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In this paper we have analysed Tsallis holographic dark energy in a flat Friedmann-Robertson-Walker model under the framework of f ( R , T ) gravity. The effects of this model in a non interactive universe are studied by taking different IR cut-offs that include particle horizon, event horizon, conformal age of the universe and GO (Granda-Oliveros) horizon. The cosmic evolution is studied by determining the conventional cosmological tools including the density parameter Ω D E , equation of state parameter ω D E and the deceleration parameter q . We have analysed the impact of these parameters by assuming different values for the matter-curvature coupling constant λ and the Tsallis parameter δ . We observe that all our four models exhibit appropriate behavior for the system parameters and support the accelerated expansion mode described by phantom-like scenario. Stability was only achieved for event horizon (partially) based on the speed of sound v s 2 . Furthermore we examined the behavior of our model by using various diagnostic mechanisms such as ω D E − ω D E ′ analysis, statefinder pair ( r , s ) , O m diagnostic and statefinder hierarchy S 3 ( 1 ) and S 4 ( 1 ) . The trajectories of the ω D E − ω D E ′ show a transition from freezing to thawing region, whereas r − s plane corresponds to a phase shift between Chaplygin gas model and quintessence model for particle and event horizon and solely Chaplygin gas model for conformal age and quintessence for GO-horizon. O m parameter also supports the quintessence era while statefinder hierarchy distinguishes our model effectively from the Λ CDM model and demonstrates the distinctive nature of all our models.

This paper explains thermodynamic irreversibility by applying the expansion of the Universe to thermodynamic systems. The effect of metric expansion is immeasurably small on shorter scales than intergalactic distances. Multi-particle systems, however, are chaotic, and amplify any small disturbance exponentially. Metric expansion gives rise to time-asymmetric behaviour in thermodynamic systems in a short time (few nanoseconds in air, few ten picoseconds in water). In contrast to existing publications, this paper explains without any additional assumptions the rise of thermodynamic irreversibility from the underlying reversible mechanics of particles. Calculations for the special case which assumes FLRW metric, slow motions ( v ≪ c ) and approximates space locally by Euclidean space show that metric expansion causes entropy increase in isolated systems. The rise of time-asymmetry, however, is not affected by these assumptions. Any influence of the expansion of the Universe on the local metric causes a coupling between local mechanics and evolution of the Universe.

A self-similar solution of the problem on the dispersion of a finite mass of an ideal (inviscid and non-heat-conducting) gas that is compressed into a point and has infinite energy and finite entropy is obtained within classical (non-relativistic) gas dynamics. In this solution the gas disperses at once into all space, and, as a result, its thermodynamic functions (including the density), unlike the conserved entropy, vanish. The velocity of the gas obtained is equal to the ratio of the distance to the time, which are measured from the point and time of dispersion, and increases from zero to infinity for any time. In self-similar variables the new solution is described by one of the singular points of the corresponding differential equation, rather than by a segment of an integral curve. It satisfies the cosmological principle, which assumes that the Universe is isotropic and homogeneous with respect to the laws that determine its expansion. The problem of the dispersion of an ideal gas from a point into a void when the gas has a mass proportional to its energy and a fixed number of particles of non-zero rest mass is also solved within relativistic gas dynamics without gravity. Here the pressure, internal energy and enthalpy at a non-zero particle number density instantaneously vanish, and the formula for the velocity of the gas is distinguished from the classical only by the restriction of the speed of light. The velocity of the gas satisfies the cosmological principle in the entire expanding Universe, and the particle number density satisfies it outside of the layer adjacent to its boundary. The gravitational correction is then determined in the classical approximation. For more than 200 NASA versions, the distribution of the gas velocity found without this correction agrees with the lifetime of the Universe and the Hubble constant more closely than all the cosmological theories used by NASA.

Open access; International audience; The main goal of this article is to show that there exist wave functions which never collapse in an infinite universe. These are the quantum states of similar quantum systems evolving in similar observable universes.

Phenomenological effect of the super-inflation in loop quantum cosmology (LQC) is discussed. We investigate the case that the Universe is filled with the interacting field between massive scalar field and radiation. Considering the damping coefficient $\Gamma$ as a constant, the changes of the scale factor during super-inflation with four different initial conditions are discussed, and we find that the changes of the scale factor depends on the initial values of energy density of the scalar field and radiation at the bounce point. But no matter which initial condition is chosen, the radiation always dominated at the late time. Moreover, we investigate whether the super-inflation can provide enough e-folding number. For the super-inflation starts from the quantum bounce point, the initial value of Hubble parameter $H(t_i)\sim0$, then it is possible to solve the flatness problem and horizon problem. As an example, following the method of \cite{Amoros-prd} to calculate particle horizon on the condition that the radiation dominated at bounce point, and we find that the Universe has had enough time to be homogeneous and isotopic., Comment: 9 pages, 4 figures. Physics Letters B, online publication complete: 13-NOV-2013

In this Letter, we study thermodynamical properties of the apparent horizon in a universe governed by quasi-topological gravity. Our aim is twofold. First, by using the variational method we derive the general form of Friedmann equation in quasi-topological gravity. Then, by applying the first law of thermodynamics on the apparent horizon, after using the entropy expression associated with the black hole horizon in quasi-topological gravity, and replacing the horizon radius, r+, with the apparent horizon radius, r~A, we derive the corresponding Friedmann equation in quasi-topological gravity. We find that these two different approaches yield the same result which shows the profound connection between the first law of thermodynamics and the gravitational field equations of quasi-topological gravity. We also study the validity of the generalized second law of thermodynamics in quasi-topological cosmology. We find that, with the assumption of the local equilibrium hypothesis, the generalized second law of thermodynamics is fulfilled for the universe enveloped by the apparent horizon for the late time cosmology. © 2013 Elsevier B.V., Research Institute for Astronomy and Astrophysics of Maragha

In this work, we have considered the magnetic universe in non-linear electrodynamics. The Einstein's field equations for non-flat FRW model have been considered when the universe is filled with the matter and magnetic field only. We have discussed the validity of the generalized second law of thermodynamics of the magntic universe bounded by Hubble, apparent, particle and event horizons using Gibb's law and the first law of thermodynamics for interacting and non-interacting scenarios. It has been shown that the GSL is always satisfied for Hubble, apparent and particle horizons but for event horizon, the GSL is violated initially and satisfied at late stage of the universe., Comment: 8 figures

It is well known that there is a Hawking radiation from the cosmological horizon of the de-sitter spacetime, and the de-sitter spacetime can be a special case of a FRW universe. Therefore, there may be a corresponding Hawking radiation in a FRW universe. Indeed, there have been several clues showing that there is a Hawking radiation from the apparent horizon of a FRW universe. In our paper, however, we find that the Hawking radiation may come from the cosmological horizon. Moreover, we also find that the Hawking radiation from the apparent horizon of a FRW universe in some previous works can be a special case in our result, and the condition is that the variation rate of cosmological horizon $\overset{.}{r}_{H}$ is zero. Note that, this condition is also consistent with the underlying integrable condition in these works from the apparent horizon., V3: 12 pages, no figure, typos corrected, new references added, version shorted and accepted by PLB

Motivated by the fact that any nonzero Λ can introduce a length scale or a time scale into Einsteinʼs theory, r Λ = c t Λ = 3 / | Λ | . Conversely, any cosmological length scale or time scale can introduce a Λ ( t ) , Λ ( t ) = 3 / r Λ 2 ( t ) = 3 / ( c 2 t Λ 2 ( t ) ) . In this Letter, we investigate the time varying Λ ( t ) corresponding to the length scales, including the Hubble horizon, the particle horizon and the future event horizon, and the time scales, including the age of the universe and the conformal time. It is found out that, in this scenario, the Λ ( t ) CDM model can be taken as the unified origin of the holographic and agegraphic dark energy models with interaction between the matter and the dark energy, where the interacting term is determined by Q = − ρ ˙ Λ . We place observational constraints on the Λ ( t ) CDM models originating from different cosmological length scales and time scales with the recently compiled “Union2 compilation” which consists of 557 Type Ia supernovae (SNIa) covering a redshift range 0.015 ⩽ z ⩽ 1.4 . In conclusion, an accelerating expansion universe can be derived in the cases taking the Hubble horizon, the future event horizon, the age of the universe and the conformal time as the length scale or the time scale.

The stability of an Einstein static universe in the DGP braneworld scenario is studied in this paper. Two separate branches denoted by $\epsilon=\pm1$ of the DGP model are analyzed. Assuming the existence of a perfect fluid with a constant equation of state, $w$, in the universe, we find that, for the branch with $\epsilon=1$, there is no a stable Einstein static solution, while, for the case with $\epsilon=-1$, the Einstein static universe exists and it is stable when $-1, Comment: 10 pages, 2 figures, to appear in PLB

Based upon a simple cosmological model with no expansion, we find that the rotational terms appearing in the G/"odel universe are too small to explain the Pioneer anomaly. Although it contributes, universal rotation is not the cause of the Pioneer effect., Comment: 13 pages, 2 figures

In this paper we revisit and extend a previous analysis where the possible relevance of quantum gravity effects in a cosmological setup was studied. The object of interest are non-local (logarithmic) terms generated in the effective action of gravity due to the exchange in loops of massless modes (such as photons or the gravitons themselves). We correct one mistake existing in the previous work and discuss the issue in a more general setting in different cosmological scenarios. We obtain the one-loop quantum-corrected evolution equations for the cosmological scale factor up to a given order in a derivative expansion in two particular cases: a matter dominated universe with vanishing cosmological constant, and in a de Sitter universe. We show that the quantum corrections, albeit tiny, may have a secular effect that eventually modifies the expansion rate. For a de Sitter universe they tend to slow down the rate of the expansion, while the effect seems to have the opposite sign in a matter dominated universe. To partly understand these effects we provide a complementary newtonian analysis., Comment: 14 pages, 3 figures

Orbifold branes are studied in the framework of the 11-dimensional Horava–Witten heterotic M-theory. It is found that the effective cosmological constant can be easily lowered to its current observational value by the mechanism of large extra dimensions. The domination of this constant over the evolution of the universe is only temporary. Due to the interaction of the bulk and the branes, the universe will be in its decelerating expansion phase again in the future, whereby all problems connected with a far future de Sitter universe are resolved.

We study a 5-dimensional f(R) brane gravity within the framework of scalar-tensor type theories. We show that such a model predicts, for a certain choice of f(R) and a spatially flat universe, an exponential potential, leading to an accelerated expanding universe driven solely by the curvature of the bulk space. This result is consistent with the observational data in the cosmological scale.

The coupling of photons and baryons by Thomson scattering in the early universe imprints features in both the Cosmic Microwave Background (CMB) and matter power spectra. The former have been used to constrain a host of cosmological parameters, the latter have the potential to strongly constrain the expansion history of the universe and dark energy. Key to this program is the means to localize the primordial features in observations of galaxy spectra which necessarily involve galaxy bias, non-linear evolution and redshift space distortions. We present calculations, based on mock catalogs produced from high-resolution N-body simulations, which show the range of behaviors we might expect of galaxies in the real universe. We investigate physically motivated fitting forms which include the effects of non-linearity, galaxy bias and redshift space distortions and discuss methods for analysis of upcoming data. In agreement with earlier work, we find that a survey of several Gpc^3 would constrain the sound horizon at z~1 to about 1%., 33 pages, to appear in Astroparticle Physics. Discussion of Blake & Glazebrook procedure changed, minor edits to match version accepted by the journal

We present a new model of dark energy which could explain the observed accelerated expansion of our Universe. We show that a five-dimensional Einstein-Yang-Mills theory defined in a flat Friedmann-Robertson-Walker universe compactified on a circle possesses degenerate vacua in four dimensions. The present Universe could be trapped in one of these degenerate vacua. With the natural requirement that the size of the extra dimension could be of the GUT scale or smaller, the energy density difference between the degenerate vacua and the true ground state can provide us with just the right amount of dark energy to account for the observed expansion rate of our Universe., Comment: 5 pages, minor changes

However you look at it, the answer seems to be "maybe". © 2006 Reed Business Information Ltd, England.

We consider a single field governed expansion of the universe from a five dimensional (5D) vacuum state. Under an appropiate change of variables the universe can be viewed in a effective manner as expanding in 4D with an effective equation of state which describes different epochs of its evolution. In the example here worked the universe fistly describes an inflationary phase, followed by a decelerated expansion. Thereafter, the universe is accelerated and describes a quintessential expansion to finally, in the future, be vacuum dominated., Comment: version accepted in Phys. Lett. B

Astroparticle physics is an interdisciplinary field that explores the connections between the physics of elementary particles and the large-scale properties of the universe. Particle physicists have developed a standard model to describe the properties of matter in the quantum world. This model explains the bewildering array of particles in terms of constructs made from two or three quarks. Quarks, leptons, and three of the fundamental forces of physics are the main components of this standard model. Cosmologists have also developed a standard model to describe the bulk properties of the universe. In this new framework, ordinary matter, such as stars and galaxies, makes up only around 4% of the material universe. The bulk of the universe is dark matter (roughly 23%) and dark energy (about 73%). This dark energy drives an acceleration that means that the expanding universe will grow ever larger. String theory, in which the universe has several invisible dimensions, might offer an opportunity to unite the quantum description of the particle world with the gravitational properties of the large-scale universe.

A model for the Universe is proposed where the general relativity is modified in order to explain the irreversible evolution of the Universe. At the same time, the dichotomy matter-field of the Einstein equation is eliminated and the physical world is described only by means of a unified field. The Universe evolution is characterized by an oscillation or exponential expansion with or without the initial singularity. In this framework, the Universe evolution is irreversible and the entropy increase is strictly associated with matter production according to the Prigogine’s ideas. High redshift supernovae recent observations are compatible with this new model.

In a recent paper, a cosmological model based on El Naschie E infinity Cantorian space–time was presented [Iovane G. Varying G, accelerating universe, and other relevant consequences of a stochastic self-similar and fractal universe. Chaos, Solitons & Fractals 2004;20:657–67]. In that work, it was claimed that the present accelerated expansion of the universe can be obtained as the effect of a scaling law on Newtonian cosmology with a certain time-dependent gravitational constant (G). In the present work we show that such a cosmological model actually describes a decelerated universe. Then starting from the scenario presented in that paper, we realize a complementary approach based on an extended Friedmann model. In fact, we apply the same scaling law and a time-dependent gravitational constant, that follows from the observational constraints, to relativistic cosmology, i.e. a (extended) Friedmann’s model. We are able to show that for a matter-dominated flat universe, with the scaling law and a varying G, an accelerated expansion emerges in such a way that the function luminosity distance vs redshift can be made close to the corresponding function that comes from the usual Friedmann’s model supplemented with a cosmological constant, of value ΩΛ ≃ 0.7. Then the measurements of high redshift supernovae, could be interpreted as a consequence of the fractal self-similarity of the G varying relativistic universe.

In this paper we investigate the epochs in which the Universe started accelerating and when it began to become dark energy-dominated (i.e., the dynamics of the expansion of the Universe dominated by the dark energy). We provide analytic expressions to calculate the redshifts of these epochs as a function of density parameters. Moreover, we review and discuss cosmological models with a dark energy component, which can have an interesting characteristic, namely, they never stop accelerating. This holds even if the Universe is at present time either flat, open, or closed. If the dark energy is the cosmological constant the Universe will eventually end up undergoing an exponentially expansion phase, and the total density parameter converging to $\Omega=1$. This is exactly what is considered in inflationary scenario to generate the initial conditions for the big bang. One can then argue that the Universe begun with an inflationary phase and will end up with another inflationary phase. Thus, it follows that in both the early and the late Universe $\Omega \to 1$. We also discuss the above issues in the context of the XCDM parametrization., Comment: 15 pages, 4 figures

A waveguiding effect is considered with respect to the large scale structure of the Universe, where the structures formation appears as if it were a classically self-similar random process at all astrophysical scales. The result is that it seems we live in an El Naschie's ϵ (∞) Cantorian space–time, where gravitational lensing and waveguiding effects can explain the appearing Universe. In particular, we consider filamentary and planar large scale structures as possible refraction channels for electromagnetic radiation coming from cosmological structures. From this vision the Universe appears like a large self-similar adaptive mirrors set. Consequently, an infinite Universe is just an optical illusion that is produced by mirroring effects connected with the large scale structure of a finite and not so large Universe. Thanks to the presented analytical model supported by a numerical simulation, it is possible to explain the quasar luminosity distribution and the presence of “twin” or “brother” objects. More generally, the infinity and the abundance of astrophysical objects could be just a mirroring effect due to the peculiar self-similarity of the Universe.

In a universe dominated by a small cosmological constant or by eternal dark energy with equation of state w < -1/3, observers are surrounded by event horizons. The horizons limit how much of the universe the observers can ever access. We argue that this implies a bound N~60 on the number of e-folds of inflation that will ever be observable in our universe if the scale of the dark energy today is ~(10^{-3} eV)^4. This bound is independent of how long inflation lasted, or for how long we continue to observe the sky. The bound arises because the imprints of the inflationary perturbations thermalize during the late acceleration of the universe. They "inflate away" just like the initial inhomogeneities during ordinary inflation. Thus the current CMB data may be looking as far back in the history of the universe as will ever be possible, making our era a most opportune time to study cosmology., 10 pages, 3 figures; v2: few typos fixed, to appear in PLB

We investigate an inflationary model of the universe based on the assumption that space-time is noncommutative in the very early universe. We analyze the effects of space-time noncommutativity on the quantum fluctuations of an inflaton field and investigate their contributions to the cosmic microwave background (CMB). We show that the angular power spectrum l(l+1)C_l generically has a sharp damping for lower l if we assume that the last scattering surface is traced back to fuzzy spheres at the times when large-scale modes cross the Hubble horizon., 17 pages, 4 figures, references added, some arguments clarified, to appear in Nuclear Physics B

We study the space-time evolution of the fine structure constant, $\alpha$, inside evolving spherical overdensities in a lambda-CDM Friedmann universe using the spherical infall model. We show that its value inside virialised regions will be significantly larger than in the low-density background universe. The consideration of the inhomogeneous evolution of the universe is therefore essential for a correct comparison of extragalactic and solar system limits on, and observations of, possible time variation in $\alpha$ and other constants. Time variation in $\alpha$ in the cosmological background can give rise to no locally observable variations inside virialised overdensities like the one in which we live, explaining the discrepancy between astrophysical and geochemical observations., Comment: 5 pages, 5 figures. An extra section added describing the spherical collapse model. References added. Accepted for publication in Phys. Lett. B

Over the past five years two teams have used type Ia supernovae to trace the expansion of the Universe to a look back time more than 70% of the age of the Universe. These observations show an accelerating Universe which is best explained by a cosmological constant, or other form of dark energy with an equation of state near w=p/ρ=−1. There are many possible lurking systematic effects, and while difficult to completely eliminate, none of these appears large enough to challenge current results. However, as future experiments attempt to better characterize the equation of state of the matter leading to the observed acceleration, these systematic effects will ultimately limit progress.

The principle of relativity, when it is applied to scale transformations, leads to the suggestion of a generalization of fundamental dilations laws. These new specialscale-relativistic resolution transformations involve log-Lorentz factors and lead to the occurrence of a minimal and of a maximal length-scale in nature, which are invariant under dilations. The minimal length-scale, that replaces the zero from the viewpoint of its physical properties, is identied with the Planck-length lP , and the maximal scale, that replaces innit y, is identied with the cosmic scale I L = 1=2 , where is the cosmological constant. The new interpretation of the Planck scale has several implications for the structure and history of the early Universe: we consider the questions of the origin, of the status of physical laws at very early times, of the horizon / causality problem and of uctuations at recombination epoch. The new interpretation of the cosmic scale has consequences for our knowledge of the present universe, concerning in particular Mach’s principle, the large number coincidence, the problem of the vacuum energy density, the nature and the value of the cosmological constant. The value (theroretically predicted ten years ago) of the scaled cosmological constant = 0:75 0:15 is now supported by several dieren t experiments (Hubble diagram of Supernovae, Boomerang measurements, gravitational lensing by clusters of galaxies). The scale-relativity framework also allows one to suggest a general solution to the missing mass problem, and to make theoretical predictions of fundamental energy scales, thanks to the interpretation of new structures in scale space: fractal /classical transitions as Compton lengths, mass-coupling relations and critical value 4 2 of inverse couplings. Among them, we nd a structure at 3:27 0:26 10 20 eV, which agrees closely with the observed highest energy cosmic rays at 3:2 0:9 10 20 eV, and another at 5:3 10 3 eV, which corresponds to the typical neutrino mass needed

In this brief communication, we have studied the validity of the first law of thermodynamics for the universe bounded by event horizon with two examples. The key point is the appropriate choice of the temperature on the event horizon. Finally, we have concluded that universe bounded by the event horizon may be a Bekenstein system and the Einstein's equations and the first law of thermodynamics on the event horizons are equivalent., Comment: 4 pages; accepted for publication in Phys. Lett. B

Superstring theory suggests a new cosmology whereby a long inflationary phase preceeded a non singular big bang-like event. After discussing how pre-big bang inflation naturally arises from an almost trivial initial state of the Universe, I will describe how present or near-future experiments can provide sensitive probes of how the Universe behaved in the pre-bang era.

With the new method which is used to determine the location and temperature of the horizon of non-stationary space-time, the horizons' equation of Vaidya-Bonner-de Sitter space-time is given, which is as same as the equation reduced by null-surface equation. Hawking temperature of the event horizon and universe horizon is also given easily via this method.

We used a spherically symmetric perturbation model and derived a relation between the average density of galactic halo and its epoch of formation. and hence obtained an estimate for the epoch of formation of our Galaxy, tv. With the age of the Galaxy, tG, represented by the age of its globular clusters, the age of the universe is TG + tv. For flat universe models with Ω λ = 0.0, 0.7 and 0.8 , we calculated the compatible range of Hubble's constant. It is shown that if the Hubble constant is as large as 80 kms−1 Mpc, then we may not be able to solve the problem of the age of the universe by introducing the cosmological constant.

To the question, “Can we observe galaxies that recede faster than light ?”, the great majority of cosmologists at present would answer, “No, such galaxies are outside our horizon”. Underlying this answer is the idea that velocity in relativistic cosmology has to be defined by the relativistic Doppler shift formula. But in cosmology, redshift is “cosmological” and not “Doppler”. And there is available an independent definition of velocity. Thanks to the Cosmological Principle, there is a distance-independent, universal time t and a time-dependent, instantaneous distance l, and velocity can naturally be defined as dl dt . With this definition and the cosmological interpretation of redshift, it is shown: (1) That “horizon”, which owes its role as the limit of observation to its association with infinite redshift, is irrelevant to the question. (2) That the answer must depend on the particular cosmological model. Specifically. the answer is NO for the steady state model, and YES for all three types (k = 0, −1, +1) of the big bang model; in the k = 0 model, all sources with redshifts greater than 1.25 would have had their recession velocities at the time of emission greater than 1 light velocity. It has been found useful to contrast the character of time and distance in cosmology and black hole physics. A brief history of time, distance, velocity and redshift is given to show that the Doppler formula is inapplicable to recession velocities. Based on the present approach, a “World Atlas of the Universe” is constructed, which shows, inter alia, that recession and photon velocities at distant points obey the old, pre-relativity law of addition, while the local speed of light is kept constant

We investigate a dynamical model of wavefunction collapse in the cosmological context by using the idea of continuous spontaneous localization of baryonic wavefunctions. By invoking a cosmological time dependence for the effective collapse rate from an appropriate epoch in the early universe up to the present time, we calculate the integrated total contribution of the liberated energy to the present energy density of the universe. This is found to be of an order of magnitude comparable with the critical density of the universe.

The early Universe was hot and dense, with frequent collisions. Therefore it was in thermal equilibrium, as indicated by the properties of the observed relic black body radiation. Consequently the free energy of the early Universe was zero. Our present world, however, is out of equilibrium; it is locally alive. One has to find places and epochs in the Universe where free energy is being created or stored.

Wave function of the universe in the superstring theory is discussed and using Vilenkin's boundary condition, the probability density of the scale factor a at a given value of the dilaton field, is obtained. It is shown that when the universe spontaneously nucleates, the minimum value of the scale factor of the classical universe is of the order of the Planck length, that is, quantum effects can prevent the universe from collapsing to a single point.

The cosmic microwave background (CMB) is a unique probe of cosmological parameters and conditions. There is a connection between anisotropy in the CMB and the topology of the Universe. Adopting a universe with the topology of a 3-Torus, or a universe where only harmonics of the fundamental mode are allowed, and using 2-years of COBE/DMR data, we obtain constraints on the topology of the Universe. We obtain more accurate results than previous work by using all multipole moments, avoiding approximations by computing their full covariance matrix. The best fit for a cubic toroidal universe is obtained at a scale of 7200h−1Mpc for n = 1. The data set a lower limit on the cell size of 4320h−1Mpc at 95% confidence and 5880h−1Mpc at 68% confidence. These results show that the most probable cell size would be around 1.2 times larger than the horizon scale, implying that the 3-Torus topology is no longer an interesting cosmological model.

We investigate the thermal history in the universe with a variable cosmological term. In particular, we show how the formation of important molecules such as H 2 and HD is influenced during the epoch for the redshift from 10000 to 1. These molecules should dominate the cooling process of primordial gas clouds which triggers the collapse of them. It is found that the molecular formation is quickened by Δz ∼ 1000 compared with the case in the standard model due to the variable cosmological term. The qualitative estimate of the mass of the first objects has been performed with use of the time scales related to the thermal evolution. It is suggested that the formation scenarios of the first objects studied so far could be changed drastically if the variable cosmological term is included in the thermal history in the universe.

We review some general properties of perturbations in the space-time curvature, which are produced during an inflationary ear in the early Universe and their possible imprints on the observed large angular scale temperature fluctuations of the Cosmic Microwave Background. Specifically, we consider the spectral slope of density perturbations and we discuss the possibility of getting power-spectra with less large-scale power than the Harrison-Zel'dovich case.

The mass difference between leptoquarks and antileptoquarks appearing due to T -symmetry violation at the early stages of the expansion of the Universe is evaluated. The results acquired can explain the observed excess of matter over antimatter.

Gravitational waves produced by the rapid expansion of the universe right after the big bang could settle which of many theories of inflation is correct

We use Vilenkin's method to discuss quantum cosmology with conformal scalar field. The corresponding Wheeler-DeWitt equation is derived and the wave function of the universe is calculated. The matter portion of the solution has the form of eigenstates of harmonic oscillators and the spatial portion is given by the WKB method. An analysis of the cosmic wave function reveals that, when quantum effect is included, the probability density of the universe appearing at a = 0 is zero and that the most probable radius of the base state of the universe is about one Planck length. The analysis also reveals that the universe is most probably in a state of small ∼φ.

Extended inflation theory can provide astrophysically interesting, nearly energy-empty bubbles at the epoch of matter-radiation equality, t = t eq . The physical size and number of such bubbles at t = t eq within the present physical horizon as a function of the model parameters is given. If non-baryonic cold dark matter (CDM) is not present in the universe, the filling fraction of these bubbles in the physical volume of the present universe becomes less than a few percent, so the bubbles are marginally detectable. If CDM is present in the universe, true vacuum bubbles can grow to occupy a major fraction of the volume of the universe today.

A system of radiation and nonrelativistic particles is studied from a thermodynamical point of view. The transfer of perturbed energy density from the radiation to the matter component is described explicitly for adiabatic perturbations inside the particle horizon. For thermal perturbations the fluctuations of the radiation energy density vanish, but the corresponding temperature fluctuations are different from zero.

The application of quantum chromodynamics to big bang cosmology predicts that the universe underwent a transition from a quark-gluon plasma to a confined hadronic phase when it was roughly 10 −5 seconds old. A first order phase transition in QCD can produce baryon density inhomogeneities in an initially homogeneous universe. Neutron diffusion converts these density inhomogeneities into variations in the local ratio of neutrons to protons, and these variations can produce detectable features in the pattern of abundances produced in primordial nucleosynthesis. In addition, the deviation from equilibrium needed to drive the phase transition can result in the production of primordial magnetic fields.

The wave function of the Universe is calculated for a cosmological model with a non-minimal coupling of the form ƒ(ϕ)R . In different limiting cases the resulting probability distributions of the initial states of the Universe are obtained and discussed.

We find that a massive U (1) vector field A μ in a charged Robertson-Walker universe for k =+1, 0, and −1 can solve the initial singularity problem even at the level of classical gravity because the energy density becomes negative as the scale factor a of the metric approaches zero. Namely, our universe might have started to expand from a finite size a 0 . The condition that the universe expands from a 0 larger than the Planck scale gives a constraint on the charge density at t =0.

We present a model of a spatially finite universe which has constant negative curvature and no boundary. Topological considerations identify a natural scale for the volume of the universe. We examine the observational consequences of such a model and find that microwave isotropy and large scale structure with a characteristic lenghth of 100–200 h −1 0 Mpc can be predicted.

The dynamics of the quantum universe under self-measurement is investigated in the framework of the path-integral approach to the quantum theory of continuous measurements. It is shown that the picture of time evolution of the quantum universe naturally emerges as a result of its self-measurement. The Wheeler-DeWitt dynamics maintains for small times.

According to a model based on “loop quantum gravity” theory, another universe before the big bang may have left an imprint