Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNon-Riemannian Cosmology: The role of Shear Hypermomentum
96
0
0.0
(
0
)
Authors
Damianos Iosifidis
Ask ChatGPT about the research
No Arabic abstract
We consider the usual Einstein-Hilbert action in a Metric-Affine setup and in the presence of a Perfect Hyperfluid. In order to decode the role of shear hypermomentum, we impose vanishing spin and dilation parts on the sources and allow only for non-vanishing shear. We then consider an FLRW background and derive the generalized Friedmann equations in the presence of shear hypermomentum. By providing one equation of state among the shear variables we study the cases for which shear has an accelerating/decelerating effect on Universes expansion. In particular, we see that shear offers a possibility to prevent the initial singularity formation. We also provide some exact solutions in the shear dominated era and discuss the physical significance of the shear current.
rate research
Read More
In arXiv:gr-qc/9504004 it was shown that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. More recently, in the attempt to extend the same approach to the case of $f(R)$ theories of gravity, it was found that a non-equilibrium setting is indeed required in order to fully describe both this theory as well as classical GR (arXiv:gr-qc/0602001). Here, elaborating on this point, we show that the dissipative character leading to a non-equilibrium spacetime thermodynamics is actually related -- both in GR as well as in $f(R)$ gravity -- to non-local heat fluxes associated with the purely gravitational/internal degrees of freedom of the theory. In particular, in the case of GR we show that the internal entropy production term is identical to the so called tidal heating term of Hartle-Hawking. Similarly, for the case of $f(R)$ gravity, we show that dissipative effects can be associated with the generalization of this term plus a scalar contribution whose presence is clearly justified within the scalar-tensor representation of the theory. Finally, we show that the allowed gravitational degrees of freedom can be fixed by the kinematics of the local spacetime causal structure, through the specific Equivalence Principle formulation. In this sense, the thermodynamical description seems to go beyond Einsteins theory as an intrinsic property of gravitation.
In this thesis, we discuss several instances in which non-linear behaviour affects cosmological evolution in the early Universe. We begin by reviewing the standard cosmological model and the tools used to understand it theoretically and to compute its observational consequences. This includes a detailed exposition of cosmological perturbation theory and the theory of inflation. We then describe the results in this thesis, starting with the non-linear evolution of the curvature perturbation in the presence of vector and tensor fluctuations, in which we identify the version of that variable that is conserved in the most general situation. Next, we use second order perturbation theory to describe the most general initial conditions for the evolution of scalar perturbations at second order in the standard cosmological model. We compute approximate solutions valid in the initial stages of the evolution, which can be used to initialize second order Boltzmann codes, and to compute many observables taking isocurvature modes into account. We then move on to the study of the inflationary Universe. We start by analysing a new way to compute the consequences of a sudden transition in the evolution of a scalar during inflation. We use the formalism of quantum quenches to compute the effect of those transitions on the spectral index of perturbations. Finally, we detail the results of the exploration of a multi-field model of inflation with a non-minimal coupling to gravity. We study popular attractor models in this regime in both the metric and the Palatini formulations of gravity and find all results for both the power spectrum and bispectrum of fluctuations to closely resemble those of the single-field case. In all systems under study we discuss the effects of non-linear dynamics and their importance for the resolution of problems in cosmology.
This Thesis is devoted to the study of Metric-Affine Theories of Gravity and Applications to Cosmology. The thesis is organized as follows. In the first Chapter we define the various geometrical quantities that characterize a non-Riemannian geometry. In the second Chapter we explore the MAG model building. In Chapter 3 we use a well known procedure to excite torsional degrees of freedom by coupling surface terms to scalars. Then, in Chapter 4 which seems to be the most important Chapter of the thesis, at least with regards to its use in applications, we present a step by step way to solve for the affine connection in non-Riemannian geometries, for the first time in the literature. A peculiar f(R) case is studied in Chapter 5. This is the conformally (as well as projective invariant) invariant theory f(R)=a R^{2} which contains an undetermined scalar degree of freedom. We then turn our attention to Cosmology with torsion and non-metricity (Chapter 6). In Chapter 7, we formulate the necessary setup for the $1+3$ splitting of the generalized spacetime. Having clarified the subtle points (that generally stem from non-metricity) in the aforementioned formulation we carefully derive the generalized Raychaudhuri equation in the presence of both torsion and non-metricity (along with curvature). This, as it stands, is the most general form of the Raychaudhuri equation that exists in the literature. We close this Thesis by considering three possible scale transformations that one can consider in Metric-Affine Geometry.
Based upon the holographic principle, Jacobson demonstrated that the spacetime can be viewed as a gas of atoms with a related entropy given by the Bekenstein-Hawking formula. Following this argument, Friedmann equations can be derived by using Clausius relation to the apparent horizon of Friedmann-Robertson-Walker (FRW) universe. Loop Quantum Gravity is a propose to description of the spacetime behavior in situations where its atomic characteristic arises. Among these situations, the behavior of our universe near the Big Bang singularity is described by Loop Quantum Cosmology (LQC). However, a derivation of the LQC equations based on the Bekenstein bound is lacking. In this work, we obtain the quantum corrected Friedmann equations from the entropy-area relation given by loop quantum black holes (LQBH), setting a still absent connection between holographic and LQC descriptions of the cosmos. Connections with braneworld cosmology have been also addressed.
Spacetime and internal symmetries can be used to severely restrict the form of the equations for the fundamental laws of physics. The success of this approach in the context of general relativity and particle physics motivates the conjecture that symmetries may help us to one day uncover the ultimate theory that provides a unique, unified description of all observed physical phenomena. We examine some of the strengths and weaknesses of this conjecture.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
