arXiv subjects
Publications and source records attributed to Yuri Shtanov.
Brane cosmology presents many interesting possibilities including: phantom acceleration (w<-1), self-acceleration, unification of dark energy with inflation, transient acceleration, loitering cosmology, new singularities at which the Hubble parameter remains finite, cosmic mimicry, etc. The existence of a time-like extra dimension can result in a singularity-free cyclic cosmology.
We describe how a certain simple modification of general relativity, in which the local cosmological constant is allowed to depend on the space-time curvature, predicts the existence of halos of modified gravity surrounding spherically-symmetric objects. We show that the gravitational mass of an object weighed together with its halo can be much larger than its gravitational mass as seen from inside the halo. This effect could provide an alternative explanation of the dark-matter phenomenon in galaxies. In this case, the local cosmological constant in the solar system must be some six orders of magnitude larger than its cosmic value obtained in the supernovae type Ia experiments. This is well within the current experimental bounds, but may be directly observable in the future high-precision experiments.
We derive a system of cosmological equations for a braneworld with induced curvature which is a junction between several bulk spaces. The permutation symmetry of the bulk spaces is not imposed, and the values of the fundamental constants, and even the signatures of the extra dimension, may be different on different sides of the brane. We then consider the usual partial case of two asymmetric bulk spaces and derive an exact closed system of scalar equations on the brane. We apply this result to the cosmological evolution on such a brane and describe its various partial cases.
A proposal is made to test Newton's inverse-square law using the perihelion shift of test masses (planets) in free fall within a spacecraft located at the Earth-Sun L2 point. Such an Artificial Planetary System In Space (APSIS) will operate in a drag-free environment with controlled experimental conditions and minimal interference from terrestrial sources of contamination. We demonstrate that such a space experiment can probe the presence of a "hidden" fifth dimension on the scale of a micron, if the perihelion shift of a "planet" can be measured to sub-arc-second accuracy. Some suggestions for spacecraft design are made.
An outstanding issue in braneworld theory concerns the setting up of proper boundary conditions for the brane-bulk system. Boundary conditions (BC's) employing regulatory branes or demanding that the bulk metric be nonsingular have yet to be implemented in full generality. In this paper, we take a different route and specify boundary conditions directly on the brane thereby arriving at a local and closed system of equations (on the brane). We consider a one-parameter family of boundary conditions involving the anisotropic stress of the projection of the bulk Weyl tensor on the brane and derive an exact system of equations describing scalar cosmological perturbations on a generic braneworld with induced gravity. Depending upon our choice of boundary conditions, perturbations on the brane either grow moderately (region of stability) or rapidly (instability). In the instability region, the evolution of perturbations usually depends upon the scale: small scale perturbations grow much more rapidly than those on larger scales. This instability is caused by a peculiar gravitational interaction between dark radiation and matter on the brane. Generalizing the boundary conditions obtained by Koyama and Maartens, we find for the Dvali-Gabadadze-Porrati model an instability, which leads to a dramatic scale-dependence of the evolution of density perturbations in matter and dark radiation. A different set of BC's, however, leads to a more moderate and scale-independent growth of perturbations. For the mimicry braneworld, which expands like LCDM, this class of BC's can lead to an earlier epoch of structure formation.
We continue the study of the non-metric theory of gravity introduced in hep-th/0611182 and gr-qc/0703002 and obtain its general spherically symmetric vacuum solution. It respects the analog of the Birkhoff theorem, i.e., the vacuum spherically symmetric solution is necessarily static. As in general relativity, the spherically symmetric solution is seen to describe a black hole. The exterior geometry is essentially the same as in the Schwarzschild case, with power-law corrections to the Newtonian potential. The behavior inside the black-hole region is different from the Schwarzschild case in that the usual spacetime singularity gets replaced by a singular surface of a new type, where all basic fields of the theory remain finite but metric ceases to exist. The theory does not admit arbitrarily small black holes: for small objects, the curvature on the would-be horizon is so strong that non-metric modifications prevent the horizon from being formed. The theory allows for modifications of gravity of very interesting nature. We discuss three physical effects, namely, (i) correction to Newton's law in the neighborhood of the source, (ii) renormalization of effective gravitational and cosmological constants at large distances from the source, and (iii) additional redshift factor between spatial regions of different curvature. The first two effects can be responsible, respectively, for the observed anomaly in the acceleration of the Pioneer spacecraft and for the alleged missing mass in spiral galaxies and other astrophysical objects. The third effect can be used to propose a non-cosmological explanation of high redshifts of quasars and gamma-ray bursts.
We investigate the braneworld model with induced gravity to clarify the role of the cross-over length scale \ell in the possible explanation of the dark-matter phenomenon in astrophysics and in cosmology. Observations of the 21 cm line from neutral hydrogen clouds in spiral galaxies reveal that the rotational velocities remain nearly constant at a value v_c ~ 10^{-3}--10^{-4} in the units of the speed of light in the region of the galactic halo. Using the smallness of v_c, we develop a perturbative scheme for reconstructing the metric in a galactic halo. In the leading order of expansion in v_c, at the distances r \gtrsim v_c \ell, our result reproduces that obtained in the Randall-Sundrum braneworld model. This inequality is satisfied in a real spiral galaxy such as our Milky Way for distances r ~ 3 kpc, at which the rotational velocity curve becomes flat, v_c ~ 7 \times 10^{-4}, if \ell \lesssim 2 Mpc. The gravitational situation in this case can be approximately described by the Einstein equations with the so-called Weyl fluid playing the role of dark matter. In the region near the gravitating body, we derive a closed system of equations for static spherically symmetric situation under the approximation of zero anisotropic stress of the Weyl fluid. We find the Schwarzschild metric to be an approximate vacuum solution of these equations at distances r \lesssim (r_g \ell^2)^{1/3}. The value \ell \lesssim 2 Mpc complies well with the solar-system tests. At the same time, in cosmology, a low-density braneworld with \ell of this order of magnitude can mimic the expansion properties of the high-density LCDM (lambda + cold dark matter) universe at late times. Combined observations of galactic rotation curves and gravitational lensing can possibly discriminate between the higher-dimensional effects and dark matter.
We investigate the possibility of boiling instability of nuclear liquid in the inner core of the proto-neutron star formed in the core collapse of a type II supernova. We derive a simple criterion for boiling to occur. Using this criterion for one of best described equations of state of supernova matter, we find that boiling is quite possible under the conditions realized inside the proto-neutron star. We discuss consequences of this process such as the increase of heat transfer rate and pressure in the boiling region. We expect that taking this effect into account in the conventional neutrino-driven delayed-shock mechanism of type II supernova explosions can increase the explosion energy and reduce the mass of the neutron-star remnant.
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.
For a broad range of parameter values, braneworld models display a remarkable property which we call cosmic mimicry. Cosmic mimicry is characterized by the fact that, at low redshifts, the Hubble parameter in the braneworld model is virtually indistinguishable from that in the LCDM cosmology. An important point to note is that the Ω_m parameters in the braneworld model and in the LCDM cosmology can nevertheless be quite different. Thus, at high redshifts (early times), the braneworld asymptotically expands like a matter-dominated universe with the value of Ω_m inferred from the observations of the local matter density. At low redshifts (late times), the braneworld model behaves almost exactly like the LCDM model but with a renormalized value of the cosmological density parameter Ω_m^{LCDM}. The redshift which characterizes cosmic mimicry is related to the parameters in the higher-dimensional braneworld Lagrangian. Cosmic mimicry is a natural consequence of the scale-dependence of gravity in braneworld models. The change in the value of the cosmological density parameter is shown to be related to the spatial dependence of the effective gravitational constant in braneworld theory. A subclass of mimicry models lead to an older age of the universe and also predict a redshift of reionization which is lower than z_{reion} \simeq 17 in the LCDM cosmology. These models might therefore provide a background cosmology which is in better agreement both with the observed quasar abundance at z \gsim 4 and with the large optical depth to reionization measured by the Wilkinson Microwave Anisotropy Probe.
The Randall-Sundrum two-brane model admits the flat-brane Lorentz-invariant vacuum solution only if the branes have exactly opposite tensions. We pay attention to this condition and propose a generalization of this model in which two branes are described by actions of the same form and with the same matter content but {\em with opposite signs}. In this way, the relation between their tensions (which are their vacuum energy densities) is naturally accounted for. We study a simple example of such a model in detail. It represents the Randall-Sundrum model supplemented by the Einstein scalar-curvature terms in the actions for the branes. We show that this model is tachyon-free for sufficiently large negative values of the brane cosmological constant, that gravitational forces on the branes are of opposite signs, and that physically most reasonable model of this type is the one where the five-dimensional gravity is localized around the visible brane. The massive gravitational modes in this model have ghost-like character, and we discuss the significance of this fact for the quantum instability of the vacuum on the visible brane.
We consider cosmological solutions and their stability with respect to homogeneous and isotropic perturbations in the braneworld model with the scalar-curvature term in the action for the brane. Part of the results are similar to those obtained by Campos and Sopuerta for the Randall-Sundrum braneworld model. Specifically, the expanding de Sitter solution is an attractor, while the expanding Friedmann solution is a repeller. In the braneworld theory with the scalar-curvature term in the action for the brane, static solutions with matter satisfying the strong energy condition exist not only with closed spatial geometry but also with open and flat ones even in the case where the dark-radiation contribution is absent. In a certain range of parameters, static solutions are stable with respect to homogeneous and isotropic perturbations.
We show that loitering at high redshifts ($z \gsim 6$) can easily arise in braneworld models of dark energy which, in addition to being spatially flat, also accelerate at late times. Loitering is characterized by the fact that the Hubble parameter dips in value over a narrow redshift range which we shall refer to as the `loitering epoch'. During loitering, density perturbations are expected to grow rapidly. In addition, since the expansion of the universe slows down, its age near loitering dramatically increases. An early epoch of loitering is expected to boost the formation of high redshift gravitationally bound systems such as $10^9 M_\odot$ black holes at $z \sim 6$ and lower-mass black holes and/or Population III stars at $z > 10$, whose existence could be problematic within the LCDM scenario. Loitering models also help to reduce the redshift of reionization from its currently (high) value of $z_{\rm reion} \simeq 17$ in LCDM cosmology, thus alleviating a significant source of tension between observations of the high-redshift universe and theoretical model building. Currently a loitering universe accelerates with an effective equation of state $w < -1$ thus mimicking phantom dark energy. Unlike phantom, however, the late-time expansion of the universe in our model is singularity free, and a universe that loitered in the past will approach a LCDM model asymptotically in the distant future.
We study gravitational perturbations in the Randall-Sundrum two-brane background with scalar-curvature terms in the action for the branes, allowing for positive as well as negative bulk gravitational constant. In the zero-mode approximation, we derive the linearized gravitational equations, which have the same form as in the original Randall-Sundrum model but with different expressions for the effective physical constants. We develop a generic method for finding tachyonic modes in the theory, which, in the model under consideration, may exist only if the bulk gravitational constant is negative. In this case, if both brane gravitational constants are nonzero, the theory contains one or two tachyonic mass eigenvalues in the gravitational sector. If one of the brane gravitational constants is set to zero, then either a single tachyonic mass eigenvalue is present or tachyonic modes are totally absent depending on the relation between the nonzero brane gravitational constant and brane separation. In the case of negative bulk gravitational constant, the massive gravitational modes have ghost-like character, while the massless gravitational mode is not a ghost in the case where tachyons are absent.
We explore a new class of braneworld models in which the scalar curvature of the (induced) brane metric contributes to the brane action. The scalar curvature term arises generically on account of one-loop effects induced by matter fields residing on the brane. Spatially flat braneworld models can enter into a regime of accelerated expansion at late times. This is true even if the brane tension and the bulk cosmological constant are tuned to satisfy the Randall--Sundrum constraint on the brane. Braneworld models admit a wider range of possibilities for dark energy than standard LCDM. In these models the luminosity distance can be both smaller and larger than the luminosity distance in LCDM. Whereas models with $d_L \leq d_L(\rm LCDM)$ imply $w = p/ρ\geq -1$ and have frequently been discussed in the literature, models with $d_L > d_L(\rm LCDM)$ have traditionally been ignored, perhaps because within the general-relativistic framework, the luminosity distance has this property {\em only if} the equation of state of matter is strongly negative ($w < -1$). Matter with $w < -1$ is beset with a host of undesirable properties, which makes this model of dark energy unattractive within the conventional framework. Braneworld models, on the other hand, have the capacity to endow dark energy with exciting new possibilities without suffering from the problems faced by models with $w < -1$. For a subclass of parameter values, braneworld dark energy and the acceleration of the universe are {\em transient} phenomena. In these models, the universe, after the current period of acceleration, re-enters the matter dominated regime so that the deceleration parameter $q(t) \to 0.5$ when $t \gg t_0$, where $t_0$ is the present epoch. Such models could help reconcile an accelerating universe with the requirements of string/M-theory.
We study cosmological braneworld models with a single timelike extra dimension. Such models admit the intriguing possibility that a contracting braneworld experiences a natural bounce without ever reaching a singular state. This feature persists in the case of anisotropic braneworlds under some additional and not very restrictive assumptions. Generalizing our study to braneworld models containing an induced brane curvature term, we find that a FRW-type singularity is once again absent if the bulk extra dimension is timelike. In this case, the universe either has a non-singular origin or commences its expansion from a quasi-singular state during which both the Hubble parameter and the energy density and pressure remain finite while the curvature tensor diverges. The non-singular and quasi-singular behaviour which we have discovered differs both qualitatively and quantitatively from what is usually observed in braneworld models with spacelike extra dimensions and could have interesting cosmological implications.
We consider the five-dimensional bulk spacetime with negative Lambda described by the Nariai metric (which is not conformally flat) and match it with a vacuum brane satisfying the proper boundary conditions. It is shown that the brane metric corresponds to a cloud of string dust of constant energy density.
Traditionally, higher-dimensional cosmological models have sought to provide a description of the fundamental forces in terms of a unifying geometrical construction. In this essay we discuss how, in their present incarnation, higher-dimensional `braneworld' models might provide answers to a number of cosmological puzzles including the issue of dark energy and the nature of the big-bang singularity.