General Relativity and Quantum Cosmology (gr-qc)

Abstract: We consider a combination of perturbative and non-perturbative corrections in K\"ahler moduli stabilizations in the configuration of three magnetised intersecting D7 branes in the type-IIB/F theory, compactified on the 6d T^6/Z_N orbifold of Calabi-Yau three-fold (CY_3). Two of the K\"ahler moduli are stabilized non-perturbatively, out of the three which get perturbative corrections up to one-loop-order multi-graviton scattering amplitudes in the large volume scenario. In this framework, the dS vacua are achieved through all K\"ahler moduli stabilizations by considering the D-term. We obtain inflaton potentials of slow-roll plateau-type, which are expected by recent cosmological observations. Calculations of cosmological parameters with the potentials yield experimentally favoured values.

Abstract: We present a novel interpretation of the thermodynamics of perfect fluid dark matter (PFDM) black hole based on Misner-Sharp energy, and then investigate its evaporation behavior. We find that the ratio between dark sector initial density and black hole horizon radius significantly influences black hole evaporation behaviors. We demonstrate that the presence of the dark sector can significantly extend the lifetime of a black hole which is similar to the Reissner-Nordstrom case. Our work reformulates the thermodynamics of PFDM black holes and points out the existence of long-lived black holes in the presence of the dark sector.

Abstract: In this paper, we present several explicit reconstructions for a novel relativistic theory of modified Newtonian dynamics (RMOND) derived from the background of Friedmann-Lema$\hat{\text{\i}}$tre-Robertson-Walker cosmological evolution. It is shown that the Einstein-Hilbert Lagrangian with a positive cosmological constant is the only Lagrangian capable of accurately replicating the exact expansion history of the $\Lambda$ cold dark matter ($\Lambda$CDM) universe filled solely with dust-like matter and the only way to achieve this expansion history for the RMOND theory is to introduce additional degrees of freedom to the matter sectors. Besides, we find that the $\Lambda$CDM-era also can be replicated without any real matter field within the framework of the RMOND theory and the cosmic evolution exhibited by both the power-law and de-Sitter solutions also can be obtained.

Abstract: Exact solution of the Hamiltonian constraint in canonical gravity and the resultant reduction of Einstein's theory reveal the synergy between gravitation and the cosmic clock of our expanding universe. In conjunction with a paradigm shift from four-covariance to just spatial diffeomorphism invariance, causal time-ordering of the quantum state of the universe and its evolution in cosmic time become meaningful. This advocated framework prompts natural extensions. A salient feature is the addition of a Cotton-York term to the physical Hamiltonian. This radically changes the solution to the initial data problem and the quantum origin of the universe. It lends support to the quantum beginning of the universe as an exact Chern-Simons Hartle-Hawking state that features Euclidean-Lorentzian instanton tunneling. A signature of this state is that it manifests, at the lowest order approximation, scale-invariant two-point correlation function for transverse traceless quantum metric fluctuations. This initial quantum state also yields, at the level of expectation values, a low-entropy hot smooth Robertson-Walker beginning that is in accord with Penrose's Weyl Curvature Hypothesis. Consequently, the gravitational arrow of time of increasing spatial volume and the thermodynamic Second Law arrow of time of increasing entropy concur as our universe expands and ages.

Abstract: We revisit the relativistic coupling between gravity and electromagnetism, putting particularly into question the status of the latter on large scales; whether it behaves as a source or as a form of gravity. Considering a metric-affine framework and a simple action principle, we find out that a component of gravity, the so-called homothetic curvature field (associated with length changes), satisfies both sets of Maxwell equations. Therefore, we arrive at a gravito-electromagnetic equivalence analogous to the mass-energy equivalence. We raise and discuss some crucial questions implied by the aforementioned finding concerning the status of electromagnetism on large scales.

Abstract: We analyse the restricted phase space thermodynamics (RPST) of Kerr-Sen-AdS black holes with the central charge $C$ and its conjugate chemical potential $\mu$ but exclude the familiar $PdV$ term in the first law of black hole thermodynamics. That gives rise to a new perspective on the thermodynamics of black holes. Using the scaling properties, we investigate the first law and the corresponding Euler formula. Such formalism has its beauty, to say, for example, the mass is considered to be a homogeneous function of the extensive variables in the first order. In contrast, the intensive variables are of zeroth order. Because of the complicated expressions of the metric, we numerically calculate the critical values of the thermodynamic quantities. We find the phase transition behaviour of the free energy and other thermodynamic conjugate variables that appear in the first law. The RPST of the Kerr-Sen-AdS black holes is like that of the Reissner-Nordstr$\ddot{o}$m-AdS and the Kerr-AdS black holes. Such notions of the phase transition behaviour show that there should be some underlying universality in the RPST formalism.

Abstract: The Teleparallel Theory is equivalent to General Relativity, but whereas in the latter gravity has do with curvature, in the former gravity is described by torsion. As is well known, there is in the literature a host of alternative theories of gravity, among them the so called extended theories, in which additional terms are added to the action, such as for example in the $f(R)$ and $f(T)$ gravities, where $R$ is the Ricci scalar and $T$ is the scalar torsion, respectively. One of the ways to probe alternative gravity is via compact objects. In fact, there is in the literature a series of papers on compact objects in $f(R)$ and $f(T)$ gravity. In particular, there are several papers that consider $f(T) = T + \xi T^2$, where $\xi$ is a real constant. In this paper, we generalise such extension considering compact stars in $f (T ) = T + \xi T^\beta$ gravity, where $\xi$ and $\beta$ are real constants} {and looking out for the implications in their maximum masses and compactness in comparison to the General Relativity.

Abstract: We study the cosmological implications of gravity models which break diffeomorphisms (Diff) invariance down to transverse diffeomorphisms (TDiff). We start from the most general gravitational action involving up to quadratic terms in derivatives of the metric tensor and identify TDiff models as the only stable theories consistent with local gravity tests. These models propagate an additional scalar graviton and although they are indistinguishable from GR at the post-Newtonian level, their cosmological dynamics exhibits a rich phenomenology. Thus we show that the model includes standard $\Lambda$CDM as a solution when the extra scalar mode is not excited, but different cosmological evolutions driven by the new term are possible. In particular, we show that for a soft Diff breaking, the new contribution always behaves as a cosmological constant at late times. When the extra contribution is not negligible, generically its evolution either behaves as dark energy or tracks the dominant background component. Depending on the initial conditions, solutions in which the universe evolves from an expanding to a contracting phase, eventually recollapsing are also possible.

Abstract: There are two versions of the dominant energy condition (=dec): The original one for Lorentzian manifolds and an associated one for initial data sets. If a Lorentzian manifold satisfies dec, then so does the induced initial set on any embedded spacelike hypersurface. In this article, we discuss the question of a potential converse of this: Is every dec initial data set the induced one on a spacelike hypersurface within a suitably chosen dec Lorentzian manifold? We provide an example showing that in general the answer is no if we require all structures to be smooth.

Abstract: We formulate $f(Q,C)$ gravity and cosmology. Such a construction is based on the symmetric teleparallel geometry, but apart form the non-metricity scalar $Q$ we incorporate in the Lagrangian the boundary term $C$ of its difference from the standard Levi-Civita Ricci scalar $\mathring R$. We extract the general metric and affine connection field equations, we apply them in a cosmological framework, and making two gauge choices we obtain the modified Friedmann equations. As we show, we acquire an effective dark-energy sector of geometrical origin, which can lead to interesting cosmological phenomenology. Additionally, we may obtain an effective interaction between matter and dark energy. Finally, examining a specific model, we show that we can obtain the usual thermal history of the universe, with the sequence of matter and dark-energy epochs, while the effective dark-energy equation-of-state parameter can be quintessence-like, phantom-like, or cross the phantom-divide during evolution.