Academic literature on the topic 'Cosmology, Gravity, Alternative theory of gravity, Mimetic gravity'

Mimetic gravity is a Weyl-symmetric extension of General Relativity, related to the latter by a singular disformal transformation, wherein the appearance of a dust-like perfect fluid can mimic cold dark matter at a cosmological level. Within this framework, it is possible to provide a unified geometrical explanation for dark matter, the late-time acceleration, and inflation, making it a very attractive theory. In this review, we summarize the main aspects of mimetic gravity, as well as extensions of the minimal formulation of the model. We devote particular focus to the reconstruction technique, which allows the realization of any desired expansionary history of the universe by an accurate choice of potential or other functions defined within the theory (as in the case of mimeticf(R)gravity). We briefly discuss cosmological perturbation theory within mimetic gravity. As a case study within which we apply the concepts previously discussed, we study a mimetic Hořava-like theory, of which we explore solutions and cosmological perturbations in detail. Finally, we conclude the review by discussing static spherically symmetric solutions within mimetic gravity and apply our findings to the problem of galactic rotation curves. Our review provides an introduction to mimetic gravity, as well as a concise but self-contained summary of recent findings, progress, open questions, and outlooks on future research directions.

A new perspective toward Einstein’s theory of general relativity, called mimetic gravity, was suggested in [A. H. Chamseddine and V. Mukhanov, J. High Energy Phys. 1311 (2013) 135] by isolating the conformal degree of freedom in a covariant fashion through a re-parametrization of the physical metric in terms of an auxiliary metric and a mimetic field. In this paper, we first derive the Friedmann equations of the Friedmann–Robertson–Walker (FRW) universe with any spatial curvature in mimetic gravity. Then, we disclose that one can always rewrite the Friedmann equations of mimetic cosmology in the form of the first law of thermodynamics, [Formula: see text], on the apparent horizon. We confirm that the entropy associated with the apparent horizon in mimetic cosmology still obeys the area law of entropy which is useful in studying the thermodynamical properties of the black holes in mimetic gravity. We also examine the time evolution of the total entropy in mimetic cosmology and show that, with the local equilibrium assumption, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon. Our study further supports the viability of the mimetic gravity from a thermodynamic viewpoint and provides a strong consistency check of this model.

We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function f(□ϕ) implementing the limiting curvature hypothesis. We show how relevant physical information can be extracted from power-law expansions of f in different regimes, corresponding e.g., to the very early universe or to late times. Our results are then applied to two specific models reproducing the cosmological background dynamics obtained in group field theory and in loop quantum cosmology, and we discuss the possibility of using this framework as providing an effective field theory description of quantum gravity. We study the evolution of anisotropies near the bounce, and discuss instabilities of scalar perturbations. Furthermore, we provide two equivalent formulations of mimetic gravity: one in terms of an effective fluid with exotic properties, the other featuring two distinct time-varying gravitational “constants” in the cosmological equations.

Modified gravity models have been constantly proposed with the purpose of evading some standard gravity shortcomings. Recently proposed by Chamseddine and Mukhanov, the Mimetic Gravity arises as an optimistic alternative. Our purpose in this work is to derive Tolman–Oppenheimer–Volkoff equations and solutions for such a gravity theory. We solve them numerically for quark star and neutron star cases. The results are carefully discussed.

This paper presents a relativistic version of Newtonian Fractional-Dimension Gravity (NFDG), an alternative gravitational model recently introduced and based on the theory of fractional-dimension spaces. This extended version—Relativistic Fractional-Dimension Gravity (RFDG)—is based on other existing theories in the literature and might be useful for astrophysical and cosmological applications. In particular, in this work, we review the mathematical theory for spaces with non-integer dimensions and its connections with the non-relativistic NFDG. The Euler–Lagrange equations for scalar fields can also be extended to spaces with fractional dimensions, by adding an appropriate weight factor, and then can be used to generalize the Laplacian operator for rectangular, spherical, and cylindrical coordinates. In addition, the same weight factor can be added to the standard Hilbert action in order to obtain the field equations, following methods used for scalar-tensor models of gravity, multi-scale spacetimes, and fractional gravity theories. We then apply the field equations to standard cosmology and to the Friedmann-Lemaître-Robertson-Walker metric. Using a suitable weight vtt, depending on the synchronous time t and on a single time-dimension parameter αt, we extend the Friedmann equations to the RFDG case. This allows for the computation of the scale factor at for different values of the fractional time-dimension αt and the comparison with standard cosmology results. Future additional work on the subject, including studies of the cosmological late-time acceleration, type Ia supernovae data, and related dark energy theory will be needed to establish this model as a relativistic alternative theory of gravity.

We develop a nonlinear quantum theory of Newtonian gravity consistent with an objective interpretation of the wavefunction. Inspired by the ideas of Schrodinger, and Bell, we seek a dimensional reduction procedure to map complex wavefunctions in configuration space onto a family of observable fields in space-time. Consideration of quasi-classical conservation laws selects the reduced one-body quantities as the basis for an explicit quasi-classical coarse-graining. These we interpret as describing the objective reality of the laboratory. Thereafter, we examine what may stand in the role of the usual Copenhagen observer to localise this quantity against macroscopic dispersion. Only a tiny change is needed, via a generically attractive self-potential. A nonlinear treatment of gravitational self-energy is thus advanced. This term sets a scale for all wavepackets. The Newtonian cosmology is thus closed, without need of an external observer. Finally, the concept of quantisation is re-interpreted as a nonlinear eigenvalue problem. To illustrate, we exhibit an elementary family of gravitationally self-bound solitary waves. Contrasting this theory with its canonically quantised analogue, we find that the given interpretation is empirically distinguishable, in principle. This result encourages deeper study of nonlinear field theories as a testable alternative to canonically quantised gravity.

The impressive success of the standard cosmological model has suggested to many that its ingredients are all that one needs to explain galaxies and their systems. I summarize a number of known problems with this programme. They might signal the failure of standard gravity theory on galaxy scales. The requisite hints as to the alternative gravity theory may lie with the modified Newtonian dynamics (MOND) paradigm, which has proved to be an effective summary of galaxy phenomenology. A simple nonlinear modified gravity theory does justice to MOND at the non-relativistic level, but cannot be consistently promoted to relativistic status. The obstacles were first side-stepped with the formulation of tensor–vector–scalar theory (T e V e S), a covariant-modified gravity theory. I review its structure, its MOND and Newtonian limits, and its performance in the face of galaxy phenomenology. I also summarize features of T e V e S cosmology and describe the confrontation with data from strong and weak gravitational lensing.

The field equations following from a Lagrangian L(R) will be deduced and solved for special cases. If L is a non-linear function of the curvature scalar, then these equations are of fourth order in the metric. In the introduction, we present the history of these equations beginning with the paper of H. Weyl from 1918, who first discussed them as alternative to Einstein's theory. In the third part, we give details about the cosmic no hair theorem, i.e. the details of how within fourth order gravity with L= R + R2, the inflationary phase of cosmic evolution turns out to be a transient attractor. Finally, the Bicknell theorem, i.e. the conformal relation from fourth order gravity to scalar-tensor theory, will be shortly presented.

The aim of this work is to provide a general description of the corpuscular theory of gravity. After reviewing some of the major conceptual issues emerging from the semiclassical and field theoretic approaches to Einstein’s gravity, we present a synthetic overview of two novel (and extremely intertwined) perspectives on quantum mechanical effects in gravity: the horizon quantum mechanics (HQM) formalism and the classicalization scheme. After this preliminary discussion, we then proceed with implementing the latter to several different scenarios, namely self-gravitating systems, the early Universe, and galactic dynamics. Concerning the first scenario, we start by describing the generation of the Newtonian potential as the result of a coherent state of toy (scalar) gravitons. After that we employ this result to study some features of the gravitational collapse and to argue that black holes can be thought of a self-sustained quantum states, at the critical point, made of a large number of soft virtual gravitons. We then refine this simplified analysis by constructing an effective theory for the gravitational potential of a static spherical symmetric system up to the first post-Newtonian correction. Additionally, we employ the HQM formalism to study the causal structure emerging from the corpuscular scenario. Finally, we present a short discussion of corpuscular black holes in lower dimensional spaces. After laying down the basics of corpuscular black holes, we present a generalization of the aforementioned arguments to cosmology. Specifically, we first introduce a corpuscular interpretation of the de Sitter spacetime. Then we use it as the starting point for a corpuscular formulation of the inflationary scenario and to provide an alternative viewpoint on the dark components of the [Formula: see text]CDM model. The key message of this work is that the corpuscular theory of gravity offers a way to unify most of the experimental observations (from astrophysical to galactic and cosmological scales) in a single framework, solely based on gravity and baryonic matter.

The origin of the late-time accelerated expansion of the universe is still a great mystery. Numerous cosmological models have been proposed to explain this phenomenon. Modern days' technology and equipment have allowed scientists to successfully execute many observations in cosmology and astrophysics: space missions, large ground-based telescopes and gravitational-wave antennas have led to important discoveries and ruled out many models. The Lambda-Cold Dark Matter, model provides a coherent and satisfactory framework to accommodate all fundamental observations. Therefore it is called the "standard model of cosmology''. Despite its many successes, Lambda CDM requires the introduction of dark energy in the form of an unnaturally small cosmological constant and is plagued by fine-tuning problems ("why do dark energy, dark matter and baryons have comparable energy densities today?''). The elementary particle candidates which are assumed to form the cold dark matter component have never been directly detected. These facts can be taken as possible indications of a potential crisis. This has motivated the introduction of various alternative models, among which a novel class of modified gravity theories, called "mimetic gravity'' or "mimetic dark matter-theory'', which aims at explaining both the dark energy and (at least part of) the dark matter components as consequences of a suitable modification of the gravitational theory w.r.t. Einstein General Relativity. (Chapter 1 and 2) In this PhD thesis, we propose the "generalized mimetic gravity theory", which arises in full generality by means of a non-invertible disformal transformation of the most general single scalar field scalar-tensor theory of gravity and implemented our idea for Horndeski and beyond-Horndeski models. This novel class of models is a generalization of the so-called mimetic dark matter theory recently introduced by Chamseddine and Mukhanov, as discussed in Chapters 2 and 3. It can source the background evolution of the universe by mimicking any perfect fluid, including radiation, dark matter, and dark energy. In this chapter, we also show that very general single-scalar-field scalar-tensor theories of gravity are generically invariant under invertible disformal transformations. In Chapter 4 we analyze linear scalar perturbations around a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) background in mimetic Horndeski gravity and show that the sound speed is zero on all backgrounds and therefore the system does not have any wave-like scalar degrees of freedom. Further, we present mimetic vector-tensor theories. In particular, we establish that the non-invertible disformal transformation at the origin of the normalization constraint term in the Einstein-Aether theory, i.e., that the Einstein-Aether theory is also in the class of mimetic theories. We shall also show that an Einstein-Maxwell system sourced by dust can be recovered in the weak limit of a minimal Einstein-Aether theory and that vector field becomes rotation and acceleration free in such a limit (Chapter 5). Finally, in the concluding Chapter 6, we wind up the thesis by discussing some applications and future research directions in mimetic theories of gravity. % So far, it is not ruled out by any observations. The Chapters 3 and 4 are based on our published papers and Chapter 5 is based on the material which will appear in a forthcoming paper (P. Karmakar, T. Koivisto, D. Mota and S. Mukohyama)<br>L'origine dell' accelerazione con cui attualmente l' universo si sta espandendo è ancora uno dei più grandi misteri della cosmologia. Diversi modelli cosmologici sono stati proposti per spiegare questo fenomeno. Le tecnologie e gli strumenti di misura moderni hanno permesso agli scienziati di eseguire con successo molte osservazioni in cosmologia e astrofisica: missioni spaziali, grandi telescopi terrestri e antenne per misurare le onde gravitazionali hanno portato a importanti scoperte ed escluso molti modelli. Il modello cosmologico cosiddetto "Lambda-Cold Dark Matter" è il modello che meglio spiega in un quadro coerente e soddisfacente tutte le osservazioni fondamentali. Per questo è chiamato il modello "standard della cosmologia". Nonostante i suoi numerosi successi, il modello Lambda CDM richiede l'introduzione della cosiddetta energia oscura sotto forma di un'innaturale piccola costante cosmologica ed è afflitto da problemi di fine-tuning (perchè l'energia oscura, la materia oscura e i barioni hanno densità di energia paragonabili oggi?'). I candidati di particelle elementari che si presume possano formare la componente di materia oscura fredda non sono mai stati rilevati direttamente. Questi fatti possono essere presi come possibili indicazioni di una potenziale crisi. Ciò ha portato all'introduzione di vari modelli alternativi, tra cui una nuova classe di teorie di gravità modificata, detta "gravità mimetica" o "teoria della materia oscura mimetica", che mira a spiegare sia l'energia oscura e (almeno parte de) i componenti di materia oscura come conseguenza di un' opportuna modifica della teoria della gravità rispetto alla Teoria della Relatività Generale di Einstein. (Capitolo 1 e 2) In questa tesi di dottorato, proponiamo la teoria della "gravità mimetica generalizzata", che emerge in piena generalità per mezzo di una trasformazione disforme non-invertibile della teoria scalare-tensoriale della gravita a singolo campo scalare più generale possibile, implementandola poi al caso dei modelli di Horndeski e di modelli che vanno oltre Horndeski. Questa nuova classe di modelli è una generalizzazione della cosiddetta teoria della materia oscura "mimetica", recentemente introdotta da Chamseddine e Mukhanov, come discusso nei capitoli 2 e 3. Essa può far da sorgente all'evoluzione di background dell'universo mimando qualsiasi fluido perfetto, tra cui un fluido di radiazione, di materia oscura e l'energia oscura. In questi capitoli mostriamo anche che teorie scalari-tensoriali della gravita` molto generali a singolo campo scalare sono genericamente invarianti per trasformazioni disformi invertibili. Nel Capitolo 4 analizziamo le perturbazioni scalari lineari intorno ad un background di Friedmann-Lemaitre-Robertson-Walker (FLRW) spazialmente piatto nell'ambito della gravità mimetica di Horndeski e dimostriamo che la velocità del suono è nulla su qualsiasi background e pertanto il sistema non dispone di eventuali gradi di libertà scalari che si propagano. Inoltre, discutiamo teorie mimetiche vettoriali-tensoriali. In particolare, si stabilisce che la condizione di non-nvertibilità della trasformazione disforme è all'origine del termine di vincolo di normalizzazione nella teoria di Einstein-Aether, ovvero che la teoria di Einstein-Aether rientra anch'essa nella classe di teorie mimetiche. Si mostrerà anche che un sistema di Einstein-Maxwell con polvere può essere recuperato nel limite debole di una teoria minimale di Einstein-Ather e che il campo vettoriale di questa teoria diventa irrotazionale e senza accelerazione in tale limite (capitolo 5). Infine, nel Capitolo conclusivo 6, finiamo la tesi discutendo alcune applicazioni e le direzioni future della ricerca in teorie di gravità mimetica. I capitoli 3 e 4 si basano sulle nostre pubblicazioni e il Capitolo 5 si basa sul materiale che apparirà in un prossimo articolo (P. Karmakar, T. Koivisto, D. Mota e S. Mukohyama.

Despite the many successes of the current standard model of cosmology on the largest physical scales, it relies on two phenomenologically motivated constituents, cold dark matter and dark energy, which account for approximately 95% of the energy-matter content of the universe. From a more fundamental point of view, however, the introduction of a dark energy (DE) component is theoretically challenging and extremely fine-tuned, despite the many proposals for its dynamics. On the other hand, the concept of cold dark matter (CDM) also suffers from several issues such as the lack of direct experimental detection, the question of its cosmological abundance and problems related to the formation of structure on small scales. A perhaps more natural solution might be that the gravitational interaction genuinely differs from that of general relativity, which expresses itself as either one or even both of the above dark components. Here we consider different possibilities on how to constrain hypothetical modifications to the gravitational sector, focusing on the subset of tensor-vector-scalar (TeVeS) theory as an alternative to CDM on galactic scales and a particular class of chameleon models which aim at explaining the coincidences of DE. Developing an analytic model for nonspherical lenses, we begin our analysis with testing TeVeS against observations of multiple-image systems. We then approach the role of low-density objects such as cosmic filaments in this framework and discuss potentially observable signatures. Along these lines, we also consider the possibility of massive neutrinos in TeVeS theory and outline a general approach for constraining this hypothesis with the help of cluster lenses. This approach is then demonstrated using the cluster lens A2390 with its remarkable straight arc. Presenting a general framework to explore the nonlinear clustering of density perturbations in coupled scalar field models, we then consider a particular chameleon model and highlight the possibility of measurable effects on intermediate scales, i.e. those relevant for galaxy clusters. Finally, we discuss the prospects of applying similar methods in the context of TeVeS and present an ansatz which allows to cast the linear perturbation equations into a more convenient form.

There have been many proposed modifications of gravitational theory, beginning with Einstein’s general relativity, modifying Newtonian gravity, and Weyl’s attempt at unifying gravity and electromagnetism. The standard model of cosmology, the Lambda CDM model, requires dark matter and dark energy to fit experimental data. There is a lack of direct evidence for dark matter and dark energy. An alternative theory called modified gravity (MOG) seeks to fit the observational data for the dynamics of galaxies and clusters of galaxies without dark matter. The MOG gravitational theory has a solution for a black hole that modifies the Schwarzschild and Kerr solutions, and can be tested using the data collected on supermassive black holes by the Event Horizon Telescope. There are many modified gravity theories proposed to explain the accelerating expansion of the universe, generally ascribed to dark energy. However, Einstein’s cosmological constant is the simplest explanation for the accelerating expansion.