Oliver Fabio Piattella

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• PhD
• Professor (Associate) at University of Insubria

Ehlers' Frame Theory is a class of geometric theories parameterized by λ := 1/c 2 and identical to the General Theory of Relativity for λ = 0. The limit λ → 0 does not recover Newtonian gravity, as one might expect, but yields the so-called Newton-Cartan theory of gravity, which is characterized by a second gravitational field ω, called the Corioli...

É apresentada a tradução do artigo de Georges Lemaître de 1927 que propôs a lei que relaciona a velocidade de recessão cósmica das galáxias com a distância que elas se encontra de nós, lei de Hubble-Lemaître.

We address the question of how to build a class of f(R) extensions of general relativity which are compatible with solar system experiments, without making any preliminary assumption on the properties of f. The aim is reached by perturbatively solving the modified Einstein equations around a Schwarzschild background and retrieving a posteriori the...

We address the question of how to build a class of $f(R)$ extensions of General Relativity which are compatible with solar system experiments, without making any preliminary assumption on the properties of $f$. The aim is reached by perturbatively solving the modified Einstein equations around a Schwarzschild background and retrieving a posteriori...

We consider cosmological models in which Dark Matter (DM) and Dark Energy (DE) are described by a single component, dubbed Unified Dark Matter (UDM) models, in which the DE-like part can have an equation state $<-1$ at late times without violating the null energy condition. In this paper, we investigate whether this feature can relieve the Hubble t...

Uma das ideias fundadoras da física quântica, a quantização da energia, foi exposta por Max Planck em 1900, durante uma reunião da Sociedade Alemã de Física. A publicação originada daquele seminário é apresentada nessa tradução direta do alemão para o português.

Rastall introduced a stress-energy tensor whose divergence is proportional to the gradient of the Ricci scalar. This proposal leads to a change in the form of the field equations of General Relativity, but it preserves the number of degrees of freedom. Rastall’s field equations can be either interpreted as GR with a redefined SET, or it can imply d...

We investigate the cosmological implications of an effective gravitational action, inspired by Sakharov's idea of induced gravity, containing non-local contributions from the operator $\left(\Box +\beta \right)^{-1} R$. The $\beta$ term is a novel feature in the panorama of non-local models of gravity, and arises naturally within Sakharov theory fr...

We extend the results obtained in previous works by Piattella and Park for gravitational lensing in the McVittie metric by including the effect of the transition from the matter-dominated epoch of the Universe to the Λ-dominated era. We derive a formula that agrees with the previous results for the McVittie metric at lowest order and compare the le...

We extend the results obtained in \cite{Piattella_2016, mcvittie_2015} for gravitational lensing in the McVittie metric by including the effect of the transition from the matter-dominated epoch of the Universe to the $\Lambda$-dominated era. We derive a formula that agrees with the previous results for the McVittie metric at lowest order, and compa...

Uma das equações mais populares da física é a famosa fórmula da energia de repouso, E = mc2, deduzida por Albert Einstein no desenvolvimento da teoria da relatividade restrita. O artigo onde as ideias que dão origem a essa equação são discutidas por Einstein é apresentado aqui em uma tradução direta do alemão para o português.

We investigate a model of gravitational collapse of matter inhomogeneities where the latter are modelled as Bianchi type IX (BIX) spacetimes. We found that this model contains, as limiting cases, both the standard spherical collapse model and the Zeldovich solution. We study how these models are affected by small anisotropies within the BIX potenti...

We investigate a model of gravitational collapse of matter inhomogeneities where the latter are modelled as Bianchi type IX (BIX) spacetimes. We found that this model contains, as limiting cases, both the standard spherical collapse model and the Zeldovich solution for a 1-dimensional perturbation. We study how these models are affected by small an...

We study how the evolution of a dark energy quintessence fluid is modified by the presence of a matter inhomogeneity. To do so, we study linear perturbations of a flat FLRW background containing dust and a slowly rolling scalar field. Under the assumptions of spherical symmetry and a static density contrast, i.e. $\dot {\delta }=0$ , we obtain simp...

We study how the evolution of a Dark Energy Quintessence fluid is modified by the presence of a matter inhomogeneity. To do so, we study linear perturbations of a flat FLRW background containing dust and a slowly rolling scalar field. Under the assumptions of spherical symmetry and a static density contrast, \textit{i.e.} $\dot{\delta}=0$, we obtai...

We study the stability of static, spherically symmetric solutions of Rastall’s theory in the presence of a scalar field with respect to spherically symmetric perturbations. The analysis of perturbations shows that there arises an inconsistency in the sense that time-dependent perturbations do not exist in any order of perturbation theory, and we ca...

In this paper we investigate three theories characterised by non-vanishing divergence of the stress-energy tensor, namely $f(R,\mathcal L_M)$, $f(R,T)$, and Rastall theory. We show that it is not possible to obtain the third from the first two, unless in some very specific case. Nonetheless, we show that in the framework of cosmology in the $f(R,T)...

We elaborate on the proposal of [Phys. Rev. Lett. 123, 131302 (2019).], about the possibility of hiding the cosmological constant in the complicated topology that one expects to exist at the Planck scale. We build a differential equation ruling the time evolution of ⟨K⟩, the spatial average of the expansion scalar. Supposing that the solution ⟨K⟩=0...

In the recent paper [3] it was shown that the consistency of the quantum theory of a sterile scalar coupled to massive fermions requires the inclusion of odd-power terms in the potential of scalar self-interaction. One of the most important examples of a sterile scalar is the inflaton, that is typically a real scalar field which does not belong to...

Apresentamos aqui uma breve e não-técnica introdução à teoria da relatividade geral, começando pelo conceito de espaço-tempo, passando pelo princípio de equivalência, e chegando nos testes clássicos que consagraram a teoria como uma das mais bonitas e bem-sucedidas da física.

O texto apresentado a seguir é a tradução, do alemão ao português, do importante artigo de Albert Einstein de 1905, “Sobre a eletrodinâmica dos corpos em movimento”, no qual o físico de Ulm introduz a teoria da relatividade restrita e a sua aplicação à eletrodinâmica. A ideia de apresentar este texto, e outros similares, nos Cadernos de Astronomia...

Sub-horizon perturbations in scalar-tensor theories have been shown to grow generically faster than in uncoupled models due to a positive, additive Yukawa force. In such cases, the amount of clustering becomes larger than in the standard cosmological model, exacerbating the observed tension in the σ8 parameter. Here we show instead that in some sim...

We elaborate on the proposal of [Phys. Rev. Lett. 123 (2019) 13, 131302], about the possibility of hiding the cosmological constant in the complicated topology that one expects to exist at the Planck scale. We build a differential equation ruling the time evolution of $\langle K\rangle$, the spatial average of the expansion scalar. Supposing that t...

We study the stability of static, spherically symmetric solutions of Rastall's theory in the presence of a scalar field with respect to spherically symmetric perturbations. It is shown that the stability analysis is inconsistent in the sense that linear time-dependent perturbations cannot exist, and we can conclude that these solutions are stable....

In a Bohmian quantum cosmology scenario, we investigate some quantum effects on the evolution of the primordial universe arising from the adoption of an alternative non-trivial ordering to the quantization of the constrained Hamiltonian of a minimally coupled scalar field. The Wheeler–DeWitt equation has a contribution from the change in factor ord...

We study a quantization via fractional derivative of a nonminimal derivative coupling cosmological theory, namely, the Fab Four John theory. Its Hamiltonian version presents the issue of fractional powers in the momenta. That problem is solved here by the application of the so-called conformable fractional derivative. This leads to a Wheeler–DeWitt...

Sub-horizon perturbations in scalar-tensor theories have been shown to grow generically faster than in uncoupled models due to a positive, additive Yukawa force. In such cases, the amount of clustering becomes larger than in the standard cosmological model, exacerbating the observed tension in the $\sigma_8$ parameter. Here we show instead that in...

We study a quantization via fractional derivative of a nonminimal derivative coupling cosmological theory, namely, the Fab Four John theory. Its Hamiltonian version presents the issue of fractional powers in the momenta. That problem is solved here by the application of the so-called conformable fractional derivative. This leads to a Wheeler-DeWitt...

We investigate the behavior of the asymptotic late-times effective equation of state for a class of nonlocal theories of gravity. These theories modify the Einstein-Hilbert Lagrangian introducing terms containing negative powers of the d’Alembert operator acting on the Ricci scalar. We find that imposing vanishing initial conditions for the nonloca...

In a Bohmian quantum cosmology scenario, we investigate some quantum effects on the evolution of the primordial universe arising from the adoption of Laplace-Beltrami ordering to the quantization of the constrained Hamiltonian of a minimally coupled scalar field. This approach is an alternative to the usually adopted trivial ordering, which is actu...

We address the issue of the existence of inequivalent definitions of gravitational mass in R2-gravity. We present several definitions of gravitational mass, and discuss the formal relations between them. We then consider the concrete case of a static and spherically symmetric neutron star, and solve numerically the equations of motion for several v...

We review the features of Dark Matter as a particle, presenting some old and new instructive models, and looking for their physical implications in the early universe and in the process of structure formation. We also present a schematic of Dark Matter searches and introduce the most promising candidates to the role of Dark Matter particle.

We review the features of Dark Matter as a particle, presenting some old and new instructive models, and looking for their physical implications in the early universe and in the process of structure formation. We also present a schematic of Dark Matter searches and introduce the most promising candidates to the role of Dark Matter particle.

We study the John term of Fab Four cosmology in the presence of a scalar potential. We show here how this theory can describe a wide range of cosmological solutions. This theory has two general functions of the scalar field: the potential V(ϕ) and the John coefficient function Vj(ϕ). We show that for very simple choices of those functions, we can d...

We investigate the features of the cosmological expansion history described by a recent model of gravity characterised by two nonlocally interacting metrics. We perform a detailed analysis of the dynamical system formed by the field equations and we find no stable critical points at finite and infinite distance. Nonetheless, we show that even if th...

We address the issue of the existence of inequivalent definitions of gravitational mass in $R^{2}$-gravity. We present several definitions of gravitational mass, and discuss the formal relations between them. We then consider the concrete case of a static and spherically symmetric neutron star, and solve numerically the equations of motion for seve...

We investigate the behavior of the asymptotic late-times effective equation of state for nonlocal theories of gravity in which a term involving the inverse of the d'Alembertian operator acting on the Ricci scalar is added to the standard Einstein-Hilbert Lagrangian in the action functional. We find that under general assumptions, imposing vanishing...

We investigate the linear regime of f(R)=R+αR2 gravity for static, spherically symmetric and asymptotically flat configurations of matter. We show that, in vacuum and deep inside the range of the extra scalar degree of freedom, the post-Newtonian parameter γ is not equal to 1/2, as established in the literature, but it assumes larger values dependi...

In this letter we establish \textit{general formulae} for the inflationary slow-roll parameters ε, η and ζ as functions of the Ricci scalar R for f(R) theories of gravity. As examples, we present the analytic and numerical solutions of ε, η and ζ as functions of the number of e-folds N in two important instances: for the Starobinsky model and for a...

We investigate the features of the cosmological expansion history described by a recent model of gravity characterised by two nonlocally interacting metrics. We perform a detailed analysis of the dynamical system formed by the field equations and we find no stable critical points at finite and infinite distance. Nonetheless, we show that even if th...

In this letter we establish \textit{general formulae} for the inflationary slow-roll parameters $\epsilon$, $\eta$ and $\zeta$ as functions of the Ricci scalar $R$ for $f(R)$ theories of gravity. As examples, we present the analytic and numerical solutions of $\epsilon$, $\eta$ and $\zeta$ as functions of the number of e-folds $N$ in two important...

We present here a quantum cosmological model with Bohm-de Broglie interpretation of the theory described by a combination of two terms of the Fab Four cosmological theory. The first term is the John Lagrangian and the second is a potential representing matter content to avoid classical trivial solutions. This model has two free functions that provi...

We investigate the linear regime of f(R) = R + alpha R^2 gravity for static, spherically symmetric and asymptotically flat configurations of matter. We show that, in vacuum and deep inside the range of the extra scalar degree of freedom, the post-Newtonian parameter gamma is not equal to 1/2, as established in the literature, but it assumes larger...

Cosmology has become a very active research field in the last decades thanks to the impressing improvement of our observational techniques which have led to landmark discoveries such as the accelerated expansion of the universe, and have put physicists in front of new mysteries to unveil, such as the quest after the nature of dark matter and dark e...

We derive in this chapter the perturbed Boltzmann equations for photons, massless neutrinos, CDM and baryons. We shall use these in order to track the evolution of small fluctuations in these components, and couple them to Einstein equations. For deriving the hierarchy of temperature and polarisation for photons we follow mainly Ma and Bertschinger...

In this Chapter we discuss the application of Boltzmann equation in cosmology. In particular, we address Big Bang Nucleosynthesis (BBN), recombination of protons and electrons in neutral hydrogen atoms and the relic abundance of CDM. Our main references are Dodelson (Modern cosmology. Academic Press, Amsterdam, 2003), Kolb and Turner (Front Phys 69...

In this chapter we attack the hierarchy of Boltzmann equations that we have found for photons and present an approximate, semi-analytic solution which will allow us to understand the temperature correlation in the CMB sky and its relation with the cosmological parameters. Our scope is to understand the features of the angular, temperature-temperatu...

We introduce in this chapter the geometric basis of cosmology and the expansion of the universe. A part from the technical treatment, historical, theological and mythological introductions to cosmology can be found in Ryden (Introduction to Cosmology, Addison-Wesley, San Francisco, 244 p 2003) and Bonometto (Cosmologia & Cosmologie, Zanichelli 2008...

The attentive reader must have noticed that, in fact, we have given no actual initial conditions on cosmological perturbations in Chap. 6. What we have done is to give the form of the primordial modes and show how, in the 5 different cases that we investigated, all scalar perturbations are sourced by a single scalar potential. For example, in the a...

In this Chapter we present an overview of cosmology, addressing its most important aspects and presenting some observational experiments and open problems.

In Chaps. 4 and 5 we have derived the evolution equations for small fluctuations about the homogeneous and isotropic FLRW background. These equations are differential and so, in order to have a well-posed Cauchy problem, we need to know which initial conditions to use. This is the topic of this chapter, where we shall be concerned with scalar pertu...

As we have seen in the previous Chapters, the assumption of homogeneous and isotropic universe is very useful and productive, but it is reliable only on very large scales (above 200 Mpc). Its shortcomings become evident when we start to investigate how structures, such as galaxies and their clusters, form, since these are huge deviations from the c...

In this Chapter we collect some extra material which extends the topics treated so far.

Here are collected miscellaneous topics which are helpful in order to understand the former chapters and to make these lecture notes as self-contained as possible.

We dedicate this chapter to inflation, a model of the primordial universe in which an almost constant H provides a scale factor a growing exponentially with the cosmic time. Inflation is able to solve some puzzles related to background cosmology and also to provide a testable prediction of the power spectrum of primordial fluctuations. Among the fi...

These lecture notes are based on the hand-written notes which I prepared for the cosmology course taught to graduate students of PPGFis and PPGCosmo at the Federal University of Esp\'irito Santo (UFES), starting from 2014. This course covers topics ranging from the evidence of the expanding universe to Cosmic Microwave Background anisotropies. They...

We show an analogy at high curvature between a $f(R) = R + aR^{n - 1} + bR^2$ theory and the $\alpha$-Attractors. We calculate the expressions of the parameters $a$, $b$ and $n$ as functions of $\alpha$ and the predictions of the model $f(R) = R + aR^{n - 1} + bR^2$ on the scalar spectral index $n_{\rm s}$ and the tensor-to-scalar ratio $r$. We fin...

We show an analogy at high curvature between a $f(R) = R + aR^{n - 1} + bR^2$ theory and the $\alpha$-Attractors. We calculate the expressions of the parameters $a$, $b$ and $n$ as functions of $\alpha$ and the predictions of the model $f(R) = R + aR^{n - 1} + bR^2$ on the scalar spectral index $n_{\rm s}$ and the tensor-to-scalar ratio $r$. We fin...

We investigate the effect of the redshift drift in strong gravitational lensing. The redshift drift produces a time variation of (i) the apparent position of a lensed source and (ii) the time delay among incoming signals from different images. We dub these effects as angular drift and time delay drift and show that they are of order of 10−10 arc se...

We investigate the effect of the redshift drift in strong gravitational lensing. The redshift drift produces a time variation of $i)$ the apparent position of a lensed source and $ii)$ the time delay among incoming signals from different images. We dub these effects as angular drift and time delay drift, respectively, and analyze their relevance in...

We consider cosmological backreaction effects in Buchert's averaging formalism on the basis of an explicit solution of the Lema\^itre-Tolman-Bondi (LTB) dynamics which is linear in the LTB curvature parameter and has an inhomogeneous bang time. The volume Hubble rate is found in terms of the volume scale factor which represents a derivation of the...

The k-essence theory with a power-law function of $(\partial\phi)^2$ and Rastall's non-conservative theory of gravity with a scalar field are shown to have the same solutions for the metric under the assumption that both the metric and the scalar fields depend on a single coordinate. This equivalence (called k-R duality) holds for static configurat...

The k-essence theory with a power-law function of $(\partial\phi)^2$ and Rastall's non-conservative theory of gravity with a scalar field are shown to have the same solutions for the metric under the assumption that both the metric and the scalar fields depend on a single coordinate. This equivalence (called k-R duality) holds for static configurat...

The Starobinsky inflationary model fits very well the observational data. We study some variations around this model by adding an exponential term in the Lagrangian. This modification allows to test the robustness of the Starobinsky model.

We analyse $f(R)$ theories of gravity from a dynamical system perspective, showing how the $R^2$ correction in Starobinsky's model plays a crucial role from the viewpoint of the inflationary paradigm. Then, we propose a modification of Starobinsky's model by adding an exponential term in the $f(R)$ Lagrangian. We show how this modification could al...

Rastall's theory belongs to the class of non-conservative theories of gravity. In vacuum, the only non-trivial static, spherically symmetric solution is the Schwarzschild one, except in a very special case. When a canonical scalar field is coupled to the gravity sector in this theory, new exact solutions appear for some values of the Rastall parame...

The cosmic microwave background (CMB) radiation provides a remarkable window onto the early universe, revealing its composition and structure. In these lectures we review and discuss the physics underlying the main features of the CMB.

We analyze the effect of the cosmological expansion on the deflection of light caused by a point mass, adopting the McVittie metric as the geometrical description of a pointlike lens embedded in an expanding universe. In the case of a generic, non-constant Hubble parameter $H$ we derive and approximately solve the null geodesic equations, finding a...

We analyze the effect of the cosmological expansion on the deflection of light caused by a point mass, adopting the McVittie metric as the geometrical description of a pointlike lens embedded in an expanding universe. In the case of a generic, non-constant Hubble parameter $H$ we derive and approximately solve the null geodesic equations, finding a...

We consider cosmological backreaction effects in Buchert's averaging formalism on the basis of an explicit solution of the Lema\^itre-Tolman-Bondi (LTB) dynamics which is linear in the LTB curvature parameter and has an inhomogeneous bang time. The volume Hubble rate is found in terms of the volume scale factor which represents a derivation of the...

We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's gravity in the zero-shear gauge assuming weak gravity and action-at-a-distance limit. The equations show proper spe...

Rastall's theory belongs to the class of non-conservative theories of gravity. In vacuum, the only non-trivial static, spherically symmetric solution is the Schwarzschild one, except in a very special case. When a canonical scalar field is coupled to the gravity sector in this theory, new exact solutions appear for some values of the Rastall parame...

DOI:http://dx.doi.org/10.1103/PhysRevD.93.129901

Analisamos o comportamento quântico de um sistema descrito por um potencial assimétrico unidimensional constituído por um degrau junto a (i) uma barreira linear ou (ii) uma barreira exponencial. Resolvemos a equação dos valores próprios da energia por meio do método da representação integral, classificando as soluções independentes como classes de...

There are some approaches, either based on General Relativity (GR) or modified gravity, that use galaxy rotation curves to derive the matter density of the corresponding galaxy, and this procedure would either indicate a partial or a complete elimination of dark matter in galaxies. Here we review these approaches, clarify the difficulties on this i...

There are some approaches, either based on General Relativity (GR) or modified gravity, that use galaxy rotation curves to derive the matter density of the corresponding galaxy, and this procedure would either indicate a partial or a complete elimination of dark matter in galaxies. Here we review these approaches, clarify the difficulties on this i...

We revisit the analysis made by Hwang and Noh [JCAP 1310 (2013)] aiming the construction of a Newtonian set of equations incorporating pressure effects typical of General Relativity theory. We perform in an explicit way the deduction of the Hwang-Noh equations, comparing it with similar computations found in the literature. Later, we investigate st...

We consider an effective viscous pressure as the result of a backreaction of inhomogeneities within Buchert’s formalism. The use of an effective metric with a time-dependent curvature radius allows us to calculate the luminosity distance of the backreaction model. This quantity is different from its counterpart for a “conventional” spatially flat b...

We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's gravity in the zero-shear gauge assuming weak gravity and action-at-a-distance limit. The equations show proper spe...

The Brans-Dicke action is one of the most natural extensions of the Einstein-Hilbert action. It is based on the introduction of a fundamental scalar field that effectively incorporates a dynamics to the gravitational coupling $G$. In spite of the diverse motivations and the rich phenomenology that comes from its solutions, Solar System tests impose...

Effects of velocity dispersion of dark matter particles on the CMB TT power spectrum and on the matter linear power spectrum are investigated using a modified CAMB code. Cold dark matter originated from thermal equilibrium processes does not produce appreciable effects but this is not the case if particles have a non-thermal origin. A cut-off in th...

In this paper, we explore two different ways of implementing quantum effects in a classical structure. The first one is through an external field. The other one is modifying the classical conservation laws. In both cases, the consequences for the description of the evolution of the universe are discussed.

The series of texts composing this book is based on the lectures presented during the II José Plínio Baptista School of Cosmology, held in Pedra Azul (Espírito Santo, Brazil) between 9 and 14 March 2014. This II JBPCosmo has been entirely devoted to the problem of understanding theoretical and observational aspects of Cosmic Background Radiation (C...

We revisit the analysis made by Hwang and Noh [JCAP 1310 (2013)] aiming the construction of a Newtonian set of equations incorporating pressure effects typical of the General Relativity theory. We explicitly derive the Hwang-Noh equations, comparing them with similar computations found in the literature. Then, we investigate $i)$ the cosmological e...

We discuss the possibility to implement a viscous cosmological model, attributing to the dark matter component a behaviour described by bulk viscosity. Since bulk viscosity implies negative pressure, this rises the possibility to unify the dark sector. At the same time, the presence of dissipative effects may alleviate the so called small scale pro...

We show that Renormalization Group extensions of the Einstein-Hilbert action for large scale physics are not, in general, a particular case of standard Scalar-Tensor (ST) gravity. We present a new class of ST actions, which are part of a more general ST picture in which the potential is not fixed at the action level, and show that this extended ST...

We investigate the effect of the cosmological expansion on the bending of light due to an isolated point-like mass. We adopt McVittie solution as the description of the geometry of the lens. Assuming a constant Hubble factor we find an analytic expression involving the bending angle, which turns out to be increased by a factor $1 + z_L$, where $z_L...

The cosmic microwave background (CMB) radiation provides a remarkable window onto the early universe, revealing its composition and structure. In these lectures we review and discuss the physics underlying the main features of the CMB.

We formulate a theory combining the principles of a scalar-tensor gravity and the Rastall proposal of a violation of the usual conservation laws. In the resulting Brans-Dicke-Rastall (BDR) theory the only exact, static, spherically symmetric solution is a Robinson-Bertotti type solution besides the trivial Schwarzschild one. The PPN constraints can...

We consider a cosmological model of the late universe constituted by standard cold dark matter plus a dark energy component with constant equation of state w and constant effective speed of sound. Neglecting fluctuations in the dark energy component we obtain an equation describing the evolution of sub-horizon cold dark matter perturbations through...

We formulate a theory combining the principles of a scalar-tensor gravity and Rastall's proposal of a violation of the usual conservation laws. We obtain a scalar-tensor theory with two parameters $\omega$ and $\lambda$, the latter quantifying the violation of the usual conservation laws. The only exact spherically symmetric solution is that of Rob...

We study the effects of sample variance in N--body simulations, as a function of the size of the simulation box, namely in connection with predictions on tomographic shear spectra. We make use of a set of 8 $\Lambda$CDM simulations in boxes of 128, 256, 512 $h^{-1}$Mpc aside, for a total of 24, differing just by the initial seeds. Among the simulat...

The matter creation cosmology is revisited, including the evolution of baryons and dark matter particles. The creation process affects only dark matter and not baryons. The dynamics of the $\Lambda$CDM model can be reproduced only if two conditions are satisfied: 1) the entropy density production rate and the particle density variation rate are equ...

The Rastall's theory is a modification of General Relativity touching one of the cornestone of gravity theory: the conservation laws. In Rastall's theory, the energy-momentum tensor is not conserved anymore, depending now on the gradient of the Ricci curvature. In this sense, this theory can be seen as a classical implementation of quantum effects...