arXiv subjects

Aleksey Toporensky

Publications and source records attributed to Aleksey Toporensky.

6 recordsLinked to original sources

arXiv2021

Conserved Currents and Superpotentials in Teleparallel Equivalent of General Relativity

We study the Teleparallel Equivalent of General Relativity (TEGR) with Lagrangian that includes the flat (inertial) spin connection and that is evidently invariant with respect to local Lorentz rotations. Applying directly the Noether theorem, we construct new expressions for conserved currents and related superpotentials. They are covariant both under coordinate transformations and local Lorentz rotations, and allow us to construct well defined conserved charges, unlike earlier approaches. The advantage is achieved by an explicit presence of a displacement vector in the new expressions that can be interpreted as a Killing vector, as a proper vector of an observer, etc. The new expressions are used to introduce a principle for definition of an inertial spin connection that is undetermined one in the TEGR from the start. Theoretical results are applied to calculate mass for the Schwarzschild black hole and densities of conserved quantities for freely falling observers both in Friedmann-Lemaitre-Robertson-Walker world of all the three signs of curvature and in (anti-)de Sitter space.

gr-qc↗

arXiv2017

Anisotropic cosmological solutions in $R + R^2$ gravity

In this paper we investigate the past evolution of an anisotropic Bianchi I universe in $R+R^2$ gravity. Using the dynamical system approach we show that there exists a new two-parameters set of solutions that includes both an isotropic "false radiation" solution and an anisotropic generalized Kasner solution, which is stable. We derive the analytic behaviour of the shear from a specific property of $f(R)$ gravity and the analytic asymptotic form of the Ricci scalar when approaching the initial singularity. Finally we numerically checked our results.

gr-qc↗

arXiv2015

Arrow of time in dissipationless cosmology

It is generally believed that a cosmological arrow of time must be associated with entropy production. Indeed, in his seminal work on cyclic cosmology, Tolman introduced a viscous fluid in order to make successive expansion/contraction cycles larger than previous ones, thereby generating an arrow of time. However, as we demonstrate in this letter, the production of entropy is not the only means by which a cosmological arrow of time may emerge. Remarkably, systems which are dissipationless may nevertheless demonstrate a preferred direction of time provided they possess attractors. An example of a system with well defined attractors is scalar-field driven cosmology. In this case, for a wide class of potentials (especially those responsible for inflation), the attractor equation of state during expansion can have the form $p \simeq -ρ$, and during contraction $p \simeq ρ$. If the resulting cosmology is cyclic, then the presence of cosmological hysteresis, $\oint p~dV \neq 0$ during successive cycles, causes an arrow of time to emerge in a system which is formally dissipationless. An important analogy is drawn between the arrow of time in cyclic cosmology and an arrow of time in an $N$-body system of gravitationally interacting particles. We find that, like the $N$-body system, a cyclic universe can evolve from a single past into two futures with oppositely directed arrows of time.

gr-qc↗

arXiv2012

Refining inflation using non-canonical scalars

This paper revisits the Inflationary scenario within the framework of scalar field models possessing a non-canonical kinetic term. We obtain closed form solutions for all essential quantities associated with chaotic inflation including slow roll parameters, scalar and tensor power spectra, spectral indices, the tensor-to-scalar ratio, etc. We also examine the Hamilton-Jacobi equation and demonstrate the existence of an inflationary attractor. Our results highlight the fact that non-canonical scalars can significantly improve the viability of inflationary models. They accomplish this by decreasing the tensor-to-scalar ratio while simultaneously increasing the value of the scalar spectral index, thereby redeeming models which are incompatible with the cosmic microwave background (CMB) in their canonical version. For instance, the non-canonical version of the chaotic inflationary potential, $V(ϕ) \sim λϕ^4$, is found to agree with observations for values of $λ$ as large as unity ! The exponential potential can also provide a reasonable fit to CMB observations. A central result of this paper is that {\em steep potentials} (such as $V \propto ϕ^{-n}$) usually associated with dark energy, can drive inflation in the non-canonical setting. Interestingly, non-canonical scalars violate the consistency relation $r = -8n_T$, which emerges as a {\em smoking gun} test for this class of models.

astro-ph.CO↗

arXiv2012

Cosmological Hysteresis and the Cyclic Universe

A Universe filled with a homogeneous scalar field exhibits `Cosmological hysteresis'. Cosmological hysteresis is caused by the asymmetry in the equation of state during expansion and contraction. This asymmetry results in the formation of a hysteresis loop: $\oint pdV$, whose value can be non-vanishing during each oscillatory cycle. For flat potentials, a negative value of the hysteresis loop leads to the increase in amplitude of consecutive cycles and to a universe with older and larger successive cycles. Such a universe appears to possess an arrow of time even though entropy production is absent and all of the equations respect time-reversal symmetry ! Cosmological hysteresis appears to be widespread and exists for a large class of scalar field potentials and mechanisms for making the universe bounce. For steep potentials, the value of the hysteresis loop can be positive as well as negative. The expansion factor in this case displays quasi-periodic behaviour in which successive cycles can be both larger as well as smaller than previous ones. This quasi-regular pattern resembles the phenomenon of BEATS displayed by acoustic systems. Remarkably, the expression relating the increase/decrease in oscillatory cycles to the quantum of hysteresis appears to be model independent. The cyclic scenario is extended to spatially anisotropic models and it is shown that the anisotropy density decreases during successive cycles if the hysteresis loop is negative.

gr-qc↗

arXiv2006

Quantum effects, soft singularities and the fate of the universe in a braneworld cosmology

We examine a class of braneworld models in which the expanding universe encounters a "quiescent" future singularity. At a quiescent singularity, the energy density and pressure of the cosmic fluid as well as the Hubble parameter remain finite while all derivatives of the Hubble parameter diverge (i.e., ${\dot H}$, ${\ddot H}$, etc. $\to \infty$). Since the Kretschmann invariant diverges ($R_{iklm}R^{iklm} \to \infty$) at the singularity, one expects quantum effects to play an important role as the quiescent singularity is approached. We explore the effects of vacuum polarization due to massless conformally coupled fields near the singularity and show that these can either cause the universe to recollapse or, else, lead to a softer singularity at which $H$, ${\dot H}$, and ${\ddot H}$ remain finite while ${\dddot H}$ and higher derivatives of the Hubble parameter diverge. An important aspect of the quiescent singularity is that it is encountered in regions of low density, which has obvious implications for a universe consisting of a cosmic web of high and low density regions -- superclusters and voids. In addition to vacuum polarization, the effects of quantum particle production of non-conformal fields are also likely to be important. A preliminary examination shows that intense particle production can lead to an accelerating universe whose Hubble parameter shows oscillations about a constant value.

gr-qc↗