Modified $f(R)$ gravity in the Palatini approach has been presently applied to Cosmology as a realistic alternative to dark energy. In this concern, a number of authors have searched for observational constraints on several $f(R)$ gravity functional forms using mainly data of type Ia supenovae (SNe Ia), Cosmic Microwave Background ({\rm CMB}) radiation and Large Scale Structure ({\rm LSS}). In this paper, by considering a homogeneous and isotropic flat universe, we use determinations of the Hubble function $H(z)$, which are based on differential age method, to place bounds on the free parameters of the $f(R) = R - β/R^{n}$ functional form. We also combine the $H(z)$ data with constraints from Baryon Acoustic Oscillations ({\rm BAO}) and {\rm CMB} measurements, obtaining ranges of values for $n$ and $β$ in agreement with other independent analyses. We find that, for some intervals of $n$ and $β$, models based on $f(R) = R - β/R^{n}$ gravity in the Palatini approach, unlike the metric formalism, can produce the sequence of radiation-dominated, matter-dominated, and accelerating periods without need of dark energy.
We explore the possibility of having a composite (self-conserved) dark energy (DE) whose dynamics is controlled by the quantum running of the cosmological parameters. We find that within this scenario it is feasible to find an explanation for the cosmological coincidence problem and at the same time a good qualitative description of the present data.
It is shown that any spatially flat and isotropic universe undergoing accelerated expansion driven by a self-interacting scalar field can be directly related to a contracting, decelerating cosmology. The duality is made manifest by expressing the scale factor and Hubble parameter as functions of the scalar field and simultaneously interchanging these two quantities. The decelerating universe can be twinned with a cosmology sourced by a phantom scalar field by inverting the scale factor and leaving the Hubble parameter invariant. The accelerating model can be related to the same phantom univers…
A linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid Universe with dynamically evolving Newton constant $G$ and cosmological constant $Λ$ is presented. A gauge-invariant formalism is developed by means of the covariant approach, and the acoustic propagation equations governing the evolution of the comoving fractional spatial gradients of the matter density, $G$, and $Λ$ are thus obtained. Explicit solutions are discussed in cosmologies where both $G$ and $Λ$ vary according to renormalization group equations in the vicinity of a fixed point.
We study cosmologies in the Randall-Sundrum models, incorporating the possibility of time-varying speed of light and Newton's constant. The cosmologies with varying speed of light (VSL) were proposed by Moffat and by Albrecht and Magueijo as an alternative to inflation for solving the cosmological problems. We consider the case in which the speed of light varies with time after the radion or the scale of the extra dimension has been stabilized. We elaborate on the conditions under which the flatness problem and the cosmological constant problem can be resolved. We find that the RS models are m…
Spatially homogeneous cosmological models with a positive cosmological constant are investigated, using dynamical systems methods. We focus on the future evolution of these models. In particular, we address the question whether there are models within this class that are de Sitter-like in the future, but are tilted.
In the framework of spatially averaged inhomogeneous cosmologies in classical General Relativity, effective Einstein equations govern the regional and the global dynamics of averaged scalar variables of cosmological models. A particular solution may be characterized by a cosmic equation of state. In this paper it is pointed out that a globally static averaged dust model is conceivable without employing a compensating cosmological constant. Much in the spirit of Einstein's original model we discuss consequences for the global, but also for the regional properties of this cosmology. We then cons…
In a class of non-singular cosmologies derived from higher-order corrections to the low-energy bosonic string action, we derive evolution equations for the most general cosmological scalar, vector and tensor perturbations. In the large scale limit, the evolutions of both scalar and tensor perturbations are characterised by conserved quantities, the usual curvature perturbation in the uniform-field gauge and the tensor-type perturbed metric. The vector perturbation is not affected, being described by the conservation of the angular momentum of the fluid component in the absence of any additiona…
A scale-dependent cosmological constant $Λ$ and the Newton constant G emerge naturally in quantum field theory in a curved space-time background leading to renormalization group running cosmologies. A scale-setting procedure is discussed in these cosmological models and the interpretation of the scale is emphasized. This setup introduces dark energy without invoking quintessence-like fields and can be applied to a variety of problems. The scale-dependent $Λ$ and G are also naturally incorporated into the generalized holographic dark energy model, and applied to different aspects of cosmology.
We compute the energy spectra for massless Kalb-Ramond axions in four-dimensional anisotropic string cosmological models. We show that, when integrated over directions, the four-dimensional anisotropic model leads to infra-red divergent spectra similar to the one found in the isotropic case.
We present a general slow-roll formalism within braneworld-motivated cosmologies with non-standard effective Friedmann equations. Full towers of parameters involving either the inflaton potential or the Hubble parameter are constructed and the dynamics of non-tachyonic and tachyonic fields are considered in detail; exact cosmological solutions and the inflationary attractor condition are provided. We compare scalar-driven and tachyon-driven accelerating eras through slow-roll correspondence and the observational imprint on early-universe structures.
Dark energy cosmologies with an equation of state parameter $w$ less than -1 are often found to violate the null energy condition and show unstable behaviour. A solution to this problem may require the existence of a consistent effective theory that violates the null energy condition only momentarily and does not develop any instabilities or other pathological features for a late time cosmology. A model which incorporates a dynamical scalar field $ϕ$ coupled to the quadratic Riemann invariant of the Gauss-Bonnet form is a viable proposal. Such an effective theory is shown to admit nonsingular …
Explaining the effects of dark matter using modified gravitational dynamics (MOND) has for decades been both an intriguing and controversial possibility. By insisting that the gravitational interaction that accounts for the Newtonian force also drives cosmic expansion, one may kinematically identify which cosmologies are compatible with MOND, without explicit reference to the underlying theory so long as the theory obeys Birkhoff's law. Using this technique, we are able to self-consistently compute a number of quantities of cosmological interest. We find that the critical acceleration a_0 must…
We consider the population evolution and evaporation of primordial black holes in the simplest braneworld cosmology, Randall-Sundrum type II. We demonstrate that black holes forming during the high-energy phase of this theory (where the expansion rate is proportional to the density) have a modified evaporation law, resulting in a longer lifetime and lower temperature at evaporation, while those forming in the standard regime behave essentially as in the standard cosmology. For sufficiently large values of the AdS radius, the high-energy regime can be the one relevant for primordial black holes…
We study the robustness of the quintessence tracking scenario in the context of more general cosmological models that derive from high-energy physics. We consider the effects of inclusion of multiple scalar fields, corrections to the Hubble expansion law (such as those that arise in brane cosmological models), and potentials that decay with expansion of the Universe. We find that in a successful tracking quintessence model the average equation of state must remain nearly constant. Overall, the conditions for successful tracking become more complex in these more general settings. Tracking can b…
We present a fitting formula for the luminosity and angular diameter distances in cosmological models with pressureless matter, a cosmological constant and zero spatial curvature. The formula has a relative error of less than 0.4% for 0.2<Ω_0<1 for any redshift, and a global relative error of less than 4% for any choice of parameters.
The modified Gauss-Bonnet gravity can be motivated by a number of physical reasons, including: the uniqueness of a gravitational Lagrangian in four and higher dimensions and the leading order $α^\prime$ corrections in superstring theory. Such an effective theory of scalar-tensor gravity has been modeled in the recent past to explain both the initial cosmological singularity problem and the observationally supported cosmological perturbations. Here I present an overview of the recent developments in the use of modified Gauss-Bonnet gravity to explain current observations, touching on key cosmol…
We use the three-year WMAP observations to determine the normalization of the matter power spectrum in inflationary cosmologies. In this context, the quantity of interest is not the normalization marginalized over all parameters, but rather the normalization as a function of the inflationary parameters n and r with marginalization over the remaining cosmological parameters. We compute this normalization and provide an accurate fitting function. The statistical uncertainty in the normalization is 3 percent, roughly half that achieved by COBE. We use the k-l relation for the standard cosmologica…
The most remarkable and interesting feature of brane world scenario is the use of bulk's curvature to localize gravity on the brane, albeit with fine tuning of the brane and bulk parameters. For FRW expanding universe on the brane, it is a moving hypersurface in Schwarzschild anti de Sitter bulk spacetime. We show that zero mass gravitons have bound state on the brane for suitable values of brane and bulk parameters. There occur various cases giving rise to different cosmological models, in particular we discuss a model with positive cosmological constant on the brane.
In a class of models designed to solve the cosmological constant problem by coupling scalar or tensor classical fields to the space-time curvature, the universal scale factor grows as a power law in the age, $a \propto t^α$, regardless of the matter content or cosmological epoch. We investigate constraints on such "power-law cosmologies" from the present age of the Universe, the magnitude-redshift relation, and from primordial nucleosynthesis. Constraints from the current age of the Universe and from the high-redshift supernovae data require "large" $α$ ($\approx 1$), while consistency with th…
We constrain cosmological parameters in flat cosmologies with tracking dark energy (or Quintessence) using the existing data on Cosmic Microwave Background (CMB) anisotropies. We perform a maximum likelihood analysis using combined data from COBE/DMR, BOOMERanG, DASI and MAXIMA, obtaining estimates for the dark energy density $Ω_{Q}$ and equation of state $w_{Q}$, the physical baryon density $Ω_{b}h^{2}$, the scalar perturbation spectral index $n_{S}$, the ratio $R$ between the tensor and scalar perturbation amplitude (or the tensor spectral index $n_{T}$). Dark energy is found to be the domin…
Exploiting the existence of two "cosmological" constants, one associated with the classical Lovelock theorem and one with the vacuum energy density, we argue, in a model independent way, that in spatially closed FLRW cosmologies with a positive definite effective cosmological constant there exists a range in this constant that serves as a sufficient condition for the satisfaction of the null, weak, strong and dominant energy conditions at a bounce. The application of energy conditions is not unambiguous and we show how the bounce can be considered classically and how, we believe more reasonabl…
Using the Einstein-Hilbert approximation of asymptotically safe quantum gravity we present a consistent renormalization group based framework for the inclusion of quantum gravitational effects into the cosmological field equations. Relating the renormalization group scale to cosmological time via a dynamical cutoff identification this framework applies to all stages of the cosmological evolution. The very early universe is found to contain a period of ``oscillatory inflation'' with an infinite sequence of time intervals during which the expansion alternates between acceleration and deceleratio…
Various astronomical observations have been consistently making a strong case for the existence of a component of dark energy with negative pressure in the universe. It is now necessary to take the dark energy component(s) into account in gravitational lensing statistics and other cosmological tests. By using the comoving distance we derive analytic but simple expressions for the optical depth of multiple image, the expected value of image separation and the probability distribution of image separation caused by an assemble of singular isothermal spheres in general FRW cosmological models with…
In this paper we study the dynamics of {\it orthogonal spatially homogeneous} Bianchi cosmologies in $R^n$-gravity. We construct a compact state space by dividing the state space into different sectors. We perform a detailed analysis of the cosmological behaviour in terms of the parameter $n$, determining all the equilibrium points, their stability and corresponding cosmological evolution. In particular, the appropriately compactified state space allows us to investigate static and bouncing solutions. We find no Einstein static solutions, but there do exist cosmologies with bounce behaviours. …
The limits imposed by the classical cosmological tests on closed and open FRW universes driven by adiabatic matter creation are investigated. Exact expressions for the lookback time, age of the universe, luminosity distance, angular diameter, and galaxy number counts versus redshift are derived and their meaning discussed in detail. An interesting consequence of these cosmological models is the possibility of an accelerated expansion today (as indicated from supernovae observations) with no need to invoke either a cosmological constant or an exotic "quintessence" component.
Dark energy and the accelerated expansion of the universe have been the direct predictions of the distant supernovae Ia observations which are also supported, indirectly, by the observations of the CMB anisotropies, gravitational lensing and the studies of galaxy clusters. Today these results are accommodated in what has become the `concordance cosmology': a universe with flat spatial sections t=constant with about 70% of its energy in the form of Einstein's cosmological constant Λ. However, we find that as more and more supernovae Ia are observed, more accurately and towards higher redshift, …
We analyse a generalisation of general relativity that incorporates a cosmic time-variation of the velocity of light in vacuum, $c,$ and the Newtonian gravitation 'constant', $G,$ proposed by Albrecht and Maguejo. We find exact solutions for Friedmann universes and determine the rate of variation of $c$ required to solve the flatness and classical cosmological constant problems. Potential problems with this approach to the resolution of the flatness and classical cosmological constant problems are highlighted. Reformulations are suggested which give the theory a more desirable limit as a theor…
"Power Law Cosmologies" are defined by their growth of the cosmological scale factor as $ t^α$ regardless of the matter content or cosmological epoch. Constraints from the current age of the Universe and from the high redshift supernovae data require ``large'' $α$ ($\approx 1$). We reinforce this by latest available observations. Such a large $α$ is also consistent with the right amount of helium and the lowest observed metallicity in the universe for a model with the baryon entropy ratio $\approx 8.1\times 10^{-9}$.
A linear evolution of the cosmological scale factor is a feature in several models designed to solve the cosmological constant problem via a coupling between scalar or tensor classical fields to the space-time curvature as well as in some alternative gravity theories. In this paper, by assuming a general time dependence of the scale factor, $R \sim t^α$, we investigate observational constraints on the dimensionless parameter $α$ from measurements of the angular size for a large sample of milliarcsecond compact radio sources. In particular, we find that a strictly linear evolution, i.e., $α\sim…
This thesis concerns the compatibility of inhomogeneous cosmologies with our present understanding of the universe. It is a problem of some interest to find the class of all relativistic cosmological models which are capable of providing a reasonable `fit' to the universe. This thesis, in some respects, is part of this process. We consider Stephani models, which are a generalisation of the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) models, which can be thought of as FLRW models with acceleration and pressure gradients. Thus these models generalise the `dust' assumption of standard cos…
Among the suggested solutions to the cosmological constant problem, we find the idea of a dynamic vacuum, with an energy density decaying with the universe expansion. We investigate the possibility of a variation in the gravitational constant as well, induced, at the cosmological scale, by the vacuum decay. We consider an effective Brans-Dicke theory in the spatially flat FLRW spacetime, finding late time solutions characterized by a constant ratio between the matter and vacuum energy densities. By using the observed limits for the universe age, we fix the only free parameter of our solutions,…
For a wide variety of cosmological models characterized by the cosmic mass density $Ω_M$ and the normalized cosmological constant $Ω_Λ$, we derive an analytic expression for the estimate of magnification cross-sections by an ensemble of isothermal spheres as models of galactic mass distributions. This provides a simple approach to demonstrate how the lensing probability by galaxies depends on the cosmological parameters. An immediate consequence is that, while a non-zero cosmological constant indeed leads to a significant increase of the lensing probability as it has been shown in the literatu…
The excitation of cosmological perturbations in an anisotropic cosmological model and in the presence of a homogeneous magnetic field has been studied, using the ideal magnetohydrodynamic (MHD) equations. In this case, the system of partial differential equations which governs the evolution of the magnetized cosmological perturbations can be solved analytically. Our results verify that fast-magnetosonic modes propagating normal to the magnetic field, are excited. But, what's most important, is that, at late times, the magnetic-induction contrast grows, resulting in the enhancement of the ambie…
The effects of differences between the local and global values of the Hubble parameter on the cosmologies consistent with studies of high-redshift Type Ia supernovæare discussed. It is found that with a local Hubble parameter around 10 per cent higher than the global value then open cosmological models (such as $Ω_{M} = 0.3, Ω_Λ=0$) are prefered and if the local value is around 20 per cent higher then standard cosmological models ($Ω_{M} = 1, Ω_Λ=0$) can be recovered. Even in the case where the Hubble parameter ratio is 1, low $Ω_M$ open cosmologies with $Ω_Λ = 0$ are not rejected at the 95 pe…
The comparison of quasar absorption spectra with numerically simulated spectra from hierarchical cosmological models of structure formation promises to be a valuable tool to discriminate among these models. We present simulation results for the column density, Doppler b parameter, and optical depth probability distributions for five popular cosmological models.
We present the results of a series of gas dynamical cosmological simulations of the formation of individual massive field galaxies in the standard concordance \LCDM and in a \LWDM cosmology. The galaxies form in an initial burst of star formation followed by accretion of small satellites. The simulated galaxies are old ($\approx$ 10 $Gyrs$) hot stellar systems with masses of $\approx 1.7 \times 10^{11} M_{\odot}$. Baryonic matter dominates the mass in the luminous part of the galaxies up to $\approx 5$ effective radii. The \LCDM galaxy is a slowly rotating spheroidal stellar system (E2) with p…
We challenge the widely held belief that the cosmological principle is an obvious consequence of the observed isotropy of the cosmic microwave background radiation, combined with the Copernican principle. We perform a detailed analysis of a class of inhomogeneous perfect fluid cosmologies admitting an isotropic radiation field, with a view to assessing their viability as models of the real universe. These spacetimes are distinguished from FLRW universes by the presence of inhomogeneous pressure, which results in an acceleration of the fundamental observers. We examine their physical, geometric…
We study the complementarity between the cosmological information obtainable with the Planck surveyour and the large scale structure (LSS) redshift surveys in LambdaCHDM cosmologies. We compute the initial full phase-space neutrino distribution function for LambdaCHDM models by using numerical simulations. As initial condition we adopt the HDM density fluctuation power spectrum normalized on the basis of the analysis of the local cluster X-ray temperature function and derive the initial neutrino phase-space distribution at each spatial wave number k by using the Zel'dovich approximation. These…
We compare a large set of cosmologies with WMAP data, performing a fit based on a MCMC algorithm. Besides of LCDM models, we take dynamical DE models, where DE and DM are uncoupled or coupled, both in the case of constant coupling and in the case when coupling varies with suitable laws. DE however arises from a scalar field self-interacting through a SUGRA potential. We find that the best fitting model is SUGRA dynamical DE, almost indipendently from the exponent alpha in the self-interaction potential. The main target of this work are however coupled DE models, for which we find limits on the…
