arXiv subjects
Publications and source records attributed to Valerio Faraoni.
The occurrence of a big smash singularity which ends the universe in a finite time in the future is investigated in the context of superquintessence, i.e. dark energy with effective equation of state parameter w<-1. The simplest model of superquintessence based on a single nonminimally coupled scalar field exhibits big smash solutions which are attractors in phase space.
There is marginal evidence that the quintessential form of matter responsible for the acceleration of the universe observed today has ratio between pressure and energy density $w<-1$. Such a regime, called superacceleration, cannot be achieved with conventional scalar field models. The simplest non-exotic model achieving superacceleration is that of a scalar field nonminimally coupled to the Ricci curvature. This model is studied for general potentials and an exact superaccelerating solution is presented. In quintessential inflation, the model can have blue gravitational wave spectra, improving the prospects for the detection of cosmological gravitational waves.
Nonminimal coupling of the inflaton field to the Ricci curvature of spacetime is generally unavoidable, and the paradigm of inflation should be generalized by including the corresponding term in the Lagrangian of the inflationary theory. This paper reports on the status of the programme of generalizing inflation. First, the problem of finding the correct value (or set of values) of the coupling constant is analyzed; the result has important consequences for the success or failure of inflationary scenarios. Then, the slow-roll approximation to generalized inflation is studied. Both the unperturbed inflating universe models and scalar/tensor perturbations are discussed, and open problems are pointed out.
Many pedagogical introductions of cosmological inflation are effective due to the simplicity of the relevant equations. Here an analytic solution of the cosmological equations is presented and used as an example to discuss fundamental aspects of the inflationary paradigm.
The slow-roll approximation to inflation is ultimately justified by the presence of inflationary attractors for the orbits of the solutions of the dynamical equations in phase space. There are many indications that the inflaton field couples nonminimally to the spacetime curvature: the existence of attractor points for inflation with nonminimal coupling is demonstrated, subject to a condition on the inflaton potential and the value of the coupling constant.
The nonminimal coupling (NMC) of the scalar field to the Ricci curvature is unavoidable in many cosmological scenarios. Inflation and quintessence models based on nonminimally coupled scalar fields are studied, with particular attention to the balance between the scalar potential and the NMC term in the action. NMC makes acceleration of the universe harder to achieve for the usual potentials, but it is beneficial in obtaining cosmic acceleration with unusual potentials. The slow-roll approximation with NMC, conformal transformation techniques, and other aspects of the physics of NMC are clarified.
Scalar-tensor theories of gravity can be formulated in the Jordan or in the Einstein frame, which are conformally related. The issue of which conformal frame is physical is a contentious one; we provide a straightforward example based on gravitational waves in order to clarify the issue.
Contrary to common belief, the standard tenet of Brans-Dicke theory reducing to general relativity when omega tends to infinity is false if the trace of the matter energy-momentum tensor vanishes. The issue is clarified in a new approach using conformal transformations. The otherwise unaccountable limiting behavior of Brans-Dicke gravity is easily understood in terms of the conformal invariance of the theory when the sources of gravity have radiation-like properties. The rigorous computation of the asymptotic behavior of the Brans-Dicke scalar field is straightforward in this new approach.
Late time mild inflation (LTMI) proposes to solve the age of the universe problem and the discrepancy between locally and globally measured values of the Hubble parameter. However, the mechanism proposed to achieve LTMI is found to be physically pathological by applying the theory of tails for the solutions of wave equations in curved spaces. Alternative mechanisms for LTMI are discussed, and the relevance of scalar wave tails for cosmology is emphasized.
A new method of solving the Einstein-Friedmann dynamical equations of a spatially homogeneous and isotropic universe is presented. The method is applicable when the equation of state of the material content assumes the form P=(g -1) rho, g = constant. The solution for the expansion factor is commonly given only for g = 0, 1 and 4/3 when the curvature index K is 1 or -1. The proposed procedure is valid for general g and K and it allows for ease of derivation of the solutions. This alternative method is useful pedagogically to introduce basic cosmology.
In recent years, the use of conformal transformation techniques has become widespread in the literature on gravitational theories alternative to general relativity, on cosmology, and on nonminimally coupled scalar fields. Typically, the transformation to the Einstein frame is generated by a fundamental scalar field already present in the theory. In this context, the problem of which conformal frame is the physical one has to be dealt with and, in the general case, it has been clarified only recently; the formulation of a theory in the ``new'' conformal frame leads to departures from canonical Einstein gravity. In this article, we review the literature on conformal transformations in classical gravitational theories and in cosmology, seen both as purely mathematical tools and as maps with physically relevant aspects. It appears particularly urgent to refer the analysis of experimental tests of Brans-Dicke and scalar-tensor theories of gravity, as well as the predictions of cosmological inflationary scenarios, to the physical conformal frame, in order to have a meaningful comparison with the observations.
The non-minimal coupling of a scalar field to the Ricci curvature in a curved spacetime is unavoidable according to several authors. The coupling constant is not a free parameter: the prescriptions for the value of the coupling constant in specific scalar field and gravity theories (in particular in general relativity) are studied. The results are applied to the most popular inflationary scenarios of cosmology and their theoretical consistence is analysed. Certain observational constraints on the coupling constant are also discussed.
The standard tenet that Brans-Dicke theory reduces to general relativity in the omega-tends-to-infinity limit has been shown to be false when the trace of the matter energy-momentum tensor vanishes. The issue is clarified in a new approach and the asymptotic behaviour of the Brans-Dicke scalar is rigorously derived.
The amplification of a light beam due to intervening gravitational waves is studied. The previous Jordan frame result according to which the amplification is many orders of magnitude larger in scalar-tensor gravity than in general relativity does not hold in the Einstein conformal frame. Lensing by gravitational waves is discussed in relation to the ongoing and proposed VLBI observations aimed at detecting the scintillation effect.
Gravitational waves act like lenses for the light propagating through them. This phenomenon is described using the vector formalism employed for ordinary gravitational lenses, which was proved to be applicable also to a non-stationary spacetime, with the appropriate modifications. In order to have multiple imaging, an approximate condition analogous to that for ordinary gravitational lenses must be satisfied. Certain astrophysical sources of gravitational waves satisfy this condition, while the gravitational wave background, on average, does not. Multiple imaging by gravitational waves is, in principle, possible, but the probability of observing such a phenomenon is extremely low.
We describe gravitational lensing by a gravitational wave, in the regime in which multiple images of a light source are created. We adapt the vector formalism employed for ordinary gravitational lenses to the case of a non-stationary spacetime, and we derive an approximate condition for multiple imaging. It is shown that certain astrophysical sources of gravitational waves satisfy this condition.
Recent theoretical work determines the correct coupling constant of a scalar field to the Ricci curvature of spacetime in general relativity. The periodicity in the redshift distribution of galaxies observed by Broadhurst {\em et al.}, if genuine, determines the coupling constant in the proposed scalar field models. As a result, these observations contain important information on the problem whether general relativity is the correct theory of gravity in the region of the universe at redshifts z<0.5.
It is shown that the amplification of a light beam by gravitational waves in scalar-tensor theories of gravity is a first order effect in the wave amplitudes. In general relativity, instead, the effect is only of second order.