A gravity theory without masses can be constructed in Minkowski spaces using a geometric Minkowski potential. The related affine spacelike spheres can be seen as the regions of the Minkowski spacelike vectors characterized by a constant Minkowski gravitational potential. These spheres point out, for each dimension $n \geq 3$, spacetime models, the de Sitter ones, which satisfy Einstein's field equations in absence of matter. In other words, it is possible to generate geometrically the cosmological constant. Even if a lot of possible parameterizations have been proposed, each one highlighting some geometric and physical properties of the de Sitter space, we present here a new natural parameterization which reveals the intrinsic geometric nature of cosmological constant relating it with the invariant affine radius coming from the so called Minkowski-Tzitzeica surfaces theory.
We show that the existence of the cosmological constant can be connected to a nonminimal derivative coupling, in the action of gravity, between the geometry and the kinetic part of a given scalar field without introducing any effective potential of scalar fields. Exact solutions are given.
In the framework of extended gravity theories, we discuss the meaning of a time dependent "cosmological constant" and give a set of conditions to recover asymptotic de Sitter behaviour for a class of cosmological models independently of initial data. To this purpose we introduce a time-dependent (effective) quantity which asymptotically becomes the true cosmological constant. We will deal with scalar-tensor, fourth and higher than fourth-order theories.
We consider a generic Metric-Affine Cosmological setup and classify some particularly interesting specific cases of Perfect Hyperfluids. In particular, we present the form of conservation laws for the cases of pure spin, pure dilation and pure shear fluids. We also develop the concept of an incompressible hyperfluid and pay special attention to the case of a hypermomentum preserving hyperfluid. We also give a specific example on the emergence of the spin, dilation and shear currents through matter-connection couplings. In addition, starting from the generalized acceleration equation for the sc…
We investigate the cosmological aspects of the most general parity preserving Metric-Affine Gravity theory quadratic in torsion and non-metricity in the presence of a cosmological hyperfluid. The equations of motion are obtained by varying the action with respect to the metric and the independent affine connection. Subsequently, considering a Friedmann-Lemaître-Robertson-Walker background, we derive the most general form of the modified Friedmann equations for the full quadratic theory. We then focus on a characteristic sub-case involving only two quadratic contributions given in terms of tors…
We derive the full set of field equations for the Metric-Affine version of the Myrzakulov gravity model and also extend this family of theories to a broader one. More specifically, we consider theories whose gravitational Lagrangian is given by $F(R,T,Q, {\cal T},{\cal D})$ where $T$, $Q$ are the torsion and non-metricity scalars, ${\cal T}$ is the trace of the energy-momentum tensor and ${\cal D}$ the divergence of the dilation current. We then consider the linear case of the aforementioned theory and assuming a cosmological setup we obtain the modified Friedmann equations. In addition, focus…
We find possible cosmological models of the Polynomial Affine Gravity described by connections that are either compatible or not with a metric. When possible, we compare them with those of General Relativity. We show that the set of cosmological vacuum solutions in General Relativity are a subset of the solutions of Polynomial Affine Gravity. In our model the cosmological constant appears as an integration constant, and additionally, we show that some forms of matter can be emulated by the affine structure---even in the metric compatible case. In the case of connections not compatible with a m…
One of the main features of unified models, based on affine geometries, is that all possible interactions and fields naturally arise under the same standard. Here, we consider, from the effective Lagrangian of the theory, the torsion induced 4-fermion interaction. In particular, how this interaction affects the cosmological term, supposing that a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early universe. We explicitly show that there is no parity-violating pseudo-scalar density, dual to the curvature tensor (Holst term) and the spinor-bilinear sc…
The Affine Coherent State Quantization procedure is applied to the case of a FRLW universe in the presence of a cosmological constant. The quantum corrections alter the dynamics of the system in the semiclassical regime, providing a potential barrier term which avoids all classical singularities, as already suggested in other models studied in the literature. Furthermore the quantum corrections are responsible for an accelerated cosmic expansion. This work intends to explore some of the implications of the recently proposed "Enhanced Quantization" procedure in a simplified model of cosmology.
The Eddington Lagrangian in the purely affine formulation of general relativity generates the Einstein equations with the cosmological constant. The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, which has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the Einstein-Maxwell Lagrangian in the metric formulation. We show that the sum of the two affine Lagrangians is dynamically inequivalent to the sum of the analogous Lagrangians in the metric-affine/metric formulation. We also show that s…
It is shown how consistent histories quantum cosmology can be realised through Isham's Histories Projection Operator consistent histories scheme. This is done by using an affine algebra instead of a canonical one and also by using cocycle representations. A regularisation scheme allows us to find a history Hamiltonian which exists as a proper self-adjoint operator. The role of a cocycle choice is also discussed.
Starting from an affinely connected space, we consider a model of gravity whose fundamental field is the connection. We build up the action using as sole premise the invariance under diffeomorphisms, and study the consequences of a cosmological ansatz for the affine connection in the torsion-free sector. Although the model is built without requiring a metric, we show that the nondegenerated Ricci curvature of the affine connection can be interpreted as an \emph{emergent} metric on the manifold. We show that there exists a parametrization in which the \((r,φ)\)-restriction of the geodesics coin…
The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, that has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the metric Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric tensor is not well-defined. This feature indicates that, for the Ferraris-Kijowski model to be physical, there must exist a background field that depends on the Ricci tensor. The simplest possibility, supported by recent astronomical observations, is the cosmological constant, generated in the…
The polynomial affine gravity is an alternative model of gravity whose fundamental field is the affine connection, and it is invariant under the complete group of diffeomorphisms. In 3+1 dimensions the field equations generalise those of Einstein--Hilbert, the coupling constants are dimensionless, the action has a finite numbers of term, and although the action does not involve a (fundamental) metric, some metric tensor fields might \emph{emerge} from the connection. Provided a cosmological ansatz, the properties of diverse cosmological models are discussed.
The polynomial affine gravity is a model that is built up without the explicit use of a metric tensor field. In this article we reformulate the three-dimensional model and, given the decomposition of the affine connection, we analyse the consistently truncated sectors. Using the cosmological ansatz for the connection, we scan the cosmological solutions on the truncated sectors. We discuss the emergence of different kinds of metrics.
We briefly describe the simplest class of affine theories of gravity in multidimensional space-times with symmetric connections and their reductions to two-dimensional dilaton - vecton gravity field theories (DVG). The distinctive feature of these theories is the presence of an absolutely neutral massive (or tachyonic) vector field (vecton) with essentially nonlinear coupling to the dilaton gravity (DG). We show that in DVG the vecton field can be consistently replaced by an effectively massive scalar field (scalaron) with an unusual coupling to dilaton gravity. With this vecton - scalaron dua…
We explore the possibility that a scalar field with appropriate Lagrangian can mimic a perfect fluid with an affine barotropic equation of state. The latter can be thought of as a generic cosmological dark component evolving as an effective cosmological constant plus a generalized dark matter. As such, it can be used as a simple, phenomenological model for either dark energy or unified dark matter. Furthermore, it can approximate (up to first order in the energy density) any barotropic dark fluid with arbitrary equation of state. We find that two kinds of Lagrangian for the scalar field can re…
Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure General Relativity with cosmological constant, $Λ$, is reexpressed as an affine algebra with the commutator of the imaginary part of the Chern-Simons functional, $Q$, and the positive-definite volume element. This demonstrates that the affine algebra quantization program of Klauder can indeed be applicable to the full Lorentzian signature theory of quantum gravity with non-vanishing cosmological constant; and it facilitates the construction of solutions to all of the constraints. Unitary, irreduci…
We introduce a new method for applying an inflationary prior to a cosmological dataset that includes relations between observables at arbitrary order in the slow roll expansion. The process is based on the inflationary flow equations, and the slow roll parameters appear explicitly in the cosmological parameter set. We contrast our method to other ways of imposing an inflationary prior on a cosmological dataset, and argue that this method is ideal for use with heterogeneous datasets. In particular, it would be well suited to exploiting any direct detection of fundamental tensor modes by a BBO-s…
Heisenberg's nonperturbative quantization technique is applied to the nonpertrubative quantization of gravity. An infinite set of equations for all Green's functions is obtained. An approximation is considered where: (a) the metric remains as a classical field; (b) the affine connection can be decomposed into classical and quantum parts; (c) the classical part of the affine connection are the Christoffel symbols; (d) the quantum part is the torsion. Using a scalar and vector fields approximation it is shown that nonperturbative quantum effects gives rise to a cosmological constant and an Eucli…
In this work, a minisuperspace model for the projectable Hořava-Lifshitz (HL) gravity without the detailed balance condition is investigated. The Wheeler-deWitt equation is derived and its solutions are studied and discussed for some particular cases where, due to HL gravity, there is a "potential barrier" nearby $a=0$. For a vanishing cosmological constant, it is found a normalizable wave function of the universe. When the cosmological constant is non-vanishing, the WKB method is used to obtain solutions for the wave function of the universe. Using the Hamilton-Jacobi equation, one discusses …
Based on Eddington affine variational principle on a locally product manifold, we derive the separate Einstein space described by its Ricci tensor. The derived field equations split into two field equations of motion that describe two maximally symmetric spaces with two cosmological constants. We argue that the invariance of the bi-field equations under projections on the separate spaces, may render one of the cosmological constants to zero. We also formulate the model in the presence of a scalar field. The resulted separate Einstein-Eddington spaces maybe considered as two states that describ…
We propose a new theory of gravitation, in which the affine connection is the only dynamical variable describing the gravitational field. We construct the simplest dynamical Lagrangian density that is entirely composed from the connection, via its curvature and torsion, and is an algebraic function of its derivatives. It is given by the contraction of the Ricci tensor with a tensor which is inverse to the symmetric, contracted square of the torsion tensor, $k_{μν}=S^ρ_{λμ}S^λ_{ρν}$. We vary the total action for the gravitational field and matter with respect to the affine connection, assuming …
A brief summary of the application of coherent states in the examination of quantum dynamics of cosmological models is given. We discuss quantization maps, phase space probability distributions and semiclassical phase spaces. The implementation of coherent states based on the affine group resolves the hardest singularities, renders self-adjoint Hamiltonians without boundary conditions and provides a completely consistent semi-classical description of the involved quantum dynamics. We consider three examples: the closed Friedmann model, the anisotropic Bianchi Type I model and the deep quantum …
We consider globally hyperbolic flat spacetimes in 2+1 and 3+1 dimensions, in which a uniform light signal is emitted on the $r$-level surface of the cosmological time for $r\to 0$. We show that the frequency of this signal, as perceived by a fixed observer, is a well-defined, bounded function which is generally not continuous. This defines a model with anisotropic background radiation that contains information about initial singularity of the spacetime. In dimension 2+1, we show that this observed frequency function is stable under suitable perturbations of the spacetime, and that, under cert…
The role of torsion in f(R) gravity is considered in the framework of metric-affine formalism. We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the Palatini formalism. As a result, the extra curvature and torsion degrees of freedom can be dealt as an effective scalar field of fully geometric origin. From a cosmological point of view, such a geometric description could account for the whole Dark Side of the Universe.
We present new rotating vacuum configurations endowed with both dynamical torsion and nonmetricity fields in the framework of Metric-Affine gauge theory of gravity. For this task, we consider scalar-flat Weyl-Cartan geometries and obtain an axisymmetric Kerr-Newman solution in the decoupling limit between the orbital and the spin angular momentum. The corresponding Kerr-Newman-de Sitter solution is also compatible with a cosmological constant and additional electromagnetic fields.
We formulate the Lagrangian of the Newtonian cosmology where the cosmological constant is also introduced. Following the affine quantization procedure, the Hamiltonian operator is derived. The wave functions of the Newtonian universe and the corresponding eigenvalues for the case of matter dominated by a negative cosmological constant are given.
The generalized projection-tensor geometry introduced in an earlier paper is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous paper and obtain fully projected decompositions of Lie derivatives of the projection tensor field, the metric and the projected parts of the metric. These results are applied to the analysis of spacetimes with isometries. The familiar cases of spacetimes with isotropic group orbits --- cosmological models and spherical symmetry --- are discussed as illustrations of the results.
We discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and develop ideas of Weyl, Eddington, and Einstein, in particular, Einstein's proposal to specify the space - time geometry by use of the Hamilton principle. More specifically, the connection coefficients are determined using a `geometric' Lagrangian that is an arbitrary function of the generalized (non-symmetric) Ricci curvature tensor (and, possibly, of other fundamental tensors) expressed in terms of the connection coefficients regarded as independent variables. Such a t…
In the context of the metric-affine Chern-Simons gravity endowed with projective invariance, we derive analytical solutions for torsion and nonmetricity in the homogeneous and isotropic cosmological case, described by a flat Friedmann-Robertson-Walker metric. We discuss in some details the general properties of the cosmological solutions in the presence of a perfect fluid, such as the dynamical stability and the emergence of big bounce points, and we examine the structure of some specific solutions reproducing de Sitter and power law behaviours for the scale factor. Then, we focus on first-ord…
Here we show that, Eddington's pure affine gravity, when extended with Riemann curvature, leads to gravitational field equations that incorporate matter. This Riemanned Eddington gravity outfits a setup in which matter gravitates normally with Newton's constant but vacuum gravitates differently with an independent gravitational constant. This novel setup enables degravitation of the vacuum to observed level not by any fine-tuning but by a large hierarchy between its gravitational constant and its energy density. Remarkably, degravitation of the cosmological constant is local, causal and natura…
We propose new models of an `affine' theory of gravity in $D$-dimensional space-times with symmetric connections. They are based on ideas of Weyl, Eddington and Einstein and, in particular, on Einstein's proposal to specify the space - time geometry by use of the Hamilton principle. More specifically, the connection coefficients are derived by varying a `geometric' Lagrangian that is supposed to be an arbitrary function of the generalized (non-symmetric) Ricci curvature tensor (and, possibly, of other fundamental tensors) expressed in terms of the connection coefficients regarded as independen…
The purpose of the present study is to show that in a particular cosmological model, with an affine equation of state, one can obtain, besides the background given by the scale factor, Hubble and deceleration parameters, a representation in terms of scalar fields and, more important, explicit mathematical expressions for the density contrast and the power spectrum. Although the model so obtained is not realistic, it reproduces features observed in some previous numerical studies and, therefore, it may be useful in the testing of numerical codes and as a pedagogical tool.
We consider metric-affine scenarios where a modified gravitational action is sourced by electrovacuum fields in a three dimensional space-time. Such scenarios are supported by the physics of crystalline structures with microscopic defects and, in particular, those that can be effectively treated as bi-dimensional (like graphene). We first study the case of $f(R)$ theories, finding deviations near the center as compared to the solutions of General Relativity. We then consider Born-Infeld gravity, which has raised a lot of interest in the last few years regarding its applications in astrophysics…
We propose an approach to induced gravity, or Sakharov's "metrical elasticity", which requires only an affine spacetime that accommodates scalar fields. The setup provides the induction of metric gravity from a "pure affine" action, and it is established in two possible ways: (i) at the classical level, Einstein-Hilbert action arises with both, metric and Newton's constant, from the nonzero potential energy of the background field (ii) at the quantum level (quantized matter), gravity scale is induced from the one-loop effective action by integrating out the scalar degrees of freedom. In the fo…
In the paper we show that the general relativity action (and Lagrangian) in recent Einstein-Palatini formulation is equivalent to the action (and Langrangian) of a gauge field. We begin with a bit of information of the Einstein-Palatini (EP) action, then we present how Einstein fields equations can be derived from it. In the next section, we consider Einstein-Palatini action integral for general relativity with a positive cosmological constant $Λ$ in terms of $\hat{F}$, the curvature of the affine connection's pulled back from de Sitter bundle to Lorentz bundle. We will see that in terms of $\…
The generic cosmological solution is analyzed both for the non-asymptotic limit to the cosmological singularity and in the asymptotic limit analytically. The Bianchi I solution and the Bianchi IX solution, described as a sequence of Bianchi I reparameterized solutions, are analyzed with respect to the asymptotic symmetry implied by the space part of the metric tensor. Numerical studies are explained. The semiclassical regime is proposed by using the degrees of freedom for the initial conditions to the Einstein field equations, i.e. those which are not necessarily characterizing for a Bianchi s…
We study different manifestations of the speed of light in theories of gravity where metric and connection are regarded as independent fields. We find that for a generic gravity theory in a frame with locally vanishing affine connection, the usual degeneracy between different manifestations of the speed of light is broken. In particular, the space-time causal structure constant ($c_{ST}$) may become variable in that local frame. For theories of the form $f(R,R^{μν} R_{μν})$, this variation in $c_{ST}$ has an impact on the definition of the luminosity distance (and distance modulus), which can …
The existence of a singularity by definition implies a preferred scale--the affine parameter distance from/to the singularity of a causal geodesic that is used to define it. However, this variable scale is also captured by the expansion along the geodesic, and this can be used to obtain a regularized state space picture by means of a conformal transformation that factors out the expansion. This leads to the conformal `Hubble-normalized' orthonormal frame approach which allows one to translate methods and results concerning spatially homogeneous models into the generic inhomogeneous context, wh…
