We study a $(4+D)$-dimensional Kaluza-Klein cosmology with a Robertson-Walker type metric having two scale factors $a$ and $R$, corresponding to $D$-dimensional internal space and 4-dimensional universe, respectively. By introducing an exotic matter in the form of perfect fluid with an special equation of state, as the space-time part of the higher dimensional energy-momentum tensor, a four dimensional effective decaying cosmological term appears as $λ\sim R^{-m}$ with $0 \leq m\leq 2$, playing the role of an evolving dark energy in the universe. By taking $m=2$, which has some interesting implications in reconciling observations with inflationary models and is consistent with quantum tunneling, the resulting Einstein's field equations yield the exponential solutions for the scale factors $a$ and $R$. These exponential behaviors may account for the dynamical compactification of extra dimensions and the accelerating expansion of the 4-dimensional universe in terms of Hubble parameter, $H$. The acceleration of the universe may be explained by the negative pressure of the exotic matter. It is shown that the rate of compactification of higher dimensions as well as expansion of 4-dimensional universe depends on the dimension, $D$. We then obtain the corresponding Wheeler-DeWitt equation and find the general exact solutions in $D$-dimensions. A good correspondence between the solutions of classical Einstein's equations and the solutions of quantum Wheeler-DeWitt equation in any dimension, $D$, is obtained based on Hartle's point of view concerning the classical limits of quantum cosmology.
We consider a (4+d)-dimensional spacetime broken up into a (4-n)-dimensional Minkowski spacetime (where n goes from 1 to 3) and a compact (n+d)-dimensional manifold. At the present time the n compactification radii are of the order of the Universe size, while the other d compactification radii are of the order of the Planck length.
We study on the third quantization of a Kaluza-Klein toy model. In this model time ($x$) is defined by the scale factor of universe, and the space coordinate ($y$) is defined by the ratio of the scales of the ordinary space and the internal space. We calculate the number density of the universes created from nothing and examine whether the compactification can be explained statistically by the idea of the third quantization.
We show that the phase transition from the decelerating universe to the accelerating universe, which is of relevance to the cosmological coincidence problem, is possible in the semiclassically quantized two-dimensional dilaton gravity by taking into account the noncommutative field variables during the finite time. Initially, the quantum-mechanically induced energy from the noncommutativity among the fields makes the early universe decelerate and subsequently the universe is accelerating because the dilaton driven cosmology becomes dominant later.
Mutidimensional cosmological models with $n\left( n\geq 2\right) $ Einstein spaces $M_i\left( i=1,\ldots ,n\right) $ are investigated. The cosmological constant and homogeneous minimally coupled scalar field as a matter sources are considered. The scalar field has a potential of general form depending on the scalar field as well as on the scale factors of $M_i$ . The general condition of existence of the solutions with spontaneous compactification is obtained and applied to physically important cases. Two particular kinds of solutions are found. One of them has a wormhole-type continuation int…
It is demonstrated by explicit solutions of the (4+n)-dimensional vacuum Einstein equations that accelerating cosmologies in the Einstein conformal frame can be obtained by a time-dependent compactification of string/M-theory, even in the case that internal dimensions are Ricci-flat, provided one includes one or more geometric twists. Such acceleration is transient. When both compact hyperbolic internal spaces and geometric twists are included, however, the period of accelerated expansion may be made arbitrarily large.
In this paper we investigate the accelerating and decelerating cosmological models with non-linear spinor fields and non-minimal interaction of $f(R)$ gravity with a scalar field. We combine two different approaches to the description of dark energy: modified gravity theory and introduction of the additional fields. Solutions for the FRW universe with power-law scale factor are reconstructed for the model under consideration with specific choice for scalar and spinor potentials. It is explained the role of scalar and spinor potentials as well as f(R) function for emergence of accelerating or d…
Cosmological solutions for homogeneous isotropic models in the framework of the Poincaré gauge theory of gravity based on gravitational Lagrangian adopted in the paper by Kun-Feng Shie, James M. Nester and Hwei-Jang Yo (Phys. Rev. D \textbf{78}, 023522 (2008)) are discussed. Cosmological solutions for accelerating Universe obtained in referred paper are compared with corresponding solutions of standard $ΛCDM$-model and also with cosmological solution obtained by authors of this Comment.
The modified gravity with 1/R term (R being scalar curvature) and the Einstein-Hilbert term is studied by incorporating the phantom scalar field. A number of cosmological solutions are derived in the presence of the phantom field in the perfect fluid background. It is shown the current inflation obtained in the modified gravity is affected by the existence the phantom field.
We give a simple interpretation of the recent solutions for cosmologies with a transient accelerating phase obtained from compactification in hyperbolic manifolds, or from S-brane solutions of string/M-theory. In the four-dimensional picture, these solutions correspond to bouncing the radion field off its exponential potential. Acceleration occurs at the turning point, when the radion stops and the potential energy momentarily dominates. The virtues and limitations of these approaches become quite transparent in this interpretation.
Compactification of type IIB theory on torus, in the presence of fluxes, is considered. The reduced effective action is expressed in manifestly S-duality invariant form. Cosmological solutions of the model are discussed in several cases in the Pre-Big Bang scenario.
The Wheeler-De Witt equation of type IIB quantum string cosmology compactified with constant internal H-fluxes on a 6-torus, whose volume modulus is frozen, is solved under the WKB approximation. The spontaneous symmetry breaking of the S-duality group by H-fluxes is also examined.
Exact string solutions are presented, where moduli fields are varying with time. They provide examples where a dynamical change of the topology of space is occurring. Some other solutions give cosmological examples where some dimensions are compactified dynamically or simulate pre-big bang type scenarios. Some lessons are drawn concerning the region of validity of effective theories and how they can be glued together, using stringy information in the region where the geometry and topology are not well defined from the low energy point of view. Other time dependent solutions are presented where…
In a semiclassically quantized two-dimensional cosmological model, it can be shown that the parameter of the equation of state for the accelerating universe can be positive due to the negative energy density and the negative pressure, which is a little different from the conventional wisdom that the parameter is negative with the positivity of the energy density. Furthermore, we show that the full parameter composed of the classical and the quantum-mechanical contributions is positive and finite even though the partial state parameter from the quantum-mechanical contribution is not positive de…
We study a $(4+D)$-dimensional Kaluza-Klein cosmology with a Robertson-Walker type metric having two scale factors $a$ and $R$, corresponding to $D$-dimensional internal space and 4-dimensional universe, respectively. By introducing an exotic matter as the space-time part of the higher dimensional energy-momentum tensor, a 4-dimensional decaying cosmological term is appeared as $Λ\sim R^{-2}$, playing the role of an evolving dark energy in the universe. The resulting field equations yield the exponential solutions for the scale factors. These exponential behaviors may account for the dynamical…
A cosmological model based on Kaluza-Klein theory is studied. A metric, in which the scale factor of the compact space evolves as an inverse power of the radius of the observable universe, is constructed. The Freedmann-Robertson-Walker equations of standard four-dimensional cosmology are obtained precisely. The pressure in our universe is an effective pressure expressed in terms of the components of the higher dimensional energy-momentum tensor. In particular, this effective pressure could be negative and might therefore explain the acceleration of our present universe. A special feature of th…
In this paper, we investigate the exact solution of an anisotropic space-time in the context of $f(Q)$ gravity, where $f\left( Q\right) $ is the arbitrary function of the non-metricity scalar $Q$. Here, we consider a specific power-law form as $f\left( Q\right) =αQ^{n+1}+β$, where $α$, $β$, and $n$ are free model parameters. Using power-law cosmology ($a\left( t\right) \propto t^{m}$), we analyze the physical behavior of cosmological parameters such as the energy density, pressure, EoS parameter, skewness parameter. Further, we validated the model with energy conditions and found that our $f\l…
Specific dark energy models with a linear inhomogeneous time-dependent equation of state, within the framework of 4d Friedman-Robertson-Walker (FRW) cosmology, are investigated. It is demonstrated that such 4d inhomogeneous fluid models may lead to a turbulence FRW cosmology. Both one-component and two-component models from 4d inhomogeneous dark fluid models are considered. In the one-component model the universe may develop from a viscous era with, for instance, a constant bulk viscosity, into a turbulent era. In the two-component model the fluid can be decomposed into two components, one non…
We find a cosmological solution corresponding to compactification of 10d supergravity on a warped conifold that easily circumvents `no-go' theorem given for a warped/flux compactification, providing new perspectives for the study of supergravity or superstring theory in cosmological backgrounds. With fixed volume moduli of the internal space, the model can explain a physical universe undergoing an accelerated expansion in the 4d Einstein frame, for a sufficiently long time. The solution found in the limit that the warp factor dependent on the radial coordinate $y$ is extremized (giving a const…
The free parameters of a flat accelerating model without dark energy are constrained by using Supernovae type Ia and observational H(z) data. Instead of the vacuum dominance, the present accelerating stage in this modified Einstein-de Sitter cosmology is a consequence of the gravitationally-induced particle production of cold dark matter. The model present a transition from a decelerating to an accelerating regime at low redshifts, and is also able to harmonize a cold dark matter picture with the latest measurements of the Hubble constant H_0, the Supernovae observations (Constitution sample),…
We examine the effect on cosmological evolution of adding a string motivated Gauss-Bonnet term to the traditional Einstein-Hilbert action for a (1 + 3) + d dimensional Friedman-Robertson- Walker (FRW) metric. By assuming that the additional dimensions compactify as the usual 3 spatial dimensions expand, we find that the Gauss Bonnet terms give perturbative corrections to the FRW equations. We find corrections that appear in the calculation of both the Hubble constant, H0, and the acceleration parameter, q0, for a variety of cases that are consistent with a dark energy equation of state.
We consider a six-dimensional Einstein-Maxwell system compactified in an axisymmetric two-dimensional space with one capped regularized conical brane of codimension one. We study the cosmological evolution which is induced on the regularized brane as it moves in between known static bulk and cap solutions. Looking at the resulting Friedmann equation, we see that the brane cosmology at high energies is dominated by a five-dimensional rho^2 energy density term. At low energies, we obtain a Friedmann equation with a term linear to the energy density with, however, negative coefficient in the smal…
The mathematical structure of homogeneous loop quantum cosmology is analyzed, starting with and taking into account the general classification of homogeneous connections not restricted to be Abelian. As a first consequence, it is seen that the usual approach of quantizing Abelian models using spaces of functions on the Bohr compactification of the real line does not capture all properties of homogeneous connections. A new, more general quantization is introduced which applies to non-Abelian models and, in the Abelian case, can be mapped by an isometric, but not unitary, algebra morphism onto c…
We study the classical and quantum cosmology of a 4+1-dimensional space-time with a non-zero cosmological constant coupled to a self interacting massive spinor field. We consider a spatially flat Robertson-Walker universe with the usual scale factor $R(t)$ and an internal scale factor $a(t)$ associated with the extra dimension. For a free spinor field the resulting equations admit exact solutions, whereas for a self interacting spinor field one should resort to a numerical method for exhibiting their behavior. These solutions give rise to a degenerate metric and exhibit signature transition fr…
We consider an empty (4+1) dimensional Kaluza-Klein universe with a negative cosmological constant and a Robertson-Walker type metric. It is shown that the solutions to Einstein field equations have degenerate metric and exhibit transitioins from a Euclidean to a Lorentzian domain. We then suggest a mechanism, based on signature transition which leads to compactification of the internal space in the Lorentzian region as $a \sim |Λ|^{1/2}$. With the assumption of a very small value for the cosmological constant we find that the size of the universe $R$ and the internal scale factor $a$ would be…
This work deals with $F(T)$ gravity models driven by real scalar fields with usual and phantom dynamics. We illustrate the results with examples of current interest, and we find some analytical solutions for scale factors and scalar fields. The results indicate that torsion-scalar models also admit the accelerated expansion of the universe.
Dark energy models can be seen as dynamical systems. In this paper we show that multi-field models with a curved field space give rise to new critical points and we analyse their stability. These are new accelerating solutions in late-time cosmology which exist even for steep potentials. This opens up the possibility to realise quintessence models even when quantum corrections spoil the flatness of the underlying potential. These non-linear sigma models arise naturally in supergravity and string models where their multi-field dynamics can help to avoid swampland bounds.
This paper studies the cosmology of accelerating expansion of the universe in modified teleparallel gravity theory. We discuss the cosmology of $f(T,B)$ gravity theory and its implication to the new general form of the equation of state parameter $w_{TB}$ for explaining the late-time accelerating expansion of the universe without the need for the cosmological constant scenario. We examine the numerical value of $w_{TB}$ in different paradigmatic $f(T,B)$ gravity models. In those models, the numerical result of $w_{TB}$ is favored with observations in the presence of the torsion scalar T associ…
We have studied the torsion cosmology model in Kaluza-Klein theory. We considered two simple models in which the torsion vectors are $A_μ=(α,0,0,0)$ and $A_μ=a(t)^2(0,β,β,β)$, respectively. For the first model, the accelerating expansion of the Universe can be not explained without dark energy which is similar to that in the standard cosmology. But for the second model, we find that without dark energy the effect of torsion can give rise to the accelerating expansion of the universe and the alleviation of the well-known age problem of the three old objects for appropriated value of the model p…
We develop the general reconstruction scheme in two scalar model. The quintom-like theory which may describe (different) non-singular Little Rip or de Sitter cosmology is reconstructed. (In)stability of such dark energy cosmologies as well as the flow to fixed points is studied. The stability of Little Rip universe which leads to dissolution of bound objects sometime in future indicates that no classical transition to de Sitter space occurs.
Ashtekar and Samuel have shown that Bianchi cosmological models with compact spatial sections must be of Bianchi class A. Motivated by general results on the symmetry reduction of variational principles, we show how to extend the Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as defined, e.g., by Singer and Thurston. In particular, it is shown that any m-dimensional homogeneous space G/K admitting a G-invariant volume form will allow a compact discrete quotient only if the Lie algebra cohomology of G relative to K is non-vanishing at degree m.
We study the dynamics of the size of an extra-dimensional manifold stabilised by fluxes. Inspecting the potential for the 4D field associated with this size (the radion), we obtain the conditions under which it can be stabilised and show that stable compactifications on hyperbolic manifolds necessarily have a negative four-dimensional cosmological constant, in contradiction with experimental observations. Assuming compactification on a positively curved (spherical) manifold we find that the radion has a mass of the order of the compactification scale, M_c, and Planck suppressed couplings. We a…
Investigations of the dynamic modes of the Poincare gauge theory of gravity found only two good propagating torsion modes; they are effectively a scalar and a pseudoscalar. Cosmology affords a natural situation where one might see observational effects of these modes. Here we consider only the ``scalar torsion'' mode. This mode has certain distinctive and interesting qualities. In particular this type of torsion does not interact directly with any known matter and it allows a critical non-zero value for the affine scalar curvature. Via numerical evolution of the coupled nonlinear equations we …
We review the accelerating (mainly, dark energy) cosmologies in modified gravity. Special attention is paid to cosmologies leading to finite-time future singularities in $F(R)$, $F(G)$ and $\mathcal{F}(R,G)$ modified gravities. The removal of the finite-time future singularities via addition of $R^2$-term which simultaneously unifies the early-time inflation with late-time acceleration is also briefly mentioned. Accelerating cosmology including the scenario unifying inflation with dark energy is considered in $F(R)$ gravity with Lagrange multipliers. In addition, we examine domain wall solutio…
The partial Hamiltonian analysis of the Hořava-type action presented in the paper by M. Chaichian, S. Nojiri, S. D. Odintsov, M. Oksanen, A. Tureanu (Class. Quant. Grav. 27 (2011) 185021) is incorrect; for the authors' choice of variables, a covariant shift, instead of a contravariant shift which is the one usually used in General Relativity (GR) in ADM variables, the true algebra of constraints differs from what they presented. The algebra of constraints for their choice of variables is explicitly given for GR and compared with the standard algebra.
We present new exact solutions of the warped spherical compactifications in the higher-dimensional gravitational theory coupled to scalar and several form field strengths. We find two classes of solutions. One has a de Sitter spacetime with a static warp factor. The other gives an accelerating universe in the non-Einstein conformal frame with a time-dependent warp factor.
The standard Friedmann universe embedded in a five dimensional and constant curvature bulk is examined without any a priori junction condition between the brane and the bulk. A geometrical explanation for the accelerated expansion of the universe is derived by using a minimum set of assumptions consistent with the brane-world program. It is shown that the extrinsic curvature of the brane can be associated to the dark energy which presumably drives the universe expansion.
We extend to multidimensional cosmology Vilenkin's prescription of tunnelling from nothing for the quantum origin of the observable Universe. Our model consists of a $D+4$-dimensional spacetime of topology ${\cal R}\times {\cal S}^3 \times{\cal S}^D$, with a scalar field (``chaotic inflaton'') for the matter component. Einstein gravity and Casimir compactification are assumed. The resulting minisuperspace is 3--dimensional. Patchwise we find an approximate analytic solution of the Wheeler--DeWitt equation through which we discuss the tunnelling picture and the probability of nucleation of the …
We propose a bigravity analogue of the $F(R)$ gravity. Our construction is based on recent ghost-free massive bigravity where additional scalar fields are added and the corresponding conformal transformation is implemented. It turns out that $F(R)$ bigravity is easier to formulate in terms of the auxiliary scalars as the explicit presentation in terms of $F(R)$ is quite cumbersome. The consistent cosmological reconstruction scheme of $F(R)$ bigravity is developed in detail, showing the possibility to realize nearly arbitrary physical universe evolution with consistent solution for second metri…
The DGP brane-world model provides a simple alternative to the standard LCDM cosmology, with the same number of parameters. There is no dark energy - the late universe self-accelerates due to an infrared modification of gravity. We compute the joint constraints on the DGP model from supernovae, the cosmic microwave background shift parameter, and the baryon oscillation peak in the SDSS luminous red galaxy sample. Flat DGP models are within the joint 2 sigma contour, but the LCDM model provides a significantly better fit to the data. These tests are based on the background dynamics of the DGP m…
We present a cosmological model with a solution that self-accelerates at late-times without signs of ghost instabilities on small scales. The model is a natural extension of the Brans-Dicke (BD) theory including a non-linear derivative interaction, which appears in a theory with the Galilean shift symmetry. The existence of the self-accelerating universe requires a negative BD parameter but, thanks to the non-linear term, small fluctuations around the solution are stable on small scales. General relativity is recovered at early times and on small scales by this non-linear interaction via the V…
We consider (4+D)-dimensional Kaluza-Klein cosmological model with two scaling factors, as real, p-adic and adelic quantum mechanical one. One of the scaling factors corresponds to the D-dimensional internal space, and second one to the 4-dimensional universe. In standard quantum cosmology, i.e. over the field of real numbers R, it leads to dynamical compactification of additional dimensions and to the accelerating evolution of 4-dimensional universe. We construct corresponding $p$-adic quantum model and explore existence of its p-adic ground state. In addition, we explore evolution of this mo…
The article gives an account of several aspects of the space known as the Bohr compactification of the line, featuring as the quantum configuration space in loop quantum cosmology, as well as of the corresponding configuration space realization of the so-called polymer representation. Analogies with loop quantum gravity are explored, providing an introduction to (part of) the mathematical structure of loop quantum gravity, in a technically simpler context.
Isotropic cosmology built in the Riemann-Cartan spacetime is investigated. Properties of homogeneous isotropic cosmological models filled with usual gravitating matter and scalar fields are studied in the beginning of cosmological expansion near the limiting energy density. It is shown that cosmological models are regular not only with respect to the Hubble parameter and the energy density but also with respect to the torsion and curvature tensors.
We study classical and quantum noncommutative cosmology with a Liouville-type scalar degree of freedom. The noncommutativity is imposed on the minisuperspace variables through a deformation of the Poisson algebra. In this paper, we investigate the effects of noncommutativity of minisuperspace variables on the accelerating behavior of the cosmic scale factor. The probability distribution in noncommutative quantum cosmology is also studied and we propose a novel candidate for interpretation of the probability distribution in terms of noncommutative arguments.
We consider the cosmological role of the scalar fields generated by the compactification of 11-dimensional Einstein gravity on a 7D elliptic twisted torus, which has the attractive features of giving rise to a positive semi-definite potential, and partially fixing the moduli. This compactification is therefore relevant for low energy M-theory, 11D supergravity. We find that slow-roll inflation with the moduli is not possible, but that there is a novel scaling solution in Friedmann cosmologies in which the massive moduli oscillate but maintain a constant energy density relative to the backgroun…
We discuss conformal issues of pure and extended teleparallel gravity. In particular, we present formulations of conformal transformation in teleparallel gravity. Furthermore, we propose conformal scalar and gauge field theories in teleparallel gravity and study conformal torsion gravity. We explicitly demonstrate that a power-law acceleration (including the $Λ$CDM universe) as well as the de Sitter expansion of the universe can be realized in extended teleparallel gravity with a conformal scalar field, and that pure teleparallel gravity with a conformal scalar field can lead to the $Λ$CDM mod…
We discuss a possible compactification of a higher-dimensional gravitational theory, which give rise to a de Sitter or an accelerating universe, to the extent that it can describe a low energy limit of string theory. Such analysis can be carried out by the usual integration over the internal space in the Einstein equations. The combined field equations in the higher-dimensional supergravity theory after integration give several new terms which may help to realize a de Sitter compactification. After developing the general framework, we describe some specific examples involving the dilaton and m…
The velocity of the Hubble expansion has been added to General Relativity by Moshe Carmeli and this resulted in new equations of motion for the expanding universe. For the first time the observational magnitude-redshift data derived from the high-$z$ supernova teams has been analysed in the framework of the Carmeli theory and the fit to that theory is achieved without the inclusion of any dark matter. Best fits to the data yield an averaged matter density for the universe at the present epoch $Ω_{m} \approx 0.021$, which falls well within the measured values of the baryonic matter density. And…
Carmeli's 5D brane cosmology has been applied to the expanding accelerating universe and it has been found that the distance redshift relation will fit the data of the high-z supernova teams without the need for dark matter. Also the vacuum energy contribution to gravity indicates that the universe is asymptotically expanding towards a spatially flat state, where the total mass/energy density tends to unity.
Cosmologies with a Chaplygin gas have recently been explored with the objective of explaining the transition from a dust dominated epoch towards an accelerating expansion stage. We consider the hypothesis that the transition to the accelerated period involves a quantum mechanical process. Three physically admissible cases are possible. In particular, we identify a minisuperspace configuration with two Lorentzian sectors, separated by a classically forbidden region. The Hartle-Hawking and Vilenkin wave functions are computed, together with the transition amplitudes towards the accelerating epoc…
An exponential potential of the form $V\sim \exp(-2c ϕ/M_p)$ arising from the hyperbolic or flux compactification of higher-dimensional theories is of interest for getting short periods of accelerated cosmological expansions. Using a similar potential but derived for the combined case of hyperbolic-flux compactification, we study the four-dimensional flat (and open) FLRW cosmologies and give analytic (and numerical) solutions with exponential behavior of scale factors. We show that, for the M-theory motivated potentials, the cosmic acceleration of the universe can be eternal if the spatial cur…
Six-dimensional Einstein-Gauss-Bonnet gravity (with a linear Gauss-Bonnet term) is investigated. This theory is inspired by basic features of results coming from string and M-theory. Dynamical compactification is carried out and it is seen that a four-dimensional accelerating FRW universe is recovered, when the two-dimensional internal space radius shrinks. A non-perturbative structure of the corresponding theory is identified which has either three or one stable fixed points, depending on the Gauss-Bonnet coupling being positive or negative. A much richer structure than in the case of the per…
In an attempt to look for a viable mechanism leading to a present-day accelerated expansion, we investigate the possibility that the observed cosmic speed up may be recovered in the framework of the Rastall's theory, relying on the non-conservativity of the stress-energy tensor, i.e. $T^μ_{ν; μ} \neq 0$. We derive the modified Friedmann equations and show that they correspond to Cardassian-like equations. We also show that, under suitable assumptions on the equation of state of the matter term sourcing the gravitational field, it is indeed possible to get an accelerated expansion, in agreement…
