Curvature perturbations from ekpyrotic collapse with multiple fields

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.

We study the CMB constraints on non-Gaussianity in CDM isocurvature perturbations.Non-Gaussian isocurvature perturbations can be produced in various models at the very early stage of the Universe. Since the isocurvature perturbations little affect thestructure formation at late times, CMB is the best probe of isocurvature non-Gaussianity at least in the near future. In this paper, we focus on non-Gaussian curvature and isocurvature perturbations of the local-type, which are uncorrelated and in the formζ = ζG+(3/5)fNL(ζG2−⟨ζG2⟩)and S = SG+fNL(ISO)(SG−⟨SG2⟩), and constrain the non-linearity parameter of isocurvature perturbations, fNL(ISO), as well as the curvature one fNL.For this purpose, we employ several state-of-art techniques for the analysis of CMB data and simulation. Assuming that isocurvature perturbations are subdominant, we apply our method to the WMAP 7-year data of temperature anisotropy and obtain constraints on a combination α2fNL(ISO),where α is the ratio of the power spectrum of isocurvature perturbationsto that of the adiabatic ones.When the adiabatic perturbations are assumed to be Gaussian, we obtained a constraint α2fNL(ISO) = 40±66assuming the power spectrum of isocurvature perturbations is scale-invariant.When we assume that the adiabatic perturbations can also be non-Gaussian, we obtain fNL = 38±24 and α2fNL(ISO) = −8±72. We also discuss implications of our results for the axion CDM isocurvature model.

The computation of the spectrum of primordial perturbations, generated by a scalar field during the super-inflationary phase of Loop Quantum Cosmology, is revisited. The calculation is performed for two different cases. The first considers the dynamics of a massless field and it is found that scale invariance can only be achieved under a severe fine tuning. The second assumes that the field evolves with a constant ratio between kinetic and potential energy, i.e. in a scaling solution. In this case, near scale invariance is a generic feature of the theory if the field rolls in a steep self interaction potential.

We discuss second-order cosmological perturbations on super-Hubble scales, in a scalar field dominated universe, such as during single field inflation. In this contest we show that the gauge-invariant curvature perturbations defined on uniform density and comoving hypersurfaces coincide and that perturbations are adiabatic in the large scale limit. Since it has been recently shown that the uniform density curvature perturbation is conserved on large scales if perturbations are adiabatic, we conclude that both the uniform density and comoving curvature perturbations at second order, in a scalar field dominated universe, are conserved. Finally, in the light of this result, we comment on the variables recently used in the literature to compute non-Gaussianities.

A simple extension of the minimal supersymmetric standard model which naturally and simultaneously solves the strong CP and mu problems via a Peccei-Quinn and a continuous R symmetry is considered. This model is supplemented with hybrid inflation and leptogenesis, but without taking the specific details of these scenarios. It is shown that the Peccei-Quinn field can successfully act as a curvaton generating the total curvature perturbation in the universe in accord with the cosmic background explorer measurements. A crucial phenomenon, which assists us to achieve this, is the "tachyonic amplification" of the perturbation acquired by this field during inflation if the field, in its subsequent evolution, happens to be stabilized for a while near a maximum of the potential. In this case, the contribution of the field to the total energy density is also enhanced ("tachyonic effect"), which helps too. The cold dark matter in the universe consists, in this model, mainly of axions which carry an isocurvature perturbation uncorrelated with the total curvature perturbation. There are also lightest sparticles (neutralinos) which, like the baryons, originate from the inflationary reheating and, thus, acquire an isocurvature perturbation fully correlated with the curvature perturbation. So, the overall isocurvature perturbation has a mixed correlation with the adiabatic one. It is shown that the presently available bound on such an isocurvature perturbation from cosmic microwave background radiation and other data is satisfied. Also, the constraint on the non-Gaussianity of the curvature perturbation obtained from the recent Wilkinson microwave anisotropy probe data is fulfilled thanks to the "tachyonic effect".

Several scenarios have been proposed in which primordial perturbations could originate from quantum vacuum fluctuations in a phase corresponding to a collapse phase (in an Einstein frame) preceding the Big Bang. I briefly review three models which could produce scale-invariant spectra during collapse: (1) curvature perturbations during pressureless collapse, (2) axion field perturbations in a pre big bang scenario, and (3) tachyonic fields during multiple-field ekpyrotic collapse. In the separate universes picture one can derive generalised perturbation equations to describe the evolution of large scale perturbations through a semi-classical bounce, assuming a large-scale limit in which inhomogeneous perturbations can be described by locally homogeneous patches. For adiabatic perturbations there exists a conserved curvature perturbation on large scales, but isocurvature perturbations can change the curvature perturbation through the non-adiabatic pressure perturbation on large scales. Different models for the origin of large scale structure lead to different observational predictions, including gravitational waves and non-Gaussianity.

The idea of the universe having a mirror sector in which all particles and forces are identical to those in the familiar sector has been proposed recently in the context of neutrino physics as well as superstring theories some time ago. Assuming that all the quark and charged lepton masses in the mirror universe are scaled by a common factor, ζ, as is required in one interpretation of the neutrino data, we investigate domains of the parameter ζ where physical conditions are favorable for the formation of compact structures given the initial condition ΩB Ω ( denoting the mirror baryon). We consider both isocurvature and curvature perturbations; we address primordial mirror molecule formation, mirror Compton cooling, mirror Silk and collisionless damping, and various mirror cooling mechanisms that can lead to compact mirror structures for various regions of ζ space, so that the mirror model can be confronted with astrophysical observations. For isocurvature perturbations, we find a variety of possible structural final states. For curvature (or adiabatic) perturbations, we find a likelihood that part of ζ space would result in detectable effects that are not observed, while a part would not.

We study adiabatic and isocurvature perturbation spectra produced by a period of cosmological inflation driven by two scalar fields. We show that there exists a model-independent consistency condition for all two-field models of slow-roll inflation, despite allowing for model-dependent linear processing of curvature and isocurvature perturbations during and after inflation on super-horizon scales. The scale dependence of all spectra are determined solely in terms of slow-roll parameters during inflation and the dimensionless cross-correlation between curvature and isocurvature perturbations. We present additional model-dependent consistency relations that may be derived in specific two-field models, such as the curvaton scenario.

We study the dynamics of gauge-invariant scalar perturbations in cosmological scenarios with a modified Friedmann equation, such as quantum gravity bouncing cosmologies. We work within a separate universe approximation which captures wavelengths larger than the cosmological horizon; this approximation has been successfully applied to loop quantum cosmology and group field theory. We consider two variables commonly used to characterise scalar perturbations: the curvature perturbation on uniform-density hypersurfaces ζ and the comoving curvature perturbation R. For standard cosmological models in general relativity as well as in loop quantum cosmology, these quantities are conserved and equal on super-horizon scales for adiabatic perturbations. Here we show that while these statements can be extended to a more general form of modified Friedmann equations similar to that of loop quantum cosmology, in other cases, such as the simplest group field theory bounce scenario, ζ is conserved across the bounce whereas R is not. We relate our results to approaches based on a second-order equation for a single perturbation variable, such as the Mukhanov–Sasaki equation.

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 uncorrelated ``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 (CDM), baryon number or lepton number] in an unperturbed universe. Specific formulas for the residual isocurvature CDM perturbation are given for most of the commonly considered CDM candidates.

Purpose: To investigate the possible improvements in the dose conformity in intensity modulated proton therapy (IMPT) plans with multiple fields as compared to widely used single field optimized (SFO) plans with two lateral fields for spot scanned proton therapy (SSPT) and to verify the accuracy of the delivered dose using the Radiological Physics Center Proton Prostate Phantom (RPCPPP). Methods: The CT images of RPCPPP were used to design multiple IMPT plans using both SFO and multi field optimization (MFO) methods in the Varian Eclipse treatment planning system (TPS). The standard SFO clinical plan used two lateral fields going through the femoral heads. Non‐standard plans were generated using three or more oblique fields based on the SFO and MFO options of the TPS. The angles were carefully chosen to avoid bladder and rectum as much as possible. The RPC phantom containing films and TLDs was irradiated using the standard clinical SFO plan and the four field MFO plan to compare the planned and delivered dose. Results: Based on the DVHs, MFO plan with multiple oblique fields is found to have superior target conformity with reduced dose to organs at risk (OAR) and normal tissue, especially in the high dose regions, as compared to SFO plans. The point doses measured by TLDs and 2‐D dose distribution measured by GafChromic films in the RPCPPP irradiation passed the commonly used RPC acceptance criteria, namely +/− 7% agreement in point does and more than 85% of the voxels meeting the gamma index criteria of 7% dose or 4 mm distance agreement. Conclusion: The MFO SSPT plans for prostatic targets with multiple fields lead to better target conformity with lower doses to OARs as compared to SFO plans. The results of irradiations of the RPCPPP show that these plans can be delivered with acceptable accuracy

In this paper, we address a possible impact of radiative corrections from a heavy scalar field χ on the curvature perturbation ζ. Integrating out χ, we derive the effective action for ζ, which includes the loop corrections of the heavy field χ. When the mass of χ is much larger than the Hubble scale H, the loop corrections of χ only yield a local contribution to the effective action and hence the effective action simply gives an action for ζ in a single field model, where, as is widely known, ζ is conserved in time after the Hubble crossing time. Meanwhile, when the mass of χ is comparable to H, the loop corrections of χ can give a non-local contribution to the effective action. Because of the non-local contribution from χ, in general, ζ may not be conserved, even if the classical background trajectory is determined only by the evolution of the inflaton. In this paper, we derive the condition that ζ is conserved in time in the presence of the radiative corrections from χ. Namely, we show that when the dilatation invariance, which is a part of the diffeomorphism invariance, is preserved at the quantum level, the loop corrections of the massive field χ do not disturb the constant evolution of ζ at super Hubble scales. In this discussion, we show the Ward-Takahashi identity for the dilatation invariance, which yields a consistency relation for the correlation functions of the massive field χ.

We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski's theory. The difference between disformally related curvature perturbations is found to be given in terms of the comoving density perturbation associated with a single canonical scalar field. In General Relativity it is well-known that this quantity vanishes on superhorizon scales through the Poisson equation that is obtained on combining the Hamiltonian and momentum constraints, and we confirm that a similar result holds for any theory that is disformally related to Horndeski's scalar-tensor theory so long as the invertibility condition for the disformal transformation is satisfied. We also consider the curvature perturbation at full nonlinear order in the unitary gauge, and find that it is invariant under a general disformal transformation if we assume that an attractor regime has been reached. Finally, we also discuss the counting of degrees of freedom in theories disformally related to Horndeski's.

The tachyonic instability is commonly associated with mass terms having a negative sign and evolving faster than the Hubble scale, leading to an unstable low-k regime. In the cosmological exploration of modified gravity, it is seldom taken into account, with more focus given to the popular no-ghost and no-gradient conditions. The latter though are intrinsically high-k statements. Here we combine all three conditions into a full set of requirements that we show to guarantee stability on the whole range of cosmological scales. We then explore the impact of the different conditions on the parameter space of scalar-tensor gravity, with particular emphasis on the no-tachyon one. We focus on Horndeski gravity and also consider separately the two subclasses of f(R) and Generalized Brans Dicke theories. We identify several interesting features, for instance in the parameter space of designer f(R) on a wCDM background, shedding light on previous findings. When looking at the phenomenological functions Σ and μ, associated to the weak lensing and clustering potential respectively, we find that in the case of Generalized Brans Dicke the no-tachyon condition clearly cuts models with μ , Σ>1. This effect is less prevalent in the Horndeski case due to the larger amount of free functions in the theory.

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