Brane world solution to the cosmological constant problem

We consider a model with two parallel (positive tension) 3-branes separated by a distance L in five-dimensional spacetime. If the interbrane space is anti--de Sitter, or is not precisely anti--de Sitter but contains no event horizons, the effective four-dimensional cosmological constant seen by observers on one of the branes (chosen to be the visible brane) becomes exponentially small as L grows large.     

From 2-dimensional surfaces to cosmological solutions

We construct perfect fluid metrics with two symmetries by means of a recently developed geometrical method [1]. The Einstein equations are reduced to a single equation for a conformal factor. Under additional assumptions we obtain new cosmological solutions of Bianchi type II, VI₀ and VII₀. The solutions depend on an arbitrary function of time, which can be specified in order to satisfy an equation of state.     

Stationary cosmological Bianchi II solutions

Stationary cosmological solutions for the Bianchi metric II are derived. In the models, use is made of a scalar field with a vacuum-averaged energy-momentum tensor, a cosmological constant, and ideal co-moving or not co-moving liquids as sources of gravitations.     

Bouncing cosmological solutions due to the self-gravitational corrections and their stability

In this paper we consider the bouncing braneworld scenario, in which the bulk is given by a five-dimensional AdS black hole spacetime with matter field confined in a 3D brane. Exploiting the CFT/FRW-cosmology relation, we consider the self-gravitational corrections to the first Friedmann-like equation which is the equation of the brane motion. The self-gravitational corrections act as a source of stiff matter contrary to standard FRW cosmology, where the charge of the black hole plays this role. Then we study the stability of solutions with respect to homogeneous and isotropic perturbations. Specifically, if we do not consider the self-gravitational corrections, the AdS black hole with zero ADM mass and open horizon is an attractor, while, if we consider the self-gravitational corrections, the AdS black hole with zero ADM mass and flat horizon is a repeller.     

Type-D vacuum solutions with cosmological constant

All type-D vacuum (nonnull orbit and null orbit) solutions with are exhibited in canonical coordinates. The nonnull orbit metrics with contain four families of solutions: the static Levi-Cività metrics, the nondivergingD's, the divergingD's, and the diverging and twisting solutions. The null orbit metrics subdivide into two subclasses of solutions: the divergenceless null orbitD's, and the diverging and twisting null orbit solution.     

Cosmological background solutions and cosmological backreactions

The cosmological backreaction proposal, which attempts to account for observations without a primary dark energy source in the stress-energy tensor, has been developed and discussed by means of different approaches. Here, we focus on the concept of cosmological background solutions in order to develop a framework to study different backreaction proposals.     

Exact solutions in cosmological inflationary models

The exact solutions of the Einstein equations that correspond to a given evolution of the scale factor in the inflationary stage in the development of the universe are considered within the framework of the theory of a self-acting scalar field that interacts minimally with a gravitational field. The form of the potential that ensures a given rate of expansion and the solution for the scalar field are calculated for each type of inflation considered. Some general laws of the relation between the form of potential and the scale factor evolution are analyzed. Moscow State University Branch in Ul'yanovsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 83–88, August, 1996.     

Static cosmological solutions in quadratic gravity

General Relativity and Gravitation - A correction to this paper has been published: https://doi.org/10.1007/s10714-021-02825-z     

Semi-local cosmic strings and the cosmological constant problem

We study the cosmological constant problem in a three-dimensional N = 2 supergravity theory with gauge groupSU (2)_global × U(1)_local. The model we consider is known to admit string-like configurations, the so-called semi-local cosmic strings. We show that the stability of these solitonic solutions is provided by supersymmetry through the existence of a lower bound for the energy, even though the manifold of the Higgs vacuum does not contain non-contractible loops. Charged Killing spinors do exist over configurations that saturate the Bogomol'nyi bound, as a consequence of an Aharonov-Bohm-like effect. Nevertheless, there are no physical fermionic zero modes on these backgrounds. The exact vanishing of the cosmological constant does not imply, then, Bose-Fermi degeneracy. This provides a non-trivial example of the recent claim made by Witten on the vanishing of the cosmological constant in three dimensions without unphysical degeneracies.     

On the cosmological constant problem and brane-world geometry

The cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.     

Stress-energy connection and cosmological constant problem

We study gravitational properties of vacuum energy by erecting a geometry on the stress-energy tensor of vacuum, matter and radiation. Postulating that the gravitational effects of matter and radiation can be formulated by an appropriate modification of the spacetime connection, we obtain varied geometrodynamical equations which properly comprise the usual gravitational field equations with, however, Planck-suppressed, non-local, higher-dimensional additional terms. The prime novelty brought about by the formalism is that, the vacuum energy does act not as the cosmological constant but as the source of the gravitational constant. The formalism thus deafens the cosmological constant problem by channeling vacuum energy to gravitational constant. Nevertheless, quantum gravitational effects, if any, restore the problem via the graviton and graviton-matter loops, and the mechanism proposed here falls short of taming such contributions to cosmological constant.     

A primordial cosmological scenario and the horizon problem

The coupling of the Einstein-Hilbert Lagrangian with a conformal field in an arbitrary even dimension leads, after reduction to four dimensions, to the ordinary gravity coupled non-trivially to two scalar fields. The vacuum solutions display an initial singularity, but with an infinite proper distance between any two points of the space-time. There is an initial contraction phase followed by an expansion phase. This is a kind of anti-Big Bang scenario. The coupling to a radiative fluid preserves this feature; however, the temperature of the radiative fluid is initially zero, increasing afterwards: its maximum value is related to the moment where the horizon crosses the radius of the Universe. The entropy in the three-dimensional space is inversely proportional to the volume of the internal space, and it can be very high today. We perform also a perturbative study of this model during the contraction phase. There is no explosive growth of the scalar perturbations.     

Thermal background can solve the cosmological moduli problem

It is shown that the coherent field oscillation of moduli fields with weak or TeV scale masses can dissipate its energy efficiently if they have a derivative coupling to standard bosonic fields in a thermal state. This mechanism provides a new solution to the cosmological moduli problem without creating too much entropy at late time.     

Decreasing vacuum temperature: A thermal approach to the cosmological constant problem

A natural thermal interpretation of the cosmological scenario is suggested in which the energy of the vacuum background is a variable function of the cosmic time; it is also shown that in this context one can easily formulate a simple phenomenological model which helps understanding, without fine-tuning, the extreme smallness of the present value of the cosmological constant.     

Singularity-free cosmological solutions with non-rotating perfect fluids

A conjecture stated by Raychaudhuri which claims that the only physical perfect fluid non-rotating non-singular cosmological models are comprised in the Ruiz–Senovilla and Fernández–Jambrina families is shown to be incorrect. An explicit counterexample is provided and the failure of the argument leading to the result is explicitly pointed out.     

Five-domensional, nonstationary cosmological solutions with rotation

Two nonstationary cosmological solutions of the five-dimensional Einstein equations are found for different metrics. In one case the sources of the gravitational field are an anisotropic fluid and a radiation field, while in the other case they are an anisotropic fluid, a radiation field, and a heat flux. Perm' State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 25–28, September, 1997.