No Arabic abstract
Recently, a new cosmological framework, dubbed Ricci Cosmology, has been proposed. Such a framework has emerged from the study of relativistic dynamics of fluids out of equilibrium in a curved background and is characterised by the presence of deviations from the equilibrium pressure in the energy-momentum tensor which are due to linear terms in the Ricci scalar and the Ricci tensor. The coefficients in front of such terms are called the second order transport coefficients and they parametrise the fluid response to the pressure terms arising from the spacetime curvature. Under the preliminary assumption that the second order transport coefficients are constant, we find the simplest solution of Ricci cosmology in which the presence of pressure terms causes a departure from the perfect fluid redshift scaling for matter components filling the Universe. In order to test the viability of this solution, we make four different ans{a}tze on the transport coefficients, giving rise to four different cases of our model. On the physical ground of the second law of thermodynamics for fluids with non-equilibrium pressure, we find some theoretical bounds (priors) on the parameters of the models. Our main concern is then the check of each of the case against the standard set of cosmological data in order to obtain the observational bounds on the second order transport coefficients. We find those bounds also realising that Ricci cosmology model is compatible with $Lambda$CDM cosmology for all the ans{a}tze.
We revisit spatially flat FLRW cosmology in light of recent advances in standard model relativistic fluid dynamics. Modern fluid dynamics requires the presence of curvature-matter terms in the energy-momentum tensor for consistency. These terms are linear in the Ricci scalar and tensor, such that the corresponding cosmological model is referred to as ``Ricci cosmology. No cosmological constant is included, there are no inflaton fields, bulk viscosity is assumed to be zero and we only employ standard Einstein gravity. Analytic solutions to Ricci cosmology are discussed, and we find that it is possible to support an early-time inflationary universe using only well-known ingredients from the Standard Model of physics and geometric properties of space-time.
We present a model of holographic dark energy in which the Infrared cutoff is determined by both the Ricci and the Gauss-Bonnet invariants. Such a construction has the significant advantage that the Infrared cutoff, and consequently the holographic dark energy density, does not depend on the future or the past evolution of the universe, but only on its current features, and moreover it is determined by invariants, whose role is fundamental in gravitational theories. We extract analytical solutions for the behavior of the dark energy density and equation-of-state parameters as functions of the redshift. These reveal the usual thermal history of the universe, with the sequence of radiation, matter and dark energy epochs, resulting in the future to a complete dark energy domination. The corresponding dark energy equation-of-state parameter can lie in the quintessence or phantom regime, or experience the phantom-divide crossing during the cosmological evolution, and its asymptotic value can be quintessence-like, phantom-like, or be exactly equal to the cosmological-constant value. Finally, we extract the constraints on the model parameters that arise from Big Bang Nucleosynthesis.
Lectures by the author at the 1986 Cargese summer school modestly corrected and uploaded for greater accessibility. Some of the authors views on the quantum mechanics of cosmology have changed from those presented here but may still be of historical interest. The material on the Born-Oppenheimer approximation for solving the Wheeler-DeWitt equation and the work on the classical geometry limit and the approximation of quantum field theory in curved spacetime are still of interest and of use.
In this Essay we investigate the observational signatures of Loop Quantum Cosmology (LQC) in the CMB data. First, we concentrate on the dynamics of LQC and we provide the basic cosmological functions. We then obtain the power spectrum of scalar and tensor perturbations in order to study the performance of LQC against the latest CMB data. We find that LQC provides a robust prediction for the main slow-roll parameters, like the scalar spectral index and the tensor-to-scalar fluctuation ratio, which are in excellent agreement within $1sigma$ with the values recently measured by the Planck collaboration. This result indicates that LQC can be seen as an alternative scenario with respect to that of standard inflation.
The universal character of the gravitational interaction provided by the equivalence principle motivates a geometrical description of gravity. The standard formulation of General Relativity `a la Einstein attributes gravity to the spacetime curvature, to which we have grown accustomed. However, this perception has masked the fact that two alternative, though equivalent, formulations of General Relativity in flat spacetimes exist, where gravity can be fully ascribed either to torsion or to non-metricity. The latter allows a simpler geometrical formulation of General Relativity that is oblivious to the affine spacetime structure. Generalisations along this line permit to generate teleparallel and symmetric teleparallel theories of gravity with exceptional properties. In this work we explore modified gravity theories based on non-linear extensions of the non-metricity scalar. After presenting some general properties and briefly studying some interesting background cosmologies (including accelerating solutions with relevance for inflation and dark energy), we analyse the behaviour of the cosmological perturbations. Tensor perturbations feature a re-scaling of the corresponding Newtons constant, while vector perturbations do not contribute in the absence of vector sources. In the scalar sector we find two additional propagating modes, hinting that $f(Q)$ theories introduce, at least, two additional degrees of freedom. These scalar modes disappear around maximally symmetric backgrounds because of the appearance of an accidental residual gauge symmetry corresponding to a restricted diffeomorphism. We finally discuss the potential strong coupling problems of these maximally symmetric backgrounds caused by the discontinuity in the number of propagating modes.