The phenomenology of squeezing and its status in non-inflationary theories

In this paper we skim the true phenomenological requirements behind the concept of inflationary squeezing. We argue that all that is required is that at horizon re-entry the fluctuations form standing waves with the correct temporal phase (specifically, sine waves). We quantify this requirement and relate it to the initial conditions fed into the radiation dominated epoch by whatever phase of the Universe produced the fluctuations. The only relevant quantity turns out to be the degree of suppression of the momentum, $p$, of the fluctuations, $y$, which we measure by $\sigma\sim \omega^2 |y|^2/|p|^2$. Even though $\sigma$ equals the squeezing parameter, $s$, in the case of inflation and bimetric varying speed of light scenarios, this is not true in general, specifically in some bouncing Universe models. It is also not necessary to produce a large $\sigma$ at the end of the primordial phase: it is enough that $\sigma$ be not too small. This is the case with scenarios based on modified dispersion relations (MDR) emulating the dispersion relations of Horava-Lifshitz theory, which produce $\sigma\sim 1$, enough to comply with the observational requirements. Scenarios based on MDR leading to a slightly red spectrum are also examined, and shown to satisfy the observational constraints.Comment: v2: Typos corrected. Matches the accepted version on JCA

Constraints on cosmological birefringence energy dependence from CMB polarization data

We study the possibility of constraining the energy dependence of cosmological birefringence by using CMB polarization data. We consider four possible behaviors, characteristic of different theoretical scenarios: energy-independent birefringence motivated by Chern-Simons interactions of the electromagnetic field, linear energy dependence motivated by a 'Weyl' interaction of the electromagnetic field, quadratic energy dependence, motivated by quantum gravity modifications of low-energy electrodynamics, and inverse quadratic dependence, motivated by Faraday rotation generated by primordial magnetic fields. We constrain the parameters associated to each kind of dependence and use our results to give constraints on the models mentioned. We forecast the sensitivity that Planck data will be able to achieve in this respect.Comment: 15 pages, 5 figures. v2 matches JCAP published versio

Reappraisal of a model for deformed special relativity

We revisit one of the earliest proposals for deformed dispersion relations in the light of recent results on dynamical dimensional reduction and production of cosmological fluctuations. Depending on the specification of the measure of integration and addition rule in momentum space the model may be completed so as to merely deform Lorentz invariance, or so as to introduce a preferred frame. Models which violate Lorentz invariance have a negative UV asymptotic dimension and a very red spectrum of quantum vacuum fluctuations. Instead, models which preserve frame independence can exhibit running to a UV dimension of 2, and a scale-invariant spectrum of fluctuations. The bispectrum of the fluctuations is another point of divergence between the two casings proposed here for the original model

Life of cosmological perturbations in MDR models, and the prospect of travelling primordial gravitational waves

We follow the life of a generic primordial perturbation mode (scalar or tensor) subject to modified dispersion relations (MDR), as its proper wavelength is stretched by expansion. A necessary condition ensuring that travelling waves can be converted into standing waves is that the mode starts its life deep inside the horizon and in the trans-Planckian regime, then leaves the horizon as the speed of light corresponding to its growing wavelength drops, to eventually become cis-Planckian whilst still outside the horizon, and finally re-enter the horizon at late times. We find that scalar modes in the observable range satisfy this condition, thus ensuring the viability of MDR models in this respect. For tensor modes we find a regime in which this does not occur, but in practice it can only be realised for wavelengths in the range probed by future gravity wave experiments if the quantum gravity scale experienced by gravity waves goes down to the PeV range. In this case travelling---rather than standing---primordial gravity waves could be the tell-tale signature of MDR scenarios.Comment: 9 pages, 1 figure. v2 matches version accepted for publicatio

Quantum Gravity phenomenology and metric formalism

In this proceedings for the MG14 conference, we discuss the construction of a phenomenology of Planck-scale effects in curved spacetimes, underline a few open issues and describe some perspectives for the future of this research line

Parity at the Planck scale

We explore the possibility that well known properties of the parity operator, such as its idempotency and unitarity, might break down at the Planck scale. Parity might then do more than just swap right and left polarized states and reverse the sign of spatial momentum ${\bf k}$: it might generate superpositions of right and left handed states, as well as mix momenta of different magnitudes. We lay down the general formalism, but also consider the concrete case of the Planck scale kinematics governed by $\kappa$-Poincar\'e symmetries, where some of the general features highlighted appear explicitly. We explore some of the observational implications for cosmological fluctuations. Different power spectra for right handed and left handed tensor modes might actually be a manifestation of deformed parity symmetry at the Planck scale. Moreover, scale-invariance and parity symmetry appear deeply interconnected

Quantization of fluctuations in DSR: the two-point function and beyond

We show that the two-point function of a quantum field theory with de Sitter momentum space (herein called DSR) can be expressed as the product of a standard delta function and an energy-dependent factor. This is a highly non-trivial technical result in any theory without a preferred frame. Applied to models exhibiting running of the dimensionality of space, this result is essential in proving that vacuum fluctuations are generally scale-invariant at high energies whenever there is running to two dimensions. This is equally true for theories with and without a preferred frame, with differences arising only as we consider higher order correlators. Specifically, the three-point function of DSR has a unique structure of "open triangles", as shown here.Comment: 5 pages, 1 figur

Including birefringence into time evolution of CMB: current and future constraints

We introduce birefringence effects within the propagation history of CMB, considering the two cases of a constant effect and of an effect that increases linearly in time, as the rotation of polarization induced by birefringence accumulates during photon propagation. Both cases result into a mixing of E and B modes before lensing effects take place, thus leading to the fact that lensing is acting on spectra that are already mixed because of birefringence. Moreover, if the polarization rotation angle increases during propagation, birefringence affects more the large scales that the small scales. We put constraints on the two cases using data from WMAP 9yr and BICEP 2013 and compare these results with the constraints obtained when the usual procedure of rotating the final power spectra is adopted, finding that this dataset combination is unable to distinguish between effects, but it nevertheless hints for a non vanishing value of the polarization rotation angle. We also forecast the sensitivity that will be obtained using data from Planck and PolarBear, highlighting how this combination is capable to rule out a vanishing birefringence angle, but still unable to distinguish the different scenarios. Nevertheless, we find that the combination of Planck and PolarBear is sensitive enough to highlight the existence of degeneracies between birefringence rotation and gravitational lensing of CMB photons, possibly leading to false detection of non standard lensing effects if birefringence is neglected.Comment: 20 pages, 10 figures. New version matching the one accepted by JCAP. Corrected typos in equations 2.17-2.1

On the initial singularity problem in rainbow cosmology

It has been recently claimed that the initial singularity might be avoided in the context of rainbow cosmology, where one attempts to account for quantum-gravitational corrections through an effective-theory description based on an energy-dependent ("rainbow") space-time metric. We here scrutinize this exciting hypothesis much more in depth than previous analyses. In particular, we take into account all requirements for singularity avoidance, while previously only a subset of these requirements had been considered. Moreover, we show that the implications of a rainbow metric for thermodynamics are more significant than previously appreciated. Through the analysis of two particularly meaningful examples of rainbow metrics we find that our concerns are not merely important conceptually, but actually change in quantitatively significant manner the outcome of the analysis. Notably we only find examples where the singularity is not avoided, though one can have that in the regime where our semi-classical picture is still reliable the approach to the singularity is slowed down when compared to the standard classical scenario. We conclude that the study of rainbow metrics provides tantalizing hints of singularity avoidance but is inconclusive, since some key questions remain to be addressed just when the scale factor is very small, a regime which, as here argued, cannot be reliably described by an effective rainbow-metric picture.Comment: v3: typo in Eq. (9) corrected, results unchanged. 10 pages, 5 figures, v2 matches published versio