraints to some specific theoretical models, axion isocurvature perturbation models and curvaton models, and give som…
Generic models for the origin of structure predict a spectrum of initial fluctuations with a mixture of adiabatic and isocurvature perturbations. Using the observed anisotropies of the cosmic microwave backgound, the matter power spectra from large scale structure surveys and the luminosity distance vs redshift relation from supernovae of type Ia, we obtain strong bounds on the possible cold dark matter/baryon as well as neutrino isocurvature contributions to the primordial fluctations in the Universe. Neglecting the possible effects of spatial curvature and tensor perturbations, we perform a …
We make a detailed calculation of the amplitude of isocurvature perturbations arising from inflationary models in which the cold dark matter is represented by a scalar field which acquires perturbations during inflation. We use this to compute the normalization to large-angle microwave background anisotropies. Unlike the case of adiabatic perturbations, the normalization to COBE fixes the spectral index of the perturbations; if adiabatic perturbations are negligible then $n_{iso} \simeq 0.4$. Such blue spectra are also favoured by other observational data. Although the pure isocurvature models…
We explicate the origin of the temperature quadrupole in the adiabatic dark energy model and explore the mechanism by which scale invariant isocurvature dark energy perturbations can lead to its sharp suppression. The model requires anticorrelated curvature and isocurvature fluctuations and is favored by the WMAP data at about the 95% confidence level in a flat scale invariant model. In an inflationary context, the anticorrelation may be established if the curvature fluctuations originate from a variable decay rate of the inflaton; such models however tend to overpredict gravitational waves. T…
We compare the latest cosmic microwave background data with theoretical predictions including correlated adiabatic and CDM isocurvature perturbations with a simple power-law dependence. We find that there is a degeneracy between the amplitude of correlated isocurvature perturbations and the spectral tilt. A negative (red) tilt is found to be compatible with a larger isocurvature contribution. Estimates of the baryon and CDM densities are found to be almost independent of the isocurvature amplitude. The main result is that current microwave background data do not exclude a dominant contribution…
In the curvaton model of inflation, where a second scalar field, the "curvaton", is responsible for the observed inhomogeneity, a non-zero neutrino degeneracy may lead to a characteristic pattern of isocurvature perturbations in the neutrino, cold dark matter and baryon components. We find the current data can only place upper limits on the level of isocurvature perturbations. These can be translated into upper limits on the neutrino degeneracy parameter. In the case that lepton number is created before curvaton decay, we find that the limit on the neutrino degeneracy parameter is comparable w…
We discuss the possible role of isocurvature perturbations for the quantum decoherence of the curvature perturbation during inflation. We point out that if the inflaton trajectory in field space is curved, the adiabatic mode is generically coupled to the isocurvature mode and thus tracing out the latter can cause the curvature perturbation to decohere. We explicitly investigate this suggestion in a model of inflation with two decoupled massive fields and find that decoherence is effective for a wide range of mass ratios. In particular, we calculate the entanglement entropy for this model and s…
We present a mechanism for the origin of the large-scale curvature perturbation in our Universe by the late decay of a massive scalar field, the curvaton. The curvaton is light during a period of cosmological inflation, when it acquires a perturbation with an almost scale-invariant spectrum. This corresponds initially to an isocurvature density perturbation, which generates the curvature perturbation after inflation when the curvaton density becomes a significant fraction of the total. The isocurvature density perturbation disappears if the curvaton completely decays into thermalised radiation…
Prospects for testing the adiabaticity of the primordial cosmological perturbations using MAP and PLANCK are evaluated. The most general cosmological perturbation in a universe with just baryons, photons, neutrinos, and a cold dark matter (CDM) component is described. In addition to the familiar adiabatic mode, there are four nonsingular isocurvature modes: a baryon isocurvature mode, a CDM isocurvature mode, a neutrino density isocurvature mode, and a neutrino velocity isocurvature mode. The most general perturbation is described by a 5x5, positive-definite, symmetric, matrix-valued function …
We examine the consequences of the existence of correlated mixtures of adiabatic and isocurvature perturbations on the CMB and large scale structure. In particular, we consider the four types of ``elementary'' totally correlated hybrid initial conditions, where only one of the four matter species (photons, baryons, neutrinos, CDM) deviates from adiabaticity. We then study the height and position of the acoustic peaks with respect to the large angular scale plateau as a function of the isocurvature to adiabatic ratio.
We show how the generation of a lepton number in the Early Universe induced by active-sterile neutrino oscillations, in presence of small baryon number inhomogeneities, gives rise to the formation of lepton domains, regions with different values of active neutrino chemical potential. The structure of these domains reflects the spectral features of the baryon number inhomogeneities that generated it. An interesting aspect of the mechanism is that the size of lepton domains can be super-horizon.
We consider effects of the isocurvature perturbation in the framework of the tracker-type quintessence models. During the inflation, fluctuations in the amplitude of the quintessence field are generated, which provide isocurvature component of the cosmic density perturbation. Contrary to the conventional notion, it is shown that effects of the isocurvature fluctuation may become sizable in some cases, and in particular, the cosmic microwave background angular power spectrum may be significantly enhanced due to the effect of the isocurvature mode. Such an enhancement may be detectable in on-goi…
Present cosmological data are well explained assuming purely adiabatic perturbations, but an admixture of isocurvature perturbations is also permitted. We use a Bayesian framework to compare the performance of cosmological models including isocurvature modes with the purely adiabatic case; this framework automatically and consistently penalizes models which use more parameters to fit the data. We compute the Bayesian evidence for fits to a dataset comprised of WMAP and other microwave anisotropy data, the galaxy power spectrum from 2dFGRS and SDSS, and Type Ia supernovae luminosity distances. …
The role of cosmic microwave background (CMB) polarisation data in constraining the presence of primordial isocurvature modes is examined. While the MAP satellite mission will be unable to simultaneously constrain isocurvature modes and cosmological parameters, the PLANCK mission will be able to set strong limits on the presence of isocurvature modes if it makes a precise measurement of the CMB polarisation sky. We find that if we allow for the possible presence of isocurvature modes, the recently obtained BOOMERANG measurement of the curvature of the universe fails. However, a comparably sens…
We use cosmic microwave background (CMB) and large-scale structure data to constrain cosmological models where the primordial perturbations have both an adiabatic and a cold dark matter (CDM) isocurvature component. We allow for a possible correlation between the adiabatic and isocurvature modes, and for different spectral indices for the power in each mode and for their correlation. We do a likelihood analysis with 11 independent parameters. We discuss the effect of choosing the pivot scale for the definition of amplitude parameters. The upper limit for the isocurvature fraction is 18% around…
The improved data on the cosmic microwave background (CMB) anisotropy allow a better determination of the adiabaticity of the primordial perturbation. Interestingly, we find that recent CMB data seem to favor a contribution of a primordial isocurvature mode where the entropy perturbation is positively correlated with the primordial curvature perturbation and has a large spectral index (niso ~ 3). With 4 additional parameters we obtain a better fit to the CMB data by Delta chi^2 = 9.7 compared to an adiabatic model. For this best-fit model the nonadiabatic contribution to the CMB temperature va…
The Cosmic Microwave Background (CMB) anisotropies measurements can provide many clues about the Universe. Although the common belief is that they will allow a very precise measurement of the cosmological parameters (that is, the current state of the Universe), they will alternatively give interesting informations about the state of the initial perturbations (that is, the state of the Universe at the end of inflation). In this paper, we study the observational consequences on the CMB anisotropies of some wide set of inital conditions, with a correlated mixture of adiabatic and isocurvature per…
We perform a general study of the primordial scalar non-Gaussianities in multi-field inflationary models in Einstein gravity. We consider models governed by a Lagrangian which is a general function of the scalar fields and their first spacetime derivatives. We use $δN$ formalism to relate scalar fields and curvature perturbations. We calculate the explicit cubic order perturbation action and the three-point function of curvature perturbation evaluated at horizon-crossing. Under reasonable assumptions, in the limit of small slow-varying parameters and a sound speed $c_s$ close to one, we find t…
We study cosmological perturbations in the case that present-day matter consists of a mixture of inflaton and curvaton decay products. We calculate how the curvaton perturbations are transferred to its decay products in the general case when it does not behave like dust. Taking into account that the decay products of the inflaton can also have perturbations results in an interesting mixture of correlated adiabatic and isocurvature perturbations. In particular, negative correlation can improve the fit to the CMB data by lowering the angular power in the Sachs-Wolfe plateau without changing the …
We study the bispectrum of the curvature perturbation on uniform energy density hypersurfaces in models of inflation with two scalar fields evolving simultaneously. In the case of a separable potential, it is possible to compute the curvature perturbation up to second order in the perturbations, generated on large scales due to the presence of non-adiabatic perturbations, by employing the $δN$-formalism, in the slow-roll approximation. In this case, we provide an analytic formula for the nonlinear parameter $f_{NL}$. We apply this formula to double inflation with two massive fields, showing th…
We examine Gaussian isocurvature hot dark matter (massive neutrino) models for large-scale structure in which the initial density perturbations are produced in the baryons with a power--law spectrum $P_B(k) = Ak^{n_B}$. We calculate the linearly-evolved power spectrum and cosmic microwave fluctuations. We find that models with only isocurvature perturbations are inconsistent with observations of damped Ly$α$ systems and COBE constraints on the power index. However, models which contain a mixture of adiabatic and isocurvature perturbations can be made consistent with COBE, galaxy surveys and da…
We consider the expected level of primordial non-Gaussianities in models in which density perturbations are produced by spatial fluctuations in the decay rate of the inflaton. We consider both the non-Gaussianities resulting from the self-couplings of the field that controls the decay rate as well as from the non-linear relation between field and curvature perturbations. We show that in these scenario non-Gaussianities are of the "local" form, that is well described be the ansatz R =Rg + f_{NL} (Rg^2 - <Rg^2>). This is a consequence of the fact that they were created when modes were already ou…
Big bang nucleosynthesis constraints on baryon isocurvature perturbations are determined. A simple model ignoring the effects of the scale of the perturbations is first reviewed. This model is then extended to test the claim that large amplitude perturbations will collapse, forming compact objects and preventing their baryons from contributing to the observed baryon density. It is found that baryon isocurvature perturbations are constrained to provide only a slight increase in the density of baryons in the universe over the standard homogeneous model. In particular it is found that models whic…
The most general homogeneous and isotropic statistical ensemble of linear scalar perturbations which are regular at early times, in a universe with only photons, baryons, neutrinos, and a cold dark matter (CDM) component, is described by a 5x5 symmetric matrix-valued generalization of the power spectrum. This description is complete if the perturbations are Gaussian, and even in the non-Gaussian case describes all observables quadratic in the small perturbations. The matrix valued power spectrum describes the auto- and cross-correlations of the adiabatic, baryon isocurvature, CDM isocurvature,…
We consider the problem of the initial conditions and behaviour of the perturbations in scalar field cosmology with general potential. We use the general definition of adiabatic and isocurvature conditions to set the appropriate initial values for the perturbation in the scalar field and in the ordinary matter and radiation components. In both the cases of initial adiabaticity and isocurvature, we solve the Einstein and fluid equation at early times and on superhorizon scales to find the initial behaviour of the relevant quantities. In particular, in the isocurvature case, we consider models i…
We present a systematic treatment of the initial conditions and evolution of cosmological perturbations in a universe containing photons, baryons, neutrinos, cold dark matter, and a scalar quintessence field. By formulating the evolution in terms of a differential equation involving a matrix acting on a vector comprised of the perturbation variables, we can use the familiar language of eigenvalues and eigenvectors. As the largest eigenvalue of the evolution matrix is fourfold degenerate, it follows that there are four dominant modes with non-diverging gravitational potential at early times, co…
