Planck 2015 results and inflation

The Planck mission prime objective was a very accurate and complete measurement of the temperature anisotropies of the Cosmic Microwave Background (CMB). Cosmological results from the intensity data of the nominal mission of a duration of 15 months were disclosed on 21 March 2013. Fortunately, the satellite kept acquiring data for at least twice longer, and we announced in February 2015 new results based on all the data acquired, both in temperature and polarization. I provide a short overview of the latest data and findings of most interest for inflation, as a basis for the other contributions to this volume. This overview is entirely based on the published or submitted works of the Planck collaboration.     

Inflation in entropic cosmology: Primordial perturbations and non-Gaussianities

We investigate thermal inflation in double-screen entropic cosmology. We find that its realization is general, resulting from the system evolution from non-equilibrium to equilibrium. Furthermore, going beyond the background evolution, we study the primordial curvature perturbations arising from the universe interior, as well as from the thermal fluctuations generated on the holographic screens. We show that the power spectrum is nearly scale-invariant with a red tilt, while the tensor-to-scalar ratio is in agreement with observations. Finally, we examine the non-Gaussianities of primordial curvature perturbations, and we find that a sizable value of the non-linearity parameter is possible due to holographic statistics on the outer screen.     

Tachyon-Chaplygin inflation on the brane

Tachyon-brane inflationary universe model in the context of a Chaplygin gas equation of state is studied. General conditions for this model to be realizable are discussed. In the high-energy limit and by using an exponential potential we describe in great details the characteristic of this model. Recent observational data from the Wilkinson Microwave Anisotropy Probe experiment are employed to restrict the parameters of the model.     

Minimal inflation

Using the universal X-superfield that measures in the UV the violation of conformal invariance we build up a model of multifield inflation. The underlying dynamics is the one controlling the natural flow of this field in the IR to the goldstino superfield once SUSY is broken. We show that flat directions satisfying the slow-roll conditions exist only if R-symmetry is broken. Naturalness of our model leads to scales of SUSY breaking of the order of 10^11–13 GeV, a nearly scale-invariant spectrum of the initial perturbations and negligible gravitational waves. We obtain that the inflaton field is lighter than the gravitino by an amount determined by the slow-roll parameter η. The existence of slow-roll conditions is directly linked to the values of supersymmetry and R-symmetry breaking scales. We make cosmological predictions of our model and compare them to current data.     

Neutrino mass and oscillation: An introductory review

After a brief introduction to neutrino mass via the see-saw model I discuss neutrino mixing and oscillation, first in vacuum and then its matter enhancement. Then the solar and atmospheric neutrino oscillation data are briefly reviewed. Finally I discuss the problem of reconciling hierarchical neutrino masses with at least one large mixing, as implied by these data. A minimal see-saw model for reconciling the two is discussed.     

Relationship between (2 + 1) and (3 + 1)-Friedmann–Robertson–Walker cosmologies; linear,non-linear,and polytropic state equations

It is shown that Friedmann–Robertson–Walker (FRW) cosmological models coupled to a single scalar field and to a perfect fluid fitting a wide class of matter perfect fluid state equations, determined in (3+1) dimensional gravity can be related to their (2+1) cosmological counterparts, and vice-versa, by using simple algebraic rules relating gravitational constants, state parameters, perfect fluid and scalar field characteristics. It should be pointed out that the demonstration of these relations for the scalar fields and potentials does not require the fulfilment of any state equation for the scalar field energy density and pressure. As far as to the perfect fluid is concerned, one has to demand the fulfilment of state equations of the form p+ = f(). If the considered cosmologies contain the inflation field alone, then any (3+1) scalar field cosmology possesses a (2+1) counterpart, and vice-versa. Various families of solutions are derived, and we exhibited their correspondence; for instance, solutions for pure matter perfect fluids and single scalar field fulfilling linear state equations, solutions for scalar fields coupled to matter perfect fluids, a general class of solutions for scalar fields subjected to a state equation of the form p + = are reported, in particular Barrow–Saich, and Barrow–Burd–Lancaster–Madsen solutions are exhibited explicitly, and finally perfect fluid solutions for polytropic state equations are given.     

Hybrid natural low scale inflation

We discuss the phenomenological implications of Hybrid Natural Inflation models in which the inflaton is a pseudo-Goldstone boson but inflation is terminated by a second scalar field. A feature of the scheme is that the scale of breaking of the Goldstone symmetry can be lower than the Planck scale and so gravitational corrections are under control. We show that, for supersymmetric models, the scale of inflation can be chosen anywhere between the Lyth upper bound and a value close to the electroweak breaking scale. The observed density perturbations and spectral index are readily obtained by the choice of the free parameters. The tensor to scalar ratio and the spectral tilt are extremely small.     

The Evolution of Primordial Black Hole Masses in the Radiation-Dominated Era

We discuss in this work the behaviour of primordial black holes (PBHs) in the radiation era. Taking into account the Hawking evaporation and the absorption of energy we revisit the complete differential equation for the evolution of the mass of a PBH. We show that the mass can grow in this cosmological phase in a very slow fashion (even when considering the very high temperature of the radiation) if at all, and give a strong upper limit to the maximum accretion of mass. We evaluate relativistic effects due to the peculiar motion relative to the CMBR and show that the existence of relativistic black holes with very high mass absorption is highly unlikely. Finally we demonstrate that thermodynamic equilibrium between black holes and the cosmic radiation can not exist for finite times, and therefore initially non-evaporating PBHs must jump to the evaporating regime. This analysis supports the several efforts performed to look for signatures of evaporating holes.     

Does inflation provide natural initial conditions for the universe

If our universe underwent inflation, its entropy during the inflationary phase was substantially lower than it is today. Because a low-entropy state is less likely to be chosen randomly than a high-entropy one, inflation is unlikely to arise through randomly-chosen initial conditions. To resolve this puzzle, we examine the notion of a natural state for the universe, and argue that it is a nearly-empty spacetime. If empty space has a small vacuum energy, however, inflation can begin spontaneously in this background. This scenario explains why a universe like ours is likely to have begun via a period of inflation, and also provides an origin for the cosmological arrow of time. This work was supported in part by the U.S. Dept. of Energy, the National Science Foundation, the NDSEG Fellowship, and the David and Lucile Packard Foundation. Second Award in the 2005 Essay Competition of the Gravity Research Foundation. - Ed.     

The imprint of inflation on the cosmic microwave background

The cosmic microwave background is the most precise and the most simple cosmological dataset. This makes it our most prominent window to the physics of the very early Universe. In this article I give an introduction to the physics of the cosmic microwave background and show in some detail how primordial fluctuations from inflation are imprinted in the temperature anisotropy and polarisation spectrum of the CMB. I discuss the main signatures that are suggesting an inflationary phase for the generation of initial fluctuations.     

Light scattering in the Solar System: An introductory review

We present a concise survey of light scattering by small particles in the atmospheres and surface layers of various Solar System bodies, comets, the interplanetary medium, and in planetary rings. Current issues and recent developments are emphasized. Special attention is given to experimental and numerical approaches for solving problems of light scattering by non-spherical particles. References to more detailed papers, websites and books are presented. Key areas for further research are pointed out.     

Inflation,LHC and the Higgs boson

After the Higgs boson has been discovered, the Standard Model of particle physics became a confirmed theory, potentially valid up to the Planck scale and allowing one to trace the evolution of the Universe from the inflationary stage till the present days. We discuss the relation between the results from the LHC and the inflationary cosmology. We overview the Higgs inflation, and its relation to the possible metastability of the electroweak vacuum. A short overview of the bounds on the metastability of the electroweak vacuum in the models with inflation not related to the Higgs boson is presented.     

Isotropization of the universe during inflation

A primordial inflationary phase allows one to erase any possible anisotropic expansion thanks to the cosmic no-hair theorem. If there is no global anisotropic stress, then the anisotropic expansion rate tends to decrease. What are the observational consequences of a possible early anisotropic phase? We first review the dynamics of anisotropic universes and report analytic approximations. We then discuss the structure of dynamical equations for perturbations and the statistical properties of observables, as well as the implication of a primordial anisotropy on the quantization of these perturbations during inflation. Finally we review briefly models based on primordial vector field that evade the cosmic no-hair theorem.     

Causal structures in inflation

This article reviews the properties and limitations associated with the existence of particle, visual, and event horizons in cosmology in general and in inflationary universes in particular, carefully distinguishing them from ‘Hubble horizons’. It explores to what extent one might be able to probe conditions beyond the visual horizon (which is close in size to the present Hubble radius), thereby showing that visual horizons place major limits on what are observationally testable aspects of a multiverse, if such exists. Indeed these limits largely prevent us from observationally proving a multiverse either does or does not exist. We emphasize that event horizons play no role at all in observational cosmology, even in the multiverse context, despite some claims to the contrary in the literature.     

Primordial curvature perturbation during and at the end of multi-field inflation

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