Cosmological Fluctuations Research Articles

Inflation and quantum gravity in a Born–Oppenheimer context

A general equation, describing the lowest order corrections coming from quantum gravitational effects to the spectrum of cosmological scalar fluctuations is obtained. These corrections are explicitly estimated for the case of a de Sitter evolution.

Kinetic theory and evolution of cosmological fluctuations with neutrino number asymmetry

We derive a kinetic equation for chiral matter at non-zero chemical potential that governs the response of the parity odd part of the distribution function to perturbations of the Robertson-Walker metric. The derivation is based on a recent evaluation of the gravitational polarization tensor at non-zero chemical potential. We also provide the equations for gravity waves that follow from the anisotropic stress tensor describing the lepton asymmetry. These equations can be used to assess the effects that a non-zero neutrino chemical potential would have on the evolution of cosmological perturbations.

Rainbow gravity and scale-invariant fluctuations

We reexamine a recently proposed scenario where the deformed dispersion relations associated with a flow of the spectral dimension to a UV value of 2 leads to a scale-invariant spectrum of cosmological fluctuations, without the need for inflation. In that scenario Einstein gravity was assumed. The theory displays a wavelength-dependent speed of light but by transforming to a suitable ``rainbow frame'' this feature can be removed, at the expense of modifying gravity. We find that the ensuing rainbow gravity theory is such that gravity switches off at high energy (or at least leads to a universal conformal coupling). This explains why the fluctuations are scale invariant on all scales: there is no horizon scale as such. For dispersion relations that do not lead to exact scale invariance we find instead esoteric inflation in the rainbow frame. We argue that these results shed light on the behavior of gravity under the phenomenon of dimensional reduction.

DBI Galileon in the effective field theory of inflation: orthogonal non-Gaussianities and constraints from the Trispectrum

Very few explicit inflationary scenarios are known to generate a large bispectrum of orthogonal shape. Dirac-Born-Infeld Galileon inflation, in which an induced gravity term is added to the DBI action, is one such model. We formulate it in the language of the effective field theory of inflation by identifying the unitary gauge operators that govern the behavior of its cosmological fluctuations. We show how to recover rather easily from this its power spectrum and bispectrum, which we calculated previously using standard cosmological perturbation theory. We push our calculations up to the determination of the fourth-order action and of the trispectrum, in which shapes absent in k-inflation arise due to the presence of higher-order derivative operators. We finally discuss the combined constraints set on this model by current observational bounds on the bispectrum and trispectrum.

Cosmology of atomic dark matter

While, to ensure successful cosmology, dark matter (DM) must kinematically decouple from the standard model plasma very early in the history of the Universe, it can remain coupled to a bath of "dark radiation" until a relatively late epoch. One minimal theory that realizes such a scenario is the Atomic Dark Matter model, in which two fermions oppositely charged under a new U(1) dark force are initially coupled to a thermal bath of "dark photons" but eventually recombine into neutral atom-like bound states and begin forming gravitationally-bound structures. As dark atoms have (dark) atom-sized geometric cross sections, this model also provides an example of self-interacting DM with a velocity-dependent cross section. Delayed kinetic decoupling in this scenario predicts novel DM properties on small scales but retains the success of cold DM on larger scales. We calculate the atomic physics necessary to capture the thermal history of this dark sector and show significant improvements over the standard atomic hydrogen calculation are needed. We solve the Boltzmann equations that govern the evolution of cosmological fluctuations in this model and find in detail the impact of the atomic DM scenario on the matter power spectrum and the cosmic microwave background (CMB). This scenario imprints a new length scale, the Dark-Acoustic-Oscillation (DAO) scale, on the matter density field. This DAO scale shapes the small-scale matter power spectrum and determines the minimal DM halo mass at late times which may be many orders of magnitude larger than in a typical WIMP scenario. This model necessarily includes an extra dark radiation component, which may be favoured by current CMB experiments, and we quantify CMB signatures that distinguish an atomic DM scenario from a standard $\Lambda$CDM model containing extra free-streaming particles. [Abridged]

Subluminal galilean genesis

We put forward an improved version of the Galilean Genesis model that addresses the problem of superluminality. We demote the full conformal group to Poincare symmetry plus dilations, supplemented with approximate galilean shift invariance in the UV and at small field values. In this way fluctuations around the NEC-violating cosmological background are made substantially subluminal, and superluminality cannot be reached by any small change of the solution, in contrast with the original model. Dilation invariance still protects the scale-invariance of correlation functions of a massless test scalar - which is the source of the observed cosmological fluctuations - but the explicit breaking of the conformal group can be potentially observed in higher-order correlators. We also highlight a subtlety in matching the NEC-violating phase with the standard cosmological evolution, and discuss the possible couplings of the Galileon to gravity.

Universal Temporal Scaling

Human social economies and the civilizing processes are basically operating as evolving energy transduction systems (since Sumer, with a monetary market circuit). The global human civilization developed on a discrete scale in universal temporal intervals via fractal stages out of natural chaos, i.e.the global civilizing process is a human cultural response to experienced entropic volatility.If we follow the prediction model of cosmological fluctuation and special relativity of chronic, varying and periodical economic process functions ( quantum space of time. energy and money), then we have to conclude that the temporal interval of human economic production will reach the historical turning point of technological singularity in the very near future ( as envisioned by J.Neuman); it is reasonable to assume that the initial process curve started in 2001 and will be based on eco-energetics, biotech, health science and AI, including new monetary economics.The spiral theory of global human history ( curved space-time) is applicable to universal temporal scaling, explaining the discrete time-scale of global wave compression.

Scale-invariant fluctuations from Galilean genesis

We study the spectrum of cosmological fluctuations inscenarios such as Galilean Genesis \\cite{Nicolis} in whicha spectator scalar field acquires a scale-invariant spectrum ofperturbations during an early phase which asymptotesin the far past to Minkowski space-time. In the case ofminimal coupling to gravity and standard scalar field Lagrangian,the induced curvature fluctuations depend quadratically on thespectator field and are hence non-scale-invariant andhighly non-Gaussian. We show that if higher dimensional operators(the same operators that lead to the η-problem for inflation)are considered,a linear coupling between background and spectator fieldfluctuations is induced which leads to scale-invariant andGaussian curvature fluctuations.

Non-Gaussian features from the inverse volume corrections in loop quantum cosmology

In this paper we study the non-Gaussian features of the primordial fluctuations in loop quantum cosmology with the inverse volume corrections. The detailed analysis is performed in the single field slow-roll inflationary models. However, our results reflect the universal characteristics of bispectrum in loop quantum cosmology. The main corrections to the scalar bispectrum come from two aspects: one is the modifications to the standard Bunch--Davies vacuum, and the other is the corrections to the background dependent variables, such as slow-roll parameters. Our calculations show that the loop quantum corrections make ${f}_{\mathrm{NL}}$ of the inflationary models increase 0.1%. Moreover, we find that two new shapes of non-Gaussian signal arise, which we name ${\mathcal{F}}_{1}$ and ${\mathcal{F}}_{2}$. The former gives a unique loop quantum feature, which is less correlated with the local, equilateral, and single types, while the latter is highly correlated with the local one.

Trans-Planckian problem in the healthy extension of Horava-Lifshitz gravity

Planck scale physics may influence the evolution of cosmological fluctuations in the early stages of cosmological evolution. Because of the quasi-exponential redshifting, which occurs during an inflationary period, the physical wavelengths of comoving scales that correspond to the present large-scale structure of the Universe were smaller than the Planck length in the early stages of the inflationary period. This trans-Planckian effect was studied before using toy models. The Horava-Lifshitz (HL) theory offers the chance to study this problem in a candidate UV complete theory of gravity. In this paper we study the evolution of cosmological perturbations according to HL gravity assuming that matter gives rise to an inflationary background. As is usually done in inflationary cosmology, we assume that the fluctuations originate in their minimum energy state. In the trans-Planckian region the fluctuations obey a non-linear dispersion relation of Corley-Jacobson type. In the "healthy extension" of HL gravity there is an extra degree of freedom which plays an important role in the UV region but decouples in the IR, and which influences the cosmological perturbations. We find that in spite of these important changes compared to the usual description, the overall scale-invariance of the power spectrum of cosmological perturbations is recovered. However, we obtain oscillations in the spectrum as a function of wavenumber with a relative amplitude of order unity and with an effective frequency which scales nonlinearly with wavenumber. Taking the usual inflationary parameters we find that the frequency of the oscillations is so large as to render the effect difficult to observe.

Zero-point quantum fluctuations in cosmology

We re-examine the classic problem of the renormalization of zero-point quantum fluctuations in a Friedmann-Robertson-Walker background. We discuss a number of issues that arise when regularizing the theory with a momentum-space cutoff, and show explicitly how introducing non-covariant counter-terms allows to obtain covariant results for the renormalized vacuum energy-momentum tensor. We clarify some confusion in the literature concerning the equation of state of vacuum fluctuations. Further, we point out that the general structure of the effective action becomes richer if the theory contains a scalar field phi with mass m smaller than the Hubble parameter H(t). Such an ultra-light particle cannot be integrated out completely to get the effective action. Apart from the volume term and the Einstein-Hilbert term, that are reabsorbed into renormalizations of the cosmological constant and Newton's constant, the effective action in general also has a term proportional to F(phi)R, for some function F(phi). As a result, vacuum fluctuations of ultra-light scalar fields naturally lead to models where the dark energy density has the form rho_{DE}(t)=rho_X(t)+rho_Z(t), where rho_X is the component that accelerates the Hubble expansion at late times and rho_Z(t) is an extra contribution proportional to H^2(t). We perform a detailed comparison of such models with CMB, SNIa and BAO data.

Quantum-to-classical transition of primordial cosmological perturbations in de Broglie–Bohm quantum theory

There is a widespread belief that the classical small inhomogeneities which gave rise to all structures in the Universe through gravitational instability originated from primordial quantum cosmological fluctuations. However, this transition from quantum to classical fluctuations is plagued with important conceptual issues, most of them related to the application of standard quantum theory to the Universe as a whole. In this paper, we show how these issues can easily be overcome in the framework of the de Broglie-Bohm quantum theory. This theory is an alternative to standard quantum theory that provides an objective description of physical reality, where rather ambiguous notions of measurement or observer play no fundamental role, and which can hence be applied to the Universe as a whole. In addition, it allows for a simple and unambiguous characterization of the classical limit.

On the redundancy of operators and the bispectrum in the most general second-order scalar-tensor theory

In this short note we explain how to use the linear equations of motion to simplify the third-order action for the cosmological fluctuations. No field redefinition is needed in this exact procedure which considerably limits the range of independent cubic operators, and hence of possible shapes of the primordial bispectrum. We demonstrate this in the context of the most general single-field scalar-tensor theory with second-order equations of motion, whose third-order action has been calculated recently in arXiv:1107.2642 and 1107.3917. In particular, we show that the three cubic operators initially pointed out in these works as new compared to k-inflation can actually be expressed in terms of standard k-inflationary operators.

Primordial magnetic fields generated by the non-adiabatic fluctuations at pre-recombination era

In the pre-recombination era, cosmological density fluctuations can naturally generate magnetic fields through Thomson scatterings. In previous studies, only the magnetic field generation from the initially- adiabatic fluctuations has been considered. Here we investigate the generation of cosmological magnetic fields sourced by the primordial non-adiabatic fluctuations based on the cosmological perturbation theory, using the tight-coupling approximations between photon and baryon fluids. It is found that the magnetic fields from the non-adiabatic fluctuations can arise at the first-order expansion of the tight coupling approximation. This result is in contrast to the case of adiabatic initial fluctuations, where the magnetic fields can be generated only at the second-order. In a general case where the primordial density perturbations contain small non-adiabatic fluctuations on the top of the dominant adiabatic ones, we show that the leading source of magnetic fields is given by the second-order coupling of the adiabatic and non-adiabatic fluctuations. We calculate the power spectrum of the generated magnetic fields when the non-adiabatic fluctuations have a blue power spectrum, which has been suggested by recent cosmological observations.

Primordial fluctuations and non-Gaussianities from multifield DBI Galileon inflation

We study a cosmological scenario in which the DBI action governing the motion of a D3-brane in a higher-dimensional spacetime is supplemented with an induced gravity term. The latter reduces to the quartic Galileon Lagrangian when the motion of the brane is non-relativistic and we show that it tends to violate the null energy condition and to render cosmological fluctuations ghosts. There nonetheless exists an interesting parameter space in which a stable phase of quasi-exponential expansion can be achieved while the induced gravity leaves non trivial imprints. We derive the exact second-order action governing the dynamics of linear perturbations and we show that it can be simply understood through a bimetric perspective. In the relativistic regime, we also calculate the dominant contribution to the primordial bispectrum and demonstrate that large non-Gaussianities of orthogonal shape can be generated, for the first time in a concrete model. More generally, we find that the sign and the shape of the bispectrum offer powerful diagnostics of the precise strength of the induced gravity.

Gravitational fluctuations in de Sitter cosmology

De Sitter spacetime plays an important role in cosmology: the geometry of most inflationary models is close to de Sitter spacetime and so will be the late-time behavior of the present universe with accelerated expansion. In linearized perturbation theory the metric fluctuations in a de Sitter cosmology describe very well the anisotropies of the microwave background and the observed large scale structure. Recently there has been some interest in the need to go beyond the linear approximation to include the effect of matter loops. This will allow testing perturbation theory in a de Sitter background, checking possible large back-reaction effects on the de Sitter geometry, and also eventually to discriminate between inflationary models that lead to similar results at tree level. Working in the framework of stochastic gravity, or equivalently in the large N expansion, one may derive the two-point correlations for the gravitational fluctuations incorporating the effects of matter loops. One may characterize the quantum gravitational fluctuations in a gauge invariant way by the two-point functions of the linearized Riemann tensor. This can be given in terms of the two-point linearized Einstein and Weyl tensors. Assuming minimally coupled scalar fields in a de Sitter invariant state, the two-point functions of the linearized Einstein tensor over the de Sitter background have been computed in terms of de Sitter invariant bi-tensors.

SELF-SIMILAR SOLUTIONS OF TRIAXIAL DARK MATTER HALOS

We investigate the collapse and internal structure of dark matter halos. We consider halo formation from initially scale-free perturbations, for which gravitational collapse is self-similar. Fillmore and Goldreich (1984) and Bertschinger (1985) solved the one dimensional (i.e. spherically symmetric) case. We generalize their results by formulating the three dimensional self-similar equations. We solve the equations numerically and analyze the similarity solutions in detail, focusing on the internal density profiles of the collapsed halos. By decomposing the total density into subprofiles of particles that collapse coevally, we identify two effects as the main determinants of the internal density structure of halos: adiabatic contraction and the shape of a subprofile shortly after collapse; the latter largely reflects the triaxiality of the subprofile. We develop a simple model that describes the results of our 3D simulations. In a companion paper, we apply this model to more realistic cosmological fluctuations, and thereby explain the origin of the nearly universal (NFW-like) density profiles found in N-body simulations.

Anisotropic inflation with non-abelian gauge kinetic function

We study an anisotropic inflation model with a gauge kinetic function for a non-abelian gauge field. We find that, in contrast to abelian models, the anisotropy can be either a prolate or an oblate type, which could lead to a different prediction from abelian models for the statistical anisotropy in the power spectrum of cosmological fluctuations. During a reheating phase, we find chaotic behaviour of the non-abelian gauge field which is caused by the nonlinear self-coupling of the gauge field. We compute a Lyapunov exponent of the chaos which turns out to be uncorrelated with the anisotropy.

Non-Gaussianities in multifield inflation: Superhorizon evolution, adiabaticity, and the fate offNL

We explore the superhorizon generation of large fnl of the local form in two field inflation. We calculate the two- and three-point observables in a general class of potentials which allow for an analytic treatment using the delta N formalism. Motivated by the conservation of the curvature perturbation outside the horizon in the adiabatic mode and also by the observed adiabaticity of the power spectrum, we follow the evolution of fnl^{local} until it is driven into the adibatic solution by passing through a phase of effectively single field inflation. We find that although large fnl^{local} may be generated during inflation, such non-gaussianities are transitory and will be exponentially damped as the cosmological fluctuations approach adiabaticity.

A matter bounce by means of ghost condensation

Assuming the existence of a scalar field which undergoes ``ghost condensation" and whichhas a suitably chosen potential, it is possible to obtain a non-singular bouncing cosmologyin the presence of regular matter and radiation. The potential for the ghost condensate fieldcan be chosen such that the cosmological bounce is stable against the presence ofanisotropic stress. Cosmological fluctuations on long wavelengths relevant to currentcosmological observations pass through the bounce unaffected by the new physicswhich yields the bounce. Thus, this model allows for the realization of the ``matter bounce"scenario, an alternative to inflationary cosmology for the generation of the observedprimordial fluctuations in which the inhomogeneities originate as quantum vacuumperturbations which exit the Hubble radius in the matter-dominated phase ofcontraction.