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In the framework of scalar-tensor gravity, we consider non-flat interacting quintessence cosmology where a scalar field is interacting with dark matter. Such a scalar field can be a standard or a phantom one. We use the Noether Symmetry Approach to obtain general exact solutions for cosmological equations and to select scalar-field self-interaction potentials. It turns out that the found solutions can reproduce the accelerated expansion of the Universe, and are compatible with observational dataset, as the SNeIa Pantheon data, gamma ray bursts Hubble diagram, and direct measurements of the Hubble parameter., Comment: 30 pages, 7 figures, in press on: Phys.Dark Univ. (2023) 101274

The detection of the accelerated expansion of the Universe has been one of the major breakthroughs in modern cosmology. Several cosmological probes (CMB, SNe Ia, BAO) have been studied in depth to better understand the nature of the mechanism driving this acceleration, and they are being currently pushed to their limits, obtaining remarkable constraints that allowed us to shape the standard cosmological model. In parallel to that, however, the percent precision achieved has recently revealed apparent tensions between measurements obtained from different methods. These are either indicating some unaccounted systematic effects, or are pointing toward new physics. Following the development of CMB, SNe, and BAO cosmology, it is critical to extend our selection of cosmological probes. Novel probes can be exploited to validate results, control or mitigate systematic effects, and, most importantly, to increase the accuracy and robustness of our results. This review is meant to provide a state-of-art benchmark of the latest advances in emerging beyond-standard cosmological probes. We present how several different methods can become a key resource for observational cosmology. In particular, we review cosmic chronometers, quasars, gamma-ray bursts, standard sirens, lensing time-delay with galaxies and clusters, cosmic voids, neutral hydrogen intensity mapping, surface brightness fluctuations, stellar ages of the oldest objects, secular redshift drift, and clustering of standard candles. The review describes the method, systematics, and results of each probe in a homogeneous way, giving the reader a clear picture of the available innovative methods that have been introduced in recent years and how to apply them. The review also discusses the potential synergies and complementarities between the various probes, exploring how they will contribute to the future of modern cosmology., Comment: Invited review article for Living Reviews in Relativity. Accepted version. 191 pages, 54 figures, 11 tables

In Cosmology and in Fundamental Physics there is a crucial question like: where the elusive substance that we call Dark Matter is hidden in the Universe and what is it made of?, that, even after 40 years from the Vera Rubin seminal discovery does not have a proper answer. Actually, the more we have investigated, the more this issue has become strongly entangled with aspects that go beyond the established Quantum Physics, the Standard Model of Elementary particles and the General Relativity and related to processes like the Inflation, the accelerated expansion of the Universe and High Energy Phenomena around compact objects. Even Quantum Gravity and very exotic DM particle candidates may play a role in framing the Dark Matter mystery that seems to be accomplice of new unknown Physics. Observations and experiments have clearly indicated that the above phenomenon cannot be considered as already theoretically framed, as hoped for decades. The Special Topic to which this review belongs wants to penetrate this newly realized mystery from different angles, including that of a contamination of different fields of Physics apparently unrelated. We show with the works of this ST that this contamination is able to guide us into the required new Physics. This review wants to provide a good number of these "paths or contamination" beyond/among the three worlds above; in most of the cases, the results presented here open a direct link with the multi-scale dark matter phenomenon, enlightening some of its important aspects. Also in the remaining cases, possible interesting contacts emerges., Comment: 64 pages 16 Figures. In print on Frontiers in Astronomy and Space Sciences, for the Research Topic: "When Planck, Einstein and Vera Rubin Meet. Dark Matter: What is it ? Where is it?"

Several independent cosmological data, collected within the last twenty years, revealed the accelerated expansion rate of the Universe, usually assumed to be driven by the so called dark energy, which, according to recent estimates, provides now about 70 % of the total amount of matter-energy in the Universe. The nature of dark energy is yet unknown. Several models of dark energy have been proposed: a non zero cosmological constant, a potential energy of some self interacting scalar field, effects related to the non homogeneous distribution of matter, or effects due to alternative theories of gravity. Recently, it turned out that the standard flat LambdaCDM is disfavored (at 4 sigma) when confronted with a high redshift Hubble diagram, consisting of supernovae of type Ia (SNIa), quasars (QSOs) and gamma ray-bursts (GRBs) ([1-3]). Here we use the same data to investigate if this tension is confirmed, using a different approach: actually in [1-3], the deviation between the best fit model and the LambdaCDM model was noticed by comparing cosmological parameters derived from cosmographic expansions of their theoretical predictions and observed high redshift Hubble diagram. In this paper we use a substantially different approach, based on a specific parametrization of the redshift dependent equation of state (EOS) of dark energy component w(z). Our statistical analysis is aimed to estimate the parameters characterizing the dark energy EOS: our results indicate (at > 3 sigma level) an evolving dark energy EOS, while the cosmological constant has a constant EOS, wLambda =-1. This result not only confirms the tension previously detected, but shows that it is not an artifact of cosmographic expansions., Comment: 14 pages, 6 figures, 4 tables

We demonstrate the possibility to create optical beams with phase singularities engraved into exotic intensity landscapes imitating the shapes of a large variety of diverse plane curves. To achieve this aim, we have developed a method for directly encoding the geometric properties of some selected curve into a single azimuthal phase factor without passing through indirect encryption methods based on lengthy numerical procedures. The outcome is utilized to mould the optic axis distribution of a liquid-crystal-based inhomogeneous waveplate. The latter is finally used to sculpt the wavefront of an input optical gaussian beam via Pancharatnam-Berry phase., Comment: 11 pages, 6 figures, Published on 21 April 2020 Front. Phys

The Noether Symmetry Approach is applied to interacting quintessence cosmology with the aim to search for exact solutions and select scalar-field self-interaction potentials. It turns out that the solutions found are compatible with the accelerated expansion of the Universe and with observational dataset, as the SNeIa Pantheon data., Comment: 21 pages, 9 figures, accepted for publication in Physics of the Dark Universe

In the last dozens of years different data sets revealed the accelerated expansion of the Universe which is driven by the so called dark energy, that now dominates the total amount of matter-energy in the Universe. In a recent paper Glavan, Prokopec and Starobinsky propose an interesting model of dark energy, which traces the Universe evolution from the very early quantum era to the present time. Here we perform a high-redshift analysis to check if this new model is compatible with present day observational data and compare predictions of this model with that of the standard $\Lambda$CDM cosmological model. In our analysis we use only the most reliable observational data, namely the distances to selected SNIa, GRB Hubble diagram, and $28$ direct measurements of the Hubble constant. Moreover we consider also non {\it geometric} data related to the growth rate of density perturbations. We explore the probability distributions of the cosmological parameters for both models. To build up their own regions of confidence, we maximize the appropriate likelihood functions using the Markov chain Monte Carlo (MCMC) method. Our statistical analysis indicates that these very different models of dark energy are compatible with present day observational data and the GPS model seems slightly favored with respect to the $\Lambda$CDM model. However to further restrict different models of dark energy it will be necessary to increase the precision of the Hubble diagram at high redshifts and to perform more detailed analysis of the influence of dark energy on the process of formation of large scale structure., Comment: accepted for publication on EPJC

Here we test different models of dark energy beyond the standard cosmological constant scenario. We start considering the CPL parameterization of the equation of state (EOS), then we consider a dark energy scalar field (Quintessense). Finally we consider models with dark energy at early times (EDE). Our analysis is based on the Union2 type Ia supernovae data set, a Gamma Ray Bursts (GRBs) Hubble diagram, a set of 28 independent measurements of the Hubble parameter, some baryon acoustic oscillations (BAO) measurements. We performed a statistical analysis and explore the probability distributions of the cosmological parameters for each of the competing models. To build up their own regions of confidence, we maximize some appropriate likelihood functions using the Markov chain Monte Carlo (MCMC) method. Our analysis indicates that the EDE and the scalar field quintessence are slightly favored by the present data. Moreover, the GRBs Hubble diagram alone is able to set the transition region from the decelerated to the accelerated expansion of the Universe in all the tested models. Perspectives for improvements in the field with the THESEUS mission are also described., Comment: To be published in the Proceedings of the THESEUS Workshop 2017 (http://www.isdc.unige.ch/theseus/workshop2017.html), Journal of the Italian Astronomical Society (Mem.SAIt), Editors L. Amati, E. Bozzo, M. Della Valle, D. Gotz, P. O'Brien. Details on the THESEUS mission concept can be found in the white paper Amati et al. 2017 (arXiv:171004638) and Stratta et al. 2017 (arXiv:1712.08153)

Gamma-ray bursts are the most energetic explosions in the Universe. They are detectable up to very high redshifts, therefore can be used to study the expansion rate of the Universe and to investigate the observational properties of dark energy, provided that empirical correlations between spectral and intensity properties are appropriately calibrated. We used the type Ia supernova luminosity distances to calibrate the correlation between the peak photon energy, $E_{p, i}$, and the isotropic equivalent radiated energy, $ E_{iso}$ in GRBs. With this correlation, we tested the reliability of applying GRBs to measure cosmological parameters and to obtain indications on the basic properties and evolution of dark energy. Using 162 GRBs with measured redshifts and spectra, we applied a local regression technique to calibrate the $E_{p, i}$-$E_{iso}$ correlation against the type Ia SN data to build a calibrated GRB Hubble diagram. We tested the possible redshift dependence of the correlation and its effect on the Hubble diagram. Finally, we used the GRB Hubble diagram to investigate the dark energy EOS. For this, we focused on the so-called Chevalier-Polarski-Linder (CPL) parametrization of the dark energy EOS and implemented the Markov chain Monte Carlo (MCMC) method to efficiently sample the space of cosmological parameters. Our analysis shows once more that the $E_{p, i}$-$E_{iso}$ correlation has no significant redshift dependence. Therefore the high-redshift GRBs can be used as a cosmological tool to determine the basic cosmological parameters and to test different models of dark energy in the redshift region ($z\geqslant 3$), which is unexplored by the SNIa and baryonic acoustic oscillations data. Our updated calibrated Hubble diagram of GRBs provides some marginal indication (at $1\sigma$ level) of an evolving dark energy EOS., Comment: 12 pages, 11 figures

Context. Explaining the accelerated expansion of the Universe is one of the fundamental challenges in physics today. Cosmography provides information about the evolution of the universe derived from measured distances, assuming only that the space time ge- ometry is described by the Friedman-Lemaitre-Robertson-Walker metric, and adopting an approach that effectively uses only Taylor expansions of basic observables. Aims. We perform a high-redshift analysis to constrain the cosmographic expansion up to the fifth order. It is based on the Union2 type Ia supernovae data set, the gamma-ray burst Hubble diagram, a data set of 28 independent measurements of the Hubble param- eter, baryon acoustic oscillations measurements from galaxy clustering and the Lyman-{\alpha} forest in the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), and some Gaussian priors on h and {\Omega}M . Methods. We performed a statistical analysis and explored the probability distributions of the cosmographic parameters. By building up their regions of confidence, we maximized our likelihood function using the Markov chain Monte Carlo method. Results. Our high-redshift analysis confirms that the expansion of the Universe currently accelerates; the estimation of the jerk parameter indicates a possible deviation from the standard {\Lambda}CDM cosmological model. Moreover, we investigate implications of our results for the reconstruction of the dark energy equation of state (EOS) by comparing the standard technique of cosmography with an alternative approach based on generalized Pad\'e approximations of the same observables. Because these expansions converge better, is possible to improve the constraints on the cosmographic parameters and also on the dark matter EOS. Conclusions. The estimation of the jerk and the DE parameters indicates at 1{\sigma} a possible deviation from the {\Lambda}CDM cosmological model., Comment: 10 pages, 7 figures, accepted for publication in A & A

In the last dozen years a wide and variegated mass of observational data revealed that the universe is now expanding at an accelerated rate. In the absence of a well-based theory to interpret the observations, cosmography provides information about the evolution of the Universe from measured distances, only assuming that the geometry of the can be described by the Friedmann-Lemaitre-Robertson -Walker metric. We perform a high-redshift analysis allows us to put constraints on the cosmographic parameters up to the 5fth order, thus inducing indirect constraints on any gravity theory. Here we are interested in the so called teleparallel gravity theory, f(T). Actually we use the analytical expressions of the present day values of f(T) and its derivatives as functions of the cosmographic parameters to map the cosmography region of confidences into confidence ranges for f(T) and its derivative. Moreover, we show how these can be used to test some teleparallel gravity models without solving the dynamical equations. Our analysis is based on the Union2 Type Ia Supernovae (SNIa) data set, a set of 28 measurements of the Hubble parameter, the Hubble diagram constructed from some Gamma Ray Bursts (GRB) luminosity distance indicators, and gaussian priors on the distance from the Baryon Acoustic Oscillations (BAO), and the Hubble constant h. To perform our statistical analysis and to explore the probability distributions of the cosmographic parameters we use the Markov Chain Monte Carlo Method (MCMC)., Comment: International Journal of Modern Physics D, 20 pages, 5 figures

Strong lensing provides popular techniques to investigate the mass distribution of intermediate redshift galaxies, testing galaxy evolution and formation scenarios. It especially probes the background cosmic expansion, hence constraining cosmological parameters. The measurement of Einstein radii and central velocity dispersions indeed allows to trace the ratio D_s/D_ls between the distance D_s from the observer to the source and the distance D_ls from the lens to the source. We present an improved method to explicitly include the two - component structure in the galaxy lens modeling, in order to analyze the role played by the redshift and the model dependence on a nuisance parameter, F_E, which is usually marginalized in the cosmological applications. We show how to deal with these problems and carry on a Fisher matrix analysis to infer the accuracy on cosmological parameters achieved by this method., Comment: 8 pages, 2 figures, 2 tables, accepted for publication on Monthly Notices of Royal Astronomical Society

Gamma -ray bursts (GRBs) observed up to redshifts $z>9.4$ can be used as possible probes to test cosmological models. Here we show how changes of the slope of the {\it luminosity $L^*_X$ -break time $T^*_a$} correlation in GRB afterglows, hereafter the LT correlation, affect the determination of the cosmological parameters. With a simulated data set of 101 GRBs with a central value of the correlation slope that differs on the intrinsic one by a $5\sigma$ factor, we find an overstimated value of the matter density parameter, $\Omega_M$, compared to the value obtained with SNe Ia, while the Hubble constant, $H_0$, best fit value is still compatible in 1$\sigma$ compared to other probes. We show that this compatibility of $H_0$ is due to the large intrinsic scatter associated with the simulated sample. Instead, if we consider a subsample of high luminous GRBs ($HighL$), we find that both the evaluation of $H_0$ and $\Omega_M$ are not more compatible in 1$\sigma$ and $\Omega_M$ is underestimated by the $13\%$. However, the $HighL$ sample choice reduces dramatically the intrinsic scatter of the correlation, thus possibly identifying this sample as the standard canonical `GRBs' confirming previous results presented in Dainotti et al. (2010,2011). Here, we consider the LT correlation as an example, but this reasoning can be extended also for all other GRB correlations. In literature so far GRB correlations are not corrected for redshift evolution and selection biases, therefore we are not aware of their intrinsic slopes and consequently how far the use of the observed correlations can influence the derived `best' cosmological settings. Therefore, we conclude that any approach that involves cosmology should take into consideration only intrinsic correlations not the observed ones., Comment: 8 pages, 4 figures, accepted to MNRAS Main Journal

The explanation of the accelerated expansion of the Universe poses one of the most fundamental questions in physics and cosmology today. If the acceleration is driven by some form of dark energy, one can try to constrain the parameters using a cosmographic approach. Our high-redshift analysis allows us to put constraints on the cosmographic expansion up to the fifth order. It is based on the Union2 Type Ia Supernovae (SNIa) data set, the Hubble diagram constructed from some Gamma Ray Bursts luminosity distance indicators, and gaussian priors on the distance from the Baryon Acoustic Oscillations (BAO), and the Hubble constant h (these priors have been included in order to help break the degeneracies among model parameters). To perform our statistical analysis and to explore the probability distributions of the cosmographic parameters we use the Markov Chain Monte Carlo Method (MCMC). We finally investigate implications of our results for the dark energy, in particular, we focus on the parametrization of the dark energy equation of state (EOS). Actually, a possibility to investigate the nature of dark energy lies in measuring the dark energy equation of state, w, and its time (or redshift) dependence at high accuracy. However, since w(z) is not directly accessible to measurement, reconstruction methods are needed to extract it reliably from observations. Here we investigate different models of dark energy, described through several parametrizations of the equation of state, by comparing the cosmographic and the EOS series., Comment: Accepted for pubblication in MNRAS. arXiv admin note: text overlap with arXiv:1005.0122, arXiv:1104.3096, arXiv:1205.3421, arXiv:0802.1583 by other authors

We first study dark energy models with a minimally-coupled scalar field and exponential potentials, admitting exact solutions for the cosmological equations: actually, it turns out that for this class of potentials the Einstein field equations exhibit alternative Lagrangians, and are completely integrable and separable (i.e. it is possible to integrate the system analytically, at least by quadratures). We analyze such solutions, especially discussing when they are compatible with a late time quintessential expansion of the universe. As a further issue, we discuss how such quintessential scalar fields can be connected to the inflationary phase, building up, for this class of potentials, a quintessential inflationary scenario: actually, it turns out that the transition from inflation toward late-time exponential quintessential tail admits a kination period, which is an indispensable ingredient of this kind of theoretical models. All such considerations have also been done by including radiation into the model., Comment: Revtex4, 10 figures

Noether symmetry for Gauss-Bonnet-Dilatonic interaction exists for a constant dilatonic scalar potential and a linear functional dependence of the coupling parameter on the scalar field. The symmetry with the same form of the potential and coupling parameter exists all in the vacuum, radiation and matter dominated era. The late time acceleration is driven by the effective cos- mological constant rather than the Gauss-Bonnet term, while the later compensates for the large value of the effective cosmological constant giving a plausible answer to the well-known coincidence problem., Comment: 17 pages, 5 figures, in press on GRG

The correlation between the peak photon energy of the internal spectrum Ep,i and isotropic equivalent radiated energy Eiso (the Amati relation) is explored in a scalar field model of dark energy. Using an updated data set of 109 high redshift GRBs, we show that the correlation parameters only weakly depend on the cosmological model. Once the parameters of Amati relation have been determined we use this relation to construct a fiducial GRBs Hubble diagram that extends up to redshifts ~ 8. Moreover we apply a local regression technique to estimate, in a model independent way, the distance modulus from the recently updated Union SNIa sample, containing 557 SNIa spanning the redshift range of 0.015 < z <1.55. The derived calibration parameters are used to construct an updated GRBs Hubble diagram, which we call the calibrated GRBs HD. We also compare the fiducial and calibrated GRBs HDs, which turned out to be fully statistically consistent, thus indicating that they are not affected by any systematic bias induced by the different calibration procedures. This means that the high redshift GRBs can be used to test different models of dark energy settling the circularity problem. Furthermore, we investigate possible evolutionary effects that might have important influence on our results. Our analysis indicates that the presently available GRBs datasets do not show statistically unambiguous evolutionary effect with the cosmological redshift. Finally we propose another approach to calibrate the GRB relations, by using an approximate luminosity distance relation, which holds in any cosmological model. We use this calibration of the Amati relation to construct an empirical approximate HD, which we compare with the calibrated GRBs HD. We finally investigate the implications of this approach for the high redshift cosmography., Comment: 18 figures and 1 table, accepted for publication on MNRAS

In the framework of renormalization-group improved cosmologies, we analyze both theoretically and observationally the exact and general solution of the matter-dominated cosmological equations, using the expression of \Lambda = \Lambda(G) already determined by the integration method employed in a previous paper. A rough comparison between such a model and the concordance \LambdaCDM model as to the magnitude-redshift relationship has been already done, without showing any appreciable differences. We here perform a more refined study of how astrophysical data (Union2 set) on type-I supernovae, gamma ray bursts (in a sample calibrated in a model independent way with the SneIa dataset), and gas fraction in galaxy clusters (using a sample of Chandra measurements of the X-ray gas mass fraction) affect the model and constrain its parameters. We also apply a cosmographic approach to our cosmological model and estimate the cosmographic parameters by fitting both the supernovae and the gamma ray bursts datasets. We show that this matter-dominated cosmological model with variable Newton parameter and variable cosmological term is indeed compatible with the observations above (on type Ia supernovae, the gamma ray bursts Hubble diagram, and the gas mass fraction in X-ray luminous galaxy clusters). The cosmographic approach adopted confirms such conclusions. Finally, it seems possible to include radiation into the model, since numerical integration of the equations derived by the presence of both radiation and matter shows that, after inflation, the total density parameter is initially dominated by the radiation contribution and later by the matter one., Comment: 31 pages, 9 figures

It has been recently empirically established that some of the directly observed pa- rameters of GRBs are correlated with their important intrinsic parameters, like the luminosity or the total radiated energy. These correlations were derived, tested and used to standardize GRBs, i.e., to derive their luminosity or radiated energy from one or more observables, in order to construct an estimated fiducial Hubble diagram, assuming that radiation propagates in the standard LambdaCDM cosmological model. We extend these analyses by considering more general models of dark energy, and an updated data set of high redshift GRBs. We show that the correlation parameters only weakly depend on the cosmological model. Moreover we apply a local regression technique to estimate, in a model independent way, the distance modulus from the recently updated SNIa sample containing 307 SNIa (Astier et al. 2006), in order to calibrate the GRBs 2D correlations, considering only GRBs with z <1.4. The derived calibration parameters are used to construct a new GRBs Hubble diagram, which we call the calibrated GRBs HD. We also compare the estimated and calibrated GRBs HDs. It turns out that for the common GRBs they are fully statistically consistent, thus indicating that both of them are not affected by any systematic bias induced by the different standardizing procedures. We finally apply our methods to calibrate 95 long GRBs with the well-known Amati relation and construct the estimated and calibrated GRBs Hubble diagram that extends to redshifts z ~ 8. Even in this case there is consistency between these datasets. This means that the high redshift GRBs can be used to test different models of dark energy. We used the calibrated GRBs HD to constrain our quintessential cosmological model and derived the likelihood values of Omega_m and w(0)., Comment: 13 pages, 12 figures, 1 table. Accepted for publication in MNRAS