1. Introduction

Cosmology has experienced a striking advance in the last years as a consequence of the development of new experiments to observe the Cosmic Microwave Background (CMB), the large scale distribution of galaxies, distant supernovae, etc. The high-quality data produced have provided us with a consistent picture of our universe, the so-called concordance model, characterized by large-scale homogeneity, spatial flatness and composed of about 73% of dark energy, 22.5% of cold dark matter and only 4.5% of baryonic matter. The data also indicate that the primordial seeds of small-scale inhomogeneities (including our own galaxy) are predominantly adiabatic and close to Gaussian distributed with a nearly scale-invariant power spectrum. It is now generally believed that the theoretical framework within which we can accommodate all these observational results is inflation, a period of accelerated expansion in the early instants after the Big-Bang. Inflation not only drives the universe towards the present large-scale homogeneity and flatness but also predicts the generation of the primordial seeds from quantum fluctuations. However, we lack a unique scenario of inflation and, what is even worse, we do not understand the physics at such high energies. New physics beyond the standard model of particle physics are needed to understand the physical processes that gave rise to the inflationary period in the early universe.

During the last two decades the study of the anisotropies in the Cosmic Microwave Background (CMB) radiation has played a crucial role in our understanding of the form and composition of the universe. This radiation is a relic of the Big Bang which propagates freely after the decoupling of matter and radiation when the universe was some 380000 years old. It is the furthest and oldest light that can be observed in the universe, reflecting the dense and hot period of its early history and representing therefore a unique proof of the Big Bang model of the universe. Since its first detection in 1965 [Pen65], a large effort was dedicated to find the small fluctuations expected in its temperature at different directions in the sky. These anisotropies would represent the unambiguous sign of the presence of density fluctuations at early times which gave rise to the formation of galaxies and the large scale structure of the universe via gravitational instability. The anisotropies were finally detected in 1992 with the NASA COBE satellite [Smo92] and, together with the confirmation of the black-body radiation spectrum [Mat90] and the detection of the CMB radiation itself, it has made possible to award the Nobel Prize already twice within the CMB field.

The anisotropies of the CMB carry a wealth of information about the properties of our universe and of its constituents. However, the anisotropies detected by COBE correspond to large angular scales (low multipoles) above 10 degrees, and are produced by the gravitational redshift suffered by the microwave photons falling to the gravitational wells formed by the matter inhomogeneities. The theory also predicted the existence of acoustic oscillations in the power spectrum of the anisotropies at angular scales of about 1 degree and below, produced by the acoustic waves formed in the primordial plasma of baryons and photons. Later ground-based and balloon-borne experiments like BOOMERANG, MAXIMA, CBI, Archeops and VSA, and specially the NASA WMAP satellite were able to not only detect those oscillations but also to measure the power spectrum down to about 10 arcmin scales, implying an accuracy in the cosmological parameters of a few percent [see e.g. Kom10, Reb04].

Planck, launched in May 14th 2009, is expected to improve the accuracy on the determination of the cosmological parameters at a level of precision of £ 1% [Pla05]. Planck has two instruments onboard, the Low Frequency and High Frequency Instruments (LFI and HFI) covering together a frequency range 30-900 GHz, and shall provide the best measurements of intensity and polarization anisotropy of the CMB in the whole sky with unprecedented sensitivity, resolution and frequency coverage. The scientific exploitation of the data is a unique opportunity to extend the frontiers of our knowledge on the Universe. All the Spanish contribution to the Planck instrument hardware has been provided by four of the groups included in this Consolider: The Departamento de Ingeniería de las Comunicaciones from Universidad de Cantabria, DICOM, (technical responsible) and the Instituto de Física de Cantabria, IFCA, (scientific responsible) provided the Back-End Modules of the 30 and 44 GHz radiometers of the LFI, which together with the Front-End Modules (provided by the group at University of Manchester) form the complete amplification chain at those two frequencies; the Instituto de Astrofísica de Canarias, IAC, provided the Radiometer Electronics Box Assembly that controls the data acquisition, compression and transmission of the whole LFI system, the group at Universidad de Granada provided the regulator electronics for the 4K cooler of the HFI. Enrique Martínez-González, Rafael Rebolo and Richard Davis are Co-Investigators of the LFI whereas Eduardo Battaner and Anthony Lasenby are Co-Investigators of the HFI. Most of the Consolider team members are associated to the Planck collaboration, a large fraction being also part of the Core Teams, many of them being Planck Scientists, and some of them coordinating some working groups and leading some scientific proposals for the data exploitation. Overall the Consolider team is expected to have a major role in the Planck scientific goals. This satellite is aimed to study many cosmological and astrophysical topics [Pla05].

The standard cosmological model also predicts that the CMB radiation is linearly polarized. The polarization signal and its cross-correlation with the temperature anisotropies constitute an important consistency check and help in breaking the degeneracies among some cosmological parameters. A net value of the Stokes parameters Q and U is expected from Thomson scattering during decoupling of photons and baryons. Since Q and U are not invariant quantities on the sphere it is convenient to transform them in a gradient field called “E-mode” and a rotational field called “B-mode”. The most important property of the E and B-mode decomposition is that from their measurement we can distinguish between primordial scalar perturbations (density) and primordial tensor perturbations (gravitational waves). More specifically, both types of perturbations can generate E-mode polarization, however only gravitational waves can produce B-mode polarization. It is this property that makes polarization a key tool for the detection of the primordial gravitational wave background (GWB) which is expected to be generated during the inflationary period of the universe. Moreover, a detection of the B-mode would directly provide the energy scale of inflation (as measured by the ratio r of tensor to scalar perturbations, see Fig. 0).

Figure 0. Top: The cosmic mean density as a function of the Universe relative size. Detecting inflationary gravitational waves with CMB polarization would directly measure the shape of the cosmic density curve in the upper left corner of the plot, while experiments trying to characterise the dark energy would measure the same curve in the lower right corner [Boc06].  Bottom: The GW energy density as a function of the frequency. Theoretical predictions and observational constraints on primordial GW from inflation are shown in this plot. It is also shown the maximum expected signal for the case of r=0.01 and r=0.001. The blue shaded region represents the range predicted for simple inflation models with the minimal number of parameters and tunings [Boc06].

2. Cosmic inflation and the early univers

Inflation is a period of accelerated expansion in the very early universe, leading to a substantial flattening and smoothing of the universe, which explains why it appears to us so regular at very large scales. Inflation, in addition to smoothing and wiping out previous inhomogeneities through expansion, also stretches short distance quantum fluctuations to large scales. Thus, the seeds of structure formation come mainly from short distance quantum fluctuations created at the beginning of inflation. The simplest models of inflation generate adiabatic density perturbations that are very nearly Gaussian and with a nearly scale-invariant spectrum [Dod03].

But how can one explain a period of accelerated expansion in the universe? The Friedmann equations that describe the evolution of a homogeneous and isotropic universe provide a hint: from these equations accelerated expansion follows if the pressure is negative enough (verifies p < -r/3 in natural units with r being the energy density). But then, how can the cosmic fluid parametrized in terms of p and r  display such peculiar equation of state? If one considers a scalar field model it can be shown that when its energy density is dominated by its potential energy contribution it has an equation of state close to p = -r. These ideas indicate that if we have one such field, usually called the inflaton, in a potential energy dominated regime, the universe will follow an accelerated expansion. Another important issue is the duration of the inflationary epoch, which is usually given in terms of e-folds, i.e. in terms of the number of e factors by which the scale factor a of the universe has grown. A duration of 60 e-folds means that the size of any region of the universe has become e60 times bigger and this is the order of the minimum duration of inflation required by current observational data.

The possibility explained above is just but one of the inflationary settings in the literature so far, the single-field models (which are the simplest ones). There are many other scenarios for inflation, which involve more fields or more complicated concepts. Among all the proposals of inflationary models a huge amount of them remain compatible with the observational data currently available.

Since inflation is thought to be a key ingredient in the generation of the seeds of inhomogeneities in our present universe (primordial density fluctuations and gravitational waves), the characteristics of the temperature and polarization anisotropies of the CMB are determined (among other parameters) by the characteristics of the primordial spectra of fluctuations resulting from inflation (scalar and tensor). The main parameters that characterize the primordial spectra are the amplitude and the tilt, ns, (also known as spectral index) for the scalar primordial spectrum, and the tensor to scalar ratio of amplitudes, r, for the tensor primordial spectrum. The measurement of these parameters to be performed in this project will provide relevant insights and constraints in the physics of inflation.

In addition, the inflationary period can lead to other effects, as the generation of primordial magnetic fields. The investigation of the mechanisms of generation and the observational implications of these primordial magnetic fields could also provide insights into the physics of inflation [Bat09].

Understanding the physics of inflation is one of the main goals in Cosmology, and the measurements of the B-mode polarization signal of the CMB is currently probably the most promising method to attain considerable progress in the study of the physics of inflation. This has been also pointed out by the ESA-ESO Working Group on Fundamental Cosmology [Pea06], together with a strong recommendation to support these measurements and the required technological developments.

As stated above, there is at present a wide set of inflationary models and for each model a wide set of inflaton potentials that satisfies the present observational constraints. Therefore, it is neither clear which is the most compelling inflationary model nor the fittest inflaton potential for each model. However, the new data are starting to constrain more restrictively the inflationary models and the inflaton potentials. For example, recent upper bounds on the tensor to scalar ratio r by WMAP combined with their bounds to the spectral index ns have led to the exclusion of chaotic single-field inflation with a monomial f4 potential that gives 60 e-folds of inflation [Kom10]. In other words, this inflationary model with this inflaton potential is excluded because it will lead to larger amplitudes in the B-mode spectrum than those observed (see Fig. 1). In this respect it is worth mentioning that Dirac-Born-Infeld single-field inflation models can be better suited to the observational constraints on r and ns  than their conventional counterparts [Spa07], and so potentials which would be in principle ruled out might actually be admissible. This possibility is associated with the presence of an additional degree of freedom (linked to the proper velocity of the DBI scenario brane in the multidimensional spacetime it lives in). In particular, an ultrarelativistic regime would lead to a really low value of r, so if such a result were obtained, one would have a theoretical framework to try and provide an explanation.

Another significant feature of this inflationary setup is the generic presence of non-gaussianity, commonly expressed in terms of the non-linear coupling parameter, fNL, which is another of the observational goals of this project. A large departure from gaussianity can also be interpreted as observational support for inflation models inspired by extradimensions, like the mentioned DBI framework.

Yet, a convincing signal of non-gaussianity in the perturbation spectrum can be also nicely accommodated in the warm inflation scenario [Ber95], which is characterized by allowing couplings of the inflaton to other fields in the theory, which result in a dissipative dynamics.

Thus, summarizing, constraints in r and ns lead to constraints in the inflationary models and their inflaton potentials, and therefore contribute to defining the physical characteristics and dynamics of the inflationary period.

Even though inflation was originally associated with the grand unification of the strong and electroweak interactions it is now clear that its energy scale, or epoch, is quite uncertain and can be above or below that of the grand unification. However, it is worth mentioning that from the value of ns obtained by WMAP and qualitative arguments on the shape of the inflaton potential in the simplest models of inflation, a value r > 0.01 has been suggested [Boy06] which is within the reach of the present project.

In any case, this project will contribute largely to progresses in the current understanding of the physics of inflation by increasing the sensitivity in the determination of the tensor to scalar ratio r and deriving consequences for inflationary models and inflaton potentials.

Figure 1: Contours show the 68% and 95% CL derived from WMAP+BAO+SN compared with the theoretical predictions for chaotic inflation models with the potential indicated in the legend. N is the number of e-folds. (This figure corresponds to the upper panel of Fig. 19 in [Kom10])

In addition, there is another topic on which this project can make a considerable impact: primordial magnetic fields. If such fields were generated before photon decoupling they could have left imprints in the CMB, as they could be responsible for non-Gaussianity, Planck spectrum distorsions, anisotropy spectrum modifications, generation of waves, Faraday Rotation and others.
Even though no clear signs of magnetic fields in CMB experiments have been found so far, the situation may get reversed with the new experiments QUIJOTE and Planck, due to their improved sensitivity, frequency coverage and angular resolution, as well as with the improved capacity to measure polarization.

This topic fits perfectly in the framework of this project, both from the experimental and theoretical dimensions as the most attractive magnetogenesis mechanism is provided by inflation. It can give fields at any scale in the same way that super-horizon energy density structures are created and observed in CMB (including the Sachs-Wolfe region of the power spectrum) and in the large scale structure. This scenario was early assumed by [Tur88] and was developed by several authors thereafter (i.e. [Gio07]; see [Bat00] and [Bat09] for a review of the different mechanisms). However the mechanism is not completely understood and its investigation is a goal of this project.

As for the observational hints, for a frequency of 30 GHz magnetic fields would provide a rotation angle of between 1 and 20 degrees, which is measurable by QUIJOTE and Planck. However the main difficulty is the weakness of the signal as compared to the noise, and the expected contamination with the Galactic contribution, which will require further developments in the modelling. These difficulties add to the intrinsic complication of the phenomenon, which clearly requires a lot of theoretical effort. This exertion adds to that devoted to the above mentioned theoretical challenges related to inflation, thus making this project have a very solid entity on the theoretical front as well.