We study cosmological tensor perturbations induced by second-order scalar perturbations in the presence of anisotropic non-Gaussianity. This class of induced tensor modes arises on superhorizon scales through the intrinsic quadrupole coupling between long modes and short modes. Scalar perturbations on all scales from the inflationary Hubble radius to the Silk damping scale at recombination contribute to the induced tensor powerspectrum at the cosmic microwave background (CMB) scale. In addition, the induced tensor spectrum becomes almost scale-invariant. The former property suggests that measurements of the CMB offer a test of tiny scale physics. However, the latter implies the secondary effect may contaminate the primordial tensor spectrum, which tells us the energy scale of inflation. We derive the induced tensor modes originated from two concrete examples of anisotropic non-Gaussianity; statistically anisotropic scalar non-Gaussianity and scalar-scalar-tensor non-Gaussianity, and discuss observational consequences of extremely short scale physics. Also, we comment on various possibilities of enhancing the induced spectrum with nonstandard early Universe physics.
We develop a theory of nonlinear cosmological perturbations on superhorizon scales for a single scalar field with a general kinetic term and a general form of the potential. We employ the ADM formalism and the spatial gradient expansion approach, characterised by $O(ε^m)$, where $ε=1/(HL)$ is a small parameter representing the ratio of the Hubble radius to the characteristic length scale $L$ of perturbations. We obtain the general solution for a full nonlinear version of the curvature perturbation valid up through second-order in $ε$ ($m=2$). We find the solution satisfies a nonlinear second-o…
We investigate the effects of the presence of relic classical superhorizon inhomogeneities during inflation. This superhorizon inhomogeneity appears as a gradient locally and picks out a preferred direction. Quantum fluctuations on this slightly inhomogeneous background are generally statistical anisotropic. We find a quadrupole modification to the ordinary isotropic spectrum. Moreover, this deviation from statistical isotropy is scale-dependent, with a $\sim -1/k^2$ factor. This result implies that the statistical anisotropy mainly appears on large scales, while the spectrum on small scales r…
We derive a general expression for the probability of observing deviations from statistical isotropy in the cosmic microwave background (CMB) if the primordial fluctuations are non-Gaussian and extend to superhorizon scales. The primary motivation is to properly characterize the monopole and dipole modulations of the primordial power spectrum that are generated by the coupling between superhorizon and subhorizon perturbations. Unlike previous proposals for generating the hemispherical power asymmetry, we do not assume that the power asymmetry results from a single large superhorizon mode. Inst…
Loop quantum cosmology (LQC) provides a resolution of the classical big bang singularity in the deep Planck era. The evolution, prior to the usual slow-roll inflation, naturally generates excited states at the onset of the slow-roll inflation. It is expected that these quantum gravitational effects could leave its fingerprints on the primordial perturbation spectrum and non-Gaussianity, and lead to some observational evidences in the cosmic microwave background (CMB). While the impact of the quantum effects on the primordial perturbation spectrum has been already studied and constrained by cur…
We study squeezed limit $f_{NL}$ generation by excited initial inflationary states in a model independent way. We restrict "excited" to mean a Bogoliubov transformation of the Bunch Davies state. We simultaneously impose the constraints that the observable power spectrum is nearly scale invariant over at least three decades and that the observable modes today be subhorizon at the beginning of inflation while not causing significant backreaction. We show that most excited initial inflationary states for single field inflationary models with negligible superhorizon evolution do not produce an ob…
In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, $\R_c$, on super-horizon scales is one of the assumptions necessary to derive the consistency condition between the squeezed limit of the bispectrum and the spectrum of the primordial curvature perturbation. However, the conservation of $\R_c$ holds only after the perturbation has reached the adiabatic limit where the constant mode of $\R_c$ dominates over the other (usually decaying) mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, $δP_{na…
We develop a theory of nonlinear cosmological perturbations on superhorizon scales where a characteristic length scale of perturbations is longer than the Hubble radius, in general theoretical frameworks. Our formalism is based on the spatial gradient expansion approach by adopting the ADM decomposition. Nonlinear superhorizon perturbation including both scalar (curvature perturbation) and tensor (gravitational waves) modes can be dealt with valid up to a second-order in the expansion. First we will review the formalism for a standard general relativity (GR) gravity plus a general kinetic sing…
In this paper the generation of the primordial curvature perturbation by vector fields of general non-Abelian groups is discussed. We show that non-Gaussianity of the perturbation is dominated by contributions from superhorizon evolution of fields. Also we find that non-Abelian vector fields of reasonably large groups can generate the total of the curvature perturbation without violating observational constraints on the angular modulation of the spectrum.
The superhorizon (iso)curvature perturbations are conserved if the following conditions are satisfied: (i) (each) non adiabatic pressure perturbation is zero, (ii) the gradient terms are ignored, that is, at the leading order of the gradient expansion (iii) (each) total energy momentum tensor is conserved. We consider the case with the violation of the last two requirements and discuss the generation of secondary isocurvature perturbations during the late time universe. Second order gradient terms are not necessarily ignored even if we are interested in the long wavelength modes because of the…
We develop a scenario of inflation with spontaneously broken time and space diffeomorphisms, with distinctive features for the primordial tensor modes. Inflationary tensor fluctuations are non adiabatic, and can acquire a mass during the inflationary epoch. They can evade the Higuchi bound around de Sitter space, thanks to interactions with the fields driving expansion. Correspondingly, the primordial stochastic gravitational wave background (SGWB) is characterised by a tuneable scale dependence, and can be detectable at interferometer scales. In this set-up, tensor non-Gaussianity can be para…
We study an inflationary scenario with a two-form field to which an inflaton couples non-trivially. First, we show that anisotropic inflation can be realized as an attractor solution and that the two-form hair remains during inflation. A statistical anisotropy can be developed because of a cumulative anisotropic interaction induced by the background two-form field. The power spectrum of curvature perturbations has a prolate-type anisotropy, in contrast to the vector models having an oblate-type anisotropy. We also evaluate the bispectrum and trispectrum of curvature perturbations by employing …
We study single field inflation in noncommutative spacetime and compute two-point and three-point correlation functions for the curvature perturbation. We find that both power spectrum and bispectrum for comoving curvature perturbation are statistically anisotropic and the bispectrum is also modified by a phase factor depending upon the noncommutative parameters. The non-linearity parameter $f_{NL}$ is small for small statistical anisotropic corrections to the bispectrum coming from the noncommutative geometry and is consistent with the recent PLANCK bounds. There is a scale dependence of $f_{…
We develop a theory of nonlinear cosmological perturbations on superhorizon scales for a multi-component scalar field with a general kinetic term and a general form of the potential in the context of inflationary cosmology. We employ the ADM formalism and the spatial gradient expansion approach, characterised by O(ε^2), where ε=1/(HL) is a small parameter representing the ratio of the Hubble radius to the characteristic length scale L of perturbations. We provide a formalism to obtain the solution in the multi-field case. This formalism can be applied to the superhorizon evolution of a primord…
If the initial quantum state of the primordial perturbations broke rotational invariance, that would be seen as a statistical anisotropy in the angular correlations of the cosmic microwave background radiation (CMBR) temperature fluctuations. This can be described by a general parameterisation of the initial conditions that takes into account the possible direction-dependence of both the amplitude and the phase of particle creation during inflation. The leading effect in the CMBR two-point function is typically a quadrupole modulation, whose coefficient is analytically constrained here to be $…
We consider inflationary models in which vector fields are responsible for part or eventually all of the primordial curvature perturbation ζ. Such models are phenomenologically interesting since they naturally introduce anisotropies in the probability distribution function of the primordial fluctuations that can leave a measurable imprint in the cosmic microwave background. Assuming that non-Gaussianity is generated due to the superhorizon evolution, we use the δN formalism to do a complete tree level calculation of the non-Gaussianity parameters f_{NL} and τ_{NL} in the presence of vector fie…
Anisotropic separate universe : Long-wavelength perturbations and conserved quantities
Ewha Womans University（梨花女子大学）；National Institute of Technology, Fukui College（福井工业技术学院）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Yokohama National University（横滨国立大学）
Superhorizon curvature perturbations in hybrid inflation revisited
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo（东京大学宇宙物质前沿科学中心（WPI））；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Correlations between intrinsic galaxy shapes on large-scales arise due to the effect of the tidal field of the large-scale structure. Anisotropic primordial non-Gaussianity induces a distinct scale-dependent imprint in these tidal alignments on large scales. Motivated by the observational finding that the alignment strength of luminous red galaxies depends on how galaxy shapes are measured, we study the use of two different shape estimators as a multi-tracer probe of intrinsic alignments. We show, by means of a Fisher analysis, that this technique promises a significant improvement on anisotro…
Inflation is an early period of accelerated cosmic expansion, thought to be sourced by high energy physics. A key task today is to use the influx of increasingly precise observational data to constrain the plethora of inflationary models suggested by fundamental theories of interactions. This requires a robust theoretical framework for quantifying the predictions of such models; helping to develop such a framework is the aim of this thesis. We provide the first complete quantization of subhorizon perturbations for the well-motivated class of multi-field inflationary models with a non-trivial f…
Using $N$-body simulations of cosmological large-scale structure formation, for the first time, we show that the anisotropic primordial non-Gaussianity (PNG) causes a scale-dependent modification, given by $1/k^2$ at small $k$ limit, in the three-dimensional power spectra of halo shapes (intrinsic alignments), whilst the conventional power spectrum of halo number density field remains unaffected. We discuss that wide-area imaging and spectrocopic surveys observing the same region of the sky allow us to constrain the quadrupole PNG coefficient $f_{\rm NL}^{s=2}$ at a precision comparable with o…
In this work we study the large scale structure bias in models of anisotropic inflation. We use the Peak Background Splitting method in Excursion Set Theory to find the scale-dependent bias. We show that the amplitude of the bias is modified by a direction- dependent factor. In the specific anisotropic inflation model which we study, the scale- dependent bias vanishes at leading order when the long wavelength mode in squeezed limit is aligned with the anisotropic direction in the sky. We also extend the scale-dependent bias formulation to the general situations with primordial anisotropy. We f…
We consider the single field chaotic m^2ϕ^2 inflationary model with a period of preheating, where the inflaton decays to another scalar field χ in the parametric resonance regime. In a recent work, one of us has shown that the χ modes circulating in the loops during preheating notably modify the <ζζ> correlation function. We first rederive this result using a different gauge condition hence reconfirm that superhorizon ζ modes are affected by the loops in preheating. Further, we examine how χ loops give rise to non-gaussianity and affect the tensor perturbations. For that, all cubic and some hi…
Non-Gaussianity in the inflationary perturbations can couple observable scales to modes of much longer wavelength (even superhorizon), leaving as a signature a large-angle modulation of the observed cosmic microwave background (CMB) power spectrum. This provides an alternative origin for a power asymmetry which is otherwise often ascribed to a breaking of statistical isotropy. The non-Gaussian modulation effect can be significant even for typical ~10^{-5} perturbations, while respecting current constraints on non-Gaussianity, if the squeezed limit of the bispectrum is sufficiently infrared div…
Many observations in recent times have shown evidence against the standard assumption of isotropy in the Big Bang model. Introducing a superhorizon scalar metric perturbation has been able to explain some of these anomalies. In this work, we probe the net velocity arising due to the perturbation. We find that this extra component does not contribute to the CMB dipole amplitude while it does contribute to the dipole in large scale structures. Thus, within this model's framework, our velocity with respect to the large scale structure is not the same as that extracted from the CMB dipole, assumin…
We develop a possibility of generating tensor non-Gaussianity in a kind of anisotropic inflation, where a $U(1)$ gauge field is kinetically coupled to a spectator scalar field. Owing to this coupling, the coherent mode of the electric field appears and softly breaks the isotropy of the Universe. We compute the bispectrum of linearly-polarized tensor perturbations sourced by the gauge field and find that it is strongly red-tilted and has distinctive statistical anisotropies including higher-order multipole moments. Interestingly, the tensor bispectra with the specific combinations of linear pol…
We show that intrinsic (not lensing-induced) correlations between galaxy shapes offer a new probe of primordial non-Gaussianity and inflationary physics which is complementary to galaxy number counts. Specifically, intrinsic alignment correlations are sensitive to an anisotropic squeezed limit bispectrum of the primordial perturbations. Such a feature arises in solid inflation, as well as more broadly in the presence of light higher spin fields during inflation (as pointed out recently by Arkani-Hamed and Maldacena). We present a derivation of the all-sky two-point correlations of intrinsic sh…
We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistenc…
Anisotropic stress perturbations induced by primordial Gaussian vector fields create non-Gaussianity in curvature perturbations. We found that such non-Gaussianity closely resembles the local-type non-Gaussianity parametrized by $f_{\rm NL}$, and generates scale-dependent bias in large-scale structures. We also found a simple relationship between the scale-dependent bias and the power spectrum of the vector fields. When the vector fields are interpreted as primordial magnetic fields, the effective $f_{\rm NL}$ is shown to be always negative. The scale-dependent bias provides a new approach to …
Multi-field inflation models and non-Bunch-Davies vacuum initial conditions both predict sizeable non-Gaussian primordial perturbations and anisotropic $μ$-type spectral distortions of the cosmic microwave background (CMB) blackbody. While CMB anisotropies allow us to probe non-Gaussianity at wavenumbers $k\simeq 0.05\,{\rm Mpc^{-1}}$, $μ$-distortion anisotropies are related to non-Gaussianity of primordial perturbation modes with much larger wavenumbers, $k\simeq 740\,{\rm Mpc^{-1}}$. Through cross-correlations between CMB and $μ$-distortion anisotropies, one can therefore shed light on the a…
We derive the linear correction term for needlet and wavelet estimators of the bispectrum and the non-linearity parameter fNL on cosmic microwave background radiation data. We show that on masked WMAP-like data with anisotropic noise, the error bars improve by 10-20% and almost reach the optimal error bars obtained with the KSW estimator (Komatsu et al 2005). In the limit of full-sky and isotropic noise, this term vanishes. We apply needlet and wavelet estimators to the WMAP 7-year data and obtain our best estimate fNL=37.5 \pm 21.8.
We present a review of vector field models of inflation and, in particular, of the statistical anisotropy and non-Gaussianity predictions of models with SU(2) vector multiplets. Non-Abelian gauge groups introduce a richer amount of predictions compared to the Abelian ones, mostly because of the presence of vector fields self-interactions. Primordial vector fields can violate isotropy leaving their imprint in the comoving curvature fluctuations zeta at late times. We provide the analytic expressions of the correlation functions of zeta up to fourth order and an analysis of their amplitudes and …
In this work we present constraints on different shapes of primordial non-Gaussianity using the Wilkinson Microwave Anisotropy Probe (WMAP) 7-year data and the spherical Mexican hat wavelet fnl estimator including the linear term correction. In particular we focus on the local, equilateral and orthogonal shapes. We first analyse the main statistical properties of the wavelet estimator and show the conditions to reach optimality. We include the linear term correction in our estimators and compare the estimates with the values already published using only the cubic term. The estimators are teste…
We investigate how well future large-scale radio surveys could measure different shapes of primordial non-Gaussianity; in particular we focus on angle-dependent non-Gaussianity arising from primordial anisotropic sources, whose bispectrum has an angle dependence between the three wavevectors that is characterized by Legendre polynomials $\mathcal{P}_L$ and expansion coefficients $c_L$. We provide forecasts for measurements of galaxy power spectrum, finding that Large-Scale Structure (LSS) data could allow measurements of primordial non-Gaussianity competitive or improving upon current constrai…
We present constraints on local primordial non-Gaussianity (PNG), parametrized through $f^{\rm loc}_{\rm NL}$, using the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample. We measure and analyze the anisotropic clustering of the quasars in Fourier space, testing for the scale-dependent bias introduced by primordial non-Gaussianity on large scales. We derive and employ a power spectrum estimator using optimal weights that account for the redshift evolution of the PNG signal. We find constraints of $-51<f^{\rm loc}_{\rm NL}<21$ at 95% conf…
Primordial magnetic fields will generate non-Gaussian signals in the cosmic microwave background (CMB) as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. We compute a new measure of magnetic non-Gaussianity, the CMB trispectrum, on large angular scales, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approximately a few times 10^{-29} and 10^{-19}, respectively. Observational limits on CMB non-Gaussianity from WMAP data…
We continue to investigate possible signatures of a pre-inflationary anisotropic phase in two-point and three point correlation functions of the curvature perturbation for high-momentum modes which exit the horizon well after isotropization. The late time dynamics of these modes is characterized by a non-Bunch Davies vacuum state which encodes all the information about initial anisotropy in the background space-time. We observe that, unlike the non-planar momenta, there exist regimes of planar momenta for which scale invariance of the power spectrum is strongly broken. This regime of planar mo…
We consider a primordial SU(2) vector multiplet during inflation in models where quantum fluctuations of vector fields are involved in producing the curvature perturbation. Recently, a lot of attention has been paid to models populated by vector fields, given the interesting possibility of generating some level of statistical anisotropy in the cosmological perturbations. The scenario we propose is strongly motivated by the fact that, for non-Abelian gauge fields, self-interactions are responsible for generating extra terms in the cosmological correlation functions, which are naturally absent i…
This thesis is centered on three main subjects within the theory of inflation and cosmological perturbations: loop corrections to the power spectrum of curvature fluctuations generated during inflation; evolution of cosmological fluctuations in anisotropic pre-inflationary cosmologies; statistical anisotropy and non-Gaussianity predictions of models of inflation populated with vector fields. Currently, what makes even more interesting the study of 2-nd and higher order corrections to cosmological correlation functions as well as the computation of higher-than-two order correlators, is the almo…
Galaxy bispectrum is a promising probe of inflationary physics in the early universe as a measure of primordial non-Gaussianity (PNG), whereas its signal-to-noise ratio is significantly affected by the mode coupling due to non-linear gravitational growth. In this paper, we examine the standard reconstruction method of linear cosmic mass density fields from non-linear galaxy density fields to de-correlate the covariance in redshift-space galaxy bispectra. In particular, we evaluate the covariance of the bispectrum for massive-galaxy-sized dark matter halos with reconstruction by using 4000 inde…
CMB Spectral Distortion Anisotropies from Acoustic Damping with primordial non-Gaussianity
Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, The University of Manchester（曼彻斯特大学物理与天文学学院乔德雷尔银行天体物理学中心）；Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University（重庆大学物理系及强耦合物理重庆市重点实验室）；Dipartimento di Fisica e Astronomia "Galileo Galilei" Università degli Studi di Padova（帕多瓦大学伽利略·伽利莱物理与天文学系）
Cosmic magnetic fields are observed to be coherent on large scales and could have a primordial origin. Non-Gaussian signals in the cosmic microwave background (CMB) are generated by primordial magnetic fields as the magnetic stresses and temperature anisotropy they induce depend quadratically on the magnetic field. We compute the CMB scalar trispectrum on large angular scales, for nearly scale-invariant magnetic fields, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approxim…
The velocity distribution function (VDF) of dark matter (DM) halos in $Λ$CDM dissipationless cosmological simulations, which must be non-separable in its radial and tangential components, is still poorly known. We present the first single-parameter, non-separable, anisotropic model for the VDF in $Λ$CDM halos, built from an isotropic $q$-Gaussian (Tsallis) VDF of the isotropic set of dimensionless spherical velocity components (after subtraction of streaming motions), normalized by the respective velocity dispersions. We test our VDF on 90 cluster-mass halos of a dissipationless cosmological s…
The gravitational coupling between large-scale perturbations and small-scale perturbations leads to anisotropic distortions of the small-scale matter distribution. The measured local small-scale power spectrum can thus be used to infer the large-scale matter distribution. In this paper, we present a new tidal reconstruction algorithm for reconstructing large-scale modes using the full three-dimensional tidal shear information. We apply it to simulated dark matter halo fields and the reconstructed large-scale density field correlates well with the original matter density field on large scales, …
If the seed magnetic fields exist in the early Universe, tensor components of their anisotropic stresses are not compensated prior to neutrino decoupling and the tensor metric perturbations generated from them survive passively. Consequently, due to the decay of these metric perturbations after recombination, the so-called integrated Sachs-Wolfe effect, the large-scale fluctuations of CMB radiation are significantly boosted. This kind of CMB anisotropy is called the "tensor passive mode." Because these fluctuations deviate largely from the Gaussian statistics due to the quadratic dependence on…
(abridged version) The separate universe conjecture states that in General Relativity a density perturbation behaves locally (i.e. on scales much smaller than the wavelength of the mode) as a separate universe with different background density and curvature. We prove this conjecture for a spherical compensated tophat density perturbation of arbitrary amplitude and radius in $Λ$CDM. We then use Conformal Fermi Coordinates to generalize this result to scalar perturbations of arbitrary configuration and scale. In this case, the separate universe conjecture holds for the isotropic part of the pert…
Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher order effect. Apart from a compensated scalar mode, stochastic primordial magnetic fields also produce scalar anisotropic stress that remains uncompensated till neutrino decoupling. This gives rise to an adiabatic-like scalar perturbation mode that evolves passively ther…
