International Journal of Modern Physics D

This paper proposes a statistical field theory of quantum reference frame underlying Perelman’s analogies between his formalism of the Ricci flow and the thermodynamics. The theory is based on a $d=4-𝜖$ quantum nonlinear sigma model (NLSM), interpreted as a quantum reference frame system which a to-be-studied quantum system is relative to. The statistic physics and thermodynamics of the quantum frame fields is studied by the density matrix obtained by the Gaussian approximation quantization. The induced Ricci flow of the frame fields and the Ricci–DeTurck flow of the frame fields associated with the density matrix are deduced. In this framework, the diffeomorphism anomaly of the theory has a deep thermodynamic interpretation. The trace anomaly is related to a Shannon entropy in terms of the density matrix, which monotonically flows and achieves its maximal value at the flow limit, called the Gradient Shrinking Ricci Soliton (GSRS), corresponding to a thermal equilibrium state of spacetime. A relative Shannon entropy with respect to the maximal entropy gives a statistical interpretation to Perelman’s partition function, which is also monotonic and gives an analogous H-theorem to the statistical frame fields system. A temporal static three-space of a GSRS four-spacetime is also a GSRS in lower three-dimension, we find that it is in a thermal equilibrium state, and Perelman’s analogies between his formalism and the thermodynamics of the frame fields in equilibrium can be explicitly given in the framework. By extending the validity of the Equivalence Principle to the quantum level, the quantum reference frame fields theory at low energy gives an effective theory of gravity, a scale-dependent Einstein–Hilbert action plus a cosmological constant is recovered. As a possible underlying microscopic theory of the gravitational system, the theory is also applied to understand the thermodynamics of the Schwarzschild black hole.

The Newman–Janis (NJ) algorithm is the standard approach to rotation in general relativity which, in vacuum, builds the Kerr metric from the Schwarzschild spacetime. Recently, we have shown that the same algorithm applied to the Papapetrou antiscalar spacetime produces a rotational metric devoid of horizons and ergospheres. Though exact in the scalar sector, this metric, however, satisfies the Einstein equations only asymptotically. We argue that this discrepancy between geometric and matter parts (essential only inside gravitational radius scale) is caused by the violation of the Hawking–Ellis energy conditions for the scalar energy–momentum tensor. The axial potential functions entering the metrics appear to be of the same form both in vacuum and scalar background, and they also coincide with the linearized Yang–Mills field, which might hint at their common nongravitational origin. As an alternative to the Kerr-type spacetimes produced by NJ algorithm we suggest the exact solution obtained by local rotational coordinate transformation from the Schwarzschild spacetime. Then, comparison with the Kerr-type metrics shows that the Lense–Thirring phenomenon might be treated as a coordinate effect, similar to the Coriolis force.

In this paper, a correspondence between scalar field fluctuations and generalized fluctuations in a hydrodynamic approximation of fields is obtained. The results presented here are of interest to field-fluid correspondences and form part of theoretical foundations in this area. The intention for such developments is to explore sub-hydro range mesoscopic physics for the relativistic fluids in curved spacetime. The fluid correspondences fall in the classical domain and can replace the quantum fields and fluctuations for scales around the hydrodynamic limits. This paper extends our earlier results with a more elaborate physical insight towards the quantum fluids and retention of partial quantum nature in a stochastic description in bulk of the fluids. This also accounts for nonthermal effects along with thermal and quantum fluctuations for the fields in the hydro limit. Hence, the expressions presented here are very general in nature for various applications. The further scope of research that such developments give is discussed in the concluding section.

We study the alteration of the Schwinger effect on radiatively corrected Higgs inflationary magneto-genesis by axial coupling function. The conformal invariance of Maxwell action should be broken by axial coupling with the inflaton field. We use the potential of [M. Kamarpour, Gen. Relativ. Gravit. 53 (2021) 53, doi:10.1007/s10714-021-02824-0; M. Kamarpour, Gen. Relativ. Gravit. 54 (2022) 32, doi:10.1007/s10714-022-02920-9] with the simplest coupling function $f(\varphi )={\chi }_1\frac{\varphi }{M_p}$ in which ${\chi }_1$ is a dimensionless coupling parameter.

In comparison to our previous work (in which we used curvature-based coupling or so-called nonminimal coupling function to gravity to break conformal invariance of action) of [M. Kamarpour, Gen. Relativ. Gravit. 54 (2022) 32, doi:10.1007/s10714-022-02920-9] we find that the Schwinger effect does alter magneto-genesis and is considerable. In fact, in comparison to our previous work of [M. Kamarpour, Gen. Relativ. Gravit. 54 (2022) 32, doi:10.1007/s10714-022-02920-9] we obtain that for some certain values of coupling parameter ${\chi }_1$ the Schwinger effect does alter magneto-genesis (see [M. Kamarpour, Gen. Relativ. Gravit. 53 (2021) 53, doi:10.1007/s10714-021-02824-0]) and the energy density of created charged particles during the Schwinger effect becomes considerable and of course comparable to the energy density of inflaton field. Therefore, the Schwinger effect decreases the value of the electric field, so that it helps to finish the inflation stage. Then the universe enters the stage of preheating.

The Schwinger effect produces charged particles, imposing the Schwinger reheating framework even before the ending of last oscillations of the inflaton field.

In this work, we consider static quark star (QS) within the framework of Rastall gravity. Rastall gravity purports to be the nonconservative theory of gravity and an unusual nonminimal coupling between matter and geometry. In our study, we consider a Quantum chromodynamics (QCD)-motivated Equation of State (EoS) to determine the properties of QSs in Rastall gravity. Depending on the values of parameters, we seek to determine the mass–radius relations for QSs in Rastall gravity, identifying the deviation from standard general relativity (GR) counterparts. Interestingly, we find the value of the maximum gravitational mass to be more than 2$M_{\odot }$ for the given equation of state (EoS). We present the essential features regarding the stability of QSs.

A Friedmann–Robertson–Walker cosmological model dominated by tachyonic — faster-than-light — dark matter can exhibit features similar to those of a standard dark energy/dark matter or $\mathrm{\Lambda }$CDM model. It can undergo expansion which decelerates to a minimum rate, passes through a “cosmic jerk,” then accelerates. But some features of a tachyon-dominated model are sufficiently distinct from those of the Standard Model that the two possibilities might be distinguished observationally. As a demonstration of concept, the distance-redshift relation of such a model is compared here with some observations of Type Ia supernovae. Other measures of the third time derivative of the cosmic scale factor — the true cosmic jerk — might be found to test a tachyonic-dark-matter hypothesis.

Cosmological features of Barrow Holographic Dark Energy (BHDE), a recent generalization of original Holographic dark energy with a richer structure, are studied in the context of Finsler–Randers universe, where the Hubble horizon is considered as the IR cutoff. Following this setup, we derive the evolution equation for the Barrow holographic dark energy-density parameter, the equation-of-state (EoS) parameter and deceleration parameter. As a result of our study, it is obtained that the model is able to describe the currently accelerating universe in both noninteractive and interactive scenarios, and that the development of the deceleration phase over to the acceleration phase also occurs later in this case. Furthermore, we discuss the statefinder diagnosis of this model, while plotting $r$ and $s$ versus redshift $z$ and the evolutionary trajectories of $\{r,s\}$. We find that the statefinder is not only superior in breaking the parsimony of the different coupling parameter values in this model, but also clearly distinguishes between the Barrow holographic dark energy model and the $\mathrm{\Lambda }\mathrm{\text{CDM}}$ model. In addition, we find that the statefinder pair performs slightly worse than $\{r,s\}$ for both $\{r,z\}$ and $\{s,z\}$ in this model. Finally, we show that the distance modulus of the theoretical model is compared with the observed data of Ia supernovae, and it is found that the theoretical model is in good agreement with the observed data. Our model satisfactorily explains the present history of the universe, thus providing a good candidate for dark energy.

We consider the Kepler two-body problem in the presence of a cosmological constant $\mathrm{\Lambda }$. Several dimensionless parameters characterizing the possible orbit typologies are used to identify open and closed trajectories. The qualitative picture of the two-body motion is described and critical parameters of the problem are found.