arXiv subjects

Giulia Gubitosi

Publications and source records attributed to Giulia Gubitosi.

At least 55 records · Page 3Linked to original sources

arXiv2017

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 $κ$-Poincaré 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.

gr-qc↗

arXiv2017

Primordial standing waves

We consider the possibility that the primordial fluctuations (scalar and tensor) might have been standing waves at their moment of creation, whether or not they had a quantum origin. We lay down the general conditions for spatial translational invariance, and isolate the pieces of the most general such theory that comply with, or break translational symmetry. We find that, in order to characterize statistically translationally invariant standing waves, it is essential to consider the correlator $\langle c_0({\mathbf k}) c_0({\mathbf k}')\rangle$ in addition to the better known $\langle c_0({\mathbf k}) c_0^\dagger({\mathbf k}')\rangle$ (where $c_0({\mathbf k})$ are the complex amplitudes of travelling waves). We then examine how the standard process of "squeezing" (responsible for converting travelling waves into standing waves while the fluctuations are outside the horizon) reacts to being fed primordial standing waves. For translationally invariant systems only one type of standing wave, with the correct temporal phase (the "sine wave"), survives squeezing. Primordial standing waves might therefore be invisible at late times -- or not -- depending on their phase. Theories with modified dispersion relations behave differently in this respect, since only standing waves with the opposite temporal phase survive at late times.

gr-qc↗

arXiv2017

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 $σ\sim ω^2 |y|^2/|p|^2$. Even though $σ$ 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 $σ$ at the end of the primordial phase: it is enough that $σ$ 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 $σ\sim 1$, 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.

gr-qc↗

arXiv2017

Squeezing of scalar and tensor primordial perturbations generated by modified dispersion relations

In recent work we analyzed the evolution of primordial perturbations satisfying Planck-scale-modified dispersion relations and showed that there is no cosmological "squeezing" in the critical model that produces perturbations with a scale invariant spectrum. Nevertheless, the perturbations reenter the horizon as standing waves with the correct temporal phase because of the late-time decay of the momentum mode. Here we shed light on the absence of primordial squeezing by re-examining the problem in the dual rainbow frame, where $c$ is set to 1, shifting the varying $c$ effects elsewhere. In this frame gravity switches off at sub-Planckian wavelengths, so that the fluctuations behave as if they were in Minkowski spacetime. This is ultimately why they are not squeezed. However, away from the critical model squeezing does occur if the fluctuations spectrum is red, as is the case for scalar perturbations. Should the primordial gravity waves have a blue spectrum, we predict that they might not reenter the horizon as standing waves, because the momentum mode would be enhanced in the primordial phase.

gr-qc↗

arXiv2017

Curved spacetimes with local $κ$-Poincaré dispersion relation

We use our previously developed identification of dispersion relations with Hamilton functions on phase space to locally implement the $κ$-Poincaré dispersion relation in the momentum spaces at each point of a generic curved spacetime. We use this general construction to build the most general Hamiltonian compatible with spherical symmetry and the Plank-scale-deformed one such that in the local frame it reproduces the $κ$-Poincaré dispersion relation. Specializing to Planck-scale-deformed Schwarzschild geometry, we find that the photon sphere around a black hole becomes a thick shell since photons of different energy will orbit the black hole on circular orbits at different altitudes. We also compute the redshift of a photon between different observers at rest, finding that there is a Planck-scale correction to the usual redshift only if the observers detecting the photon have different masses.

gr-qc↗

arXiv2017

Correlation between opposite-helicity gravitons: Imprints on gravity-wave and microwave backgrounds

We examine some of the roots of parity violation for gravitons and uncover a closely related new effect: correlations between right and left handed gravitons. Such correlators have spin 4 if they involve gravitons moving along the same direction, and spin zero for gravitons moving with opposite directions. In the first case, the most immediate implication would be a degree of linear polarization for the tensor vacuum fluctuations, which could be seen by gravity wave detectors sensitive enough to probe the primordial background, its degree of polarization and anisotropies. Looking at the anisotropy of the gravity waves linear polarization we identify the parity respecting and violating components of the effect. The imprint on the CMB temperature and polarization would be more elusive, since it averages to zero in the two-point functions, appearing only in their cosmic variance or in fourth order correlators. In contrast, spin zero correlations would have an effect on the two point function of the CMB temperature and polarization, enhancing the $BB$ component if they were anti-correlations. Such correlations represent an amplitude for the production of standing waves, as first envisaged by Grishchuk, and could also leave an interesting signature for gravity wave detectors.

gr-qc↗

arXiv2016

Primordial perturbations in a rainbow universe with running Newton constant

We compute the spectral index of primordial perturbations in a rainbow universe. We allow the Newton constant $G$ to run at (super-)Planckian energies and we consider both vacuum and thermal perturbations. If the rainbow metric is the one associated to a generalized Horava-Lifshitz dispersion relation, we find that only when $G$ tends asymptotically to zero can one match the observed value of the spectral index and solve the horizon problem, both for vacuum and thermal perturbations. For vacuum fluctuations the observational constraints imply that the primordial universe expansion can be both accelerating or decelerating, while in the case of thermal perturbations only decelerating expansion is allowed.

gr-qc↗

arXiv2016

Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes

The covariant understanding of dispersion relations as level sets of Hamilton functions on phase space enables us to derive the most general dispersion relation compatible with homogeneous and isotropic spacetimes. We use this concept to present a Planck-scale deformation of the Hamiltonian of a particle in Friedman-Lemaître-Robertson-Walker (FLRW) geometry that is locally identical to the $κ$-Poincaré dispersion relation, in the same way as the dispersion relation of point particles in general relativity is locally identical to the one valid in special relativity. Studying the motion of particles subject to such Hamiltonian we derive the redshift and lateshift as observable consequences of the Planck-scale deformed FLRW universe.

gr-qc↗

arXiv2016

Thermal dimension of quantum spacetime

Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular for various scenarios of "dynamical dimensional reduction" which have been discussed in the literature. We are here concerned with the fact that the related research effort has been based mostly on analyses of the "spectral dimension", which involves an unphysical Euclideanization of spacetime and is highly sensitive to the off-shell properties of a theory. As here shown, different formulations of the same physical theory can have wildly different spectral dimension. We propose that dynamical dimensional reduction should be described in terms of the "thermal dimension" which we here introduce, a notion that only depends on the physical content of the theory. We analyze a few models with dynamical reduction both of the spectral dimension and of our thermal dimension, finding in particular some cases where thermal and spectral dimension agree, but also some cases where the spectral dimension has puzzling properties while the thermal dimension gives a different and meaningful picture.

hep-th↗

arXiv2016

Bayesian evidence and predictivity of the inflationary paradigm

In this paper we consider the issue of paradigm evaluation by applying Bayes' theorem along the following nested hierarchy of progressively more complex structures: i) parameter estimation (within a model), ii) model selection and comparison (within a paradigm), iii) paradigm evaluation. In such a hierarchy the Bayesian evidence works both as the posterior's normalization at a given level and as the likelihood function at the next level up. Whilst raising no objections to the standard application of the procedure at the two lowest levels, we argue that it should receive a considerable modification when evaluating paradigms, when testability and fitting data are equally important. By considering toy models we illustrate how models and paradigms that are difficult to falsify are always favoured by the Bayes factor. We argue that the evidence for a paradigm should not only be high for a given dataset, but exceptional with respect to what it would have been, had the data been different. With this motivation we propose a measure which we term predictivity, as well as a prior to be incorporated into the Bayesian framework, penalising unpredictivity as much as not fitting data. We apply this measure to inflation seen as a whole, and to a scenario where a specific inflationary model is hypothetically deemed as the only one viable as a result of information alien to cosmology (e.g. Solar System gravity experiments, or particle physics input). We conclude that cosmic inflation is currently hard to falsify, but that this could change were external/additional information to cosmology to select one of its many models. We also compare this state of affairs to bimetric varying speed of light cosmology.

astro-ph.CO↗

arXiv2016

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.

gr-qc↗

arXiv2015

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.

gr-qc↗

arXiv2015

Kinematics of particles with quantum de Sitter symmetries

We present the first detailed study of the kinematics of free relativistic particles whose symmetries are described by a quantum deformation of the de Sitter algebra, known as $q$-de Sitter Hopf algebra. The quantum deformation parameter is a function of the Planck length $\ell$ and the de Sitter radius $H^{-1}$, such that when the Planck length vanishes, the algebra reduces to the de Sitter algebra, while when the de Sitter radius is sent to infinity one recovers the $κ$-Poincaré Hopf algebra. In the first limit the picture is that of a particle with trivial momentum space geometry moving on de Sitter spacetime, in the second one the picture is that of a particle with de Sitter momentum space geometry moving on Minkowski spacetime. When both the Planck length and the inverse of the de Sitter radius are non-zero, effects due to spacetime curvature and non-trivial momentum space geometry are both present and affect each other. The particles' motion is then described in a full phase space picture. We find that redshift effects that are usually associated to spacetime curvature become energy-dependent. Also, the energy dependence of particles' travel times that is usually associated to momentum space non-trivial properties is modified in a curvature-dependent way.

gr-qc↗

arXiv2015

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.

gr-qc↗

arXiv2015

Hamilton geometry: Phase space geometry from modified dispersion relations

We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $κ$-Poincaré quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum space, while for the second case the manifold is flat and only the momentum space possesses a nonzero, momentum dependent curvature. In contrast, for a dispersion relation that is induced by a spacetime metric, as in General Relativity, the Hamilton geometry yields a flat momentum space and the usual curved spacetime geometry with only position dependent geometric objects.

gr-qc↗

arXiv2015

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.

astro-ph.CO↗

arXiv2015

Vacuum fluctuations in theories with deformed dispersion relations

We examine vacuum fluctuations in theories with modified dispersion relations which represent dimensional reduction at high energies. By changing units of energy and momentum we can obtain a description rendering the dispersion relations undeformed and transferring all the non-trivial effects to the integration measure in momentum space. Using this description we propose a general quantization procedure, which should be applicable whether or not the theory explicitly introduces a preferred frame. Based on this scheme we evaluate the power spectrum of quantum vacuum fluctuations. We find that in {\it all} theories which run to 2 dimensions in the ultraviolet the vacuum fluctuations, in the ultraviolet regime, are scale-invariant. This is true in flat space but also for "inside the horizon" modes in an expanding universe. We spell out the conditions upon the gravity theory for this scale-invariance to be preserved as the modes are frozen-in outside the horizon. We also digress on the meaning of dimensionality (in momentum and position space) and suggest that the spectral index could itself provide an operational definition of dimensionality.

gr-qc↗

arXiv2015

Gravity as the breakdown of conformal invariance

We propose that at the beginning of the universe gravity existed in a limbo either because it was switched off or because it was only conformally coupled to all particles. This picture can be reverse-engineered from the requirement that the cosmological perturbations be (nearly) scale-invariant without the need for inflation. It also finds support in recent results in quantum gravity suggesting that spacetime becomes two-dimensional at super-Planckian energies. We advocate a novel top-down approach to cosmology based on the idea that gravity and the Big Bang Universe are relics from the mechanism responsible for breaking the fundamental conformal invariance. Such a mechanism should leave clear signatures in departures from scale-invariance in the primordial power spectrum and the level of gravity waves generated.

gr-qc↗